http://www.lagamine.uliege.be/dokuwiki/ 2026-05-24T05:19:58+0200 http://www.lagamine.uliege.be/dokuwiki/ http://www.lagamine.uliege.be/dokuwiki/lib/tpl/dokuwiki/images/favicon.ico text/html 2020-08-25T15:46:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/acmeg?rev=1598363184&do=diff ACMEG Description Elasto-plastic constitutive law for saturated soils under non-isothermal conditions with two plastic mechanisms. It can take into account : * linear or non-linear thermo-elasticity * the progressive plasticity inside the yield limit$\in$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon}_{\theta}$$\rightarrow$ text/html 2020-08-25T15:46:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/adv3d?rev=1598363184&do=diff ADV3D Description Advection-diffusion constitutive law for 3D solid eulerian elements (ADVE3) The model This law is only used for linear pollutant transport in isotropic solids by upwind methods. This constitutive law takes into account the advection‑dispersion in the moving fluid but also degradation, adsorption on the solid matrix and immobile fluid effect as linear phenomena. This law is used for three‑dimensional flow. $1 + \theta_s \rho_s p K_d / \theta_m$$1 + \theta_s \rho_s (1-p) K_… text/html 2020-08-25T15:46:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/advec?rev=1598363184&do=diff ADVEC Description Advection-diffusion constitutive law for solid eulerian elements (element CONV2 and ADVE2) The model This law is only used for linear pollutant transport in isotropic solids by upwind methods. This constitutive law takes into account the advection‑dispersion in the moving fluid but also degradation, adsorption on the solid matrix and immobile fluid effect as linear phenomena. $\in \left[0,1\right] \rightarrow$$\in \left[0,1\right] \rightarrow$$\in \left[0,1\right] \righ… text/html 2020-08-25T15:46:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ani3vh?rev=1598363184&do=diff ANI3VH Description Anisotropic elasto-plastic law based on texture for solid elements at constant temperature. The model This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.$\alpha_{23}$$\alpha_{13}$$\alpha_{12}$$\alpha_{44}/2$$\alpha_{55}/2$$\alpha_{66}/2$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$\[\sigma=K(\varepsilon_0+\varepsilon_{eq})^N\]\[\tau=K'(\Gamma^{\circ}+\Gamma)… text/html 2020-08-25T15:46:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/anidam?rev=1598363184&do=diff ANI-DAM Description Elasto(-visco)-plastic damage law of anisotropic materials for solid elements at variable temperature The model Mechanical analysis of thermo-elasto(-visco)-plastic-damage orthotropic solids undergoing large strains, plastic mixed hardening and damage isotropic hardening are assumed. $\rightarrow$$\rightarrow$$\rightarrow$$rightarrow$$\rightarrow$$\rightarrow$$rightarrow$$\rightarrow$$\rightarrow$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{ZZ}$$\sigma_{XY}$$\sigma_{XZ}$$\sigma_{Y… text/html 2020-08-25T15:46:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/arbth?rev=1598363184&do=diff ARBTH Description Elasto-plastic constitutive law with thermal effects for solid elements at variable temperature Developed from 1985 to 2005 by AM Habraken, F. Libon, De Montleau - 3D version by C. Lequesne (2005) Project: Use Coupled thermo-mechanical analysis of elasto-plastic solids undergoing large strains$\frac{dE}{dT}$$\frac{d\nu}{dT}$$\frac{d\alpha}{dT}$$\alpha$$\int \alpha dT$$\sigma$$\varepsilon$$\sigma$$\varepsilon$$\alpha$$\sigma_{y1}$$\sigma_{y2}$$\varepsilon_2$$\alpha$$\va… text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/arbthmet?rev=1598363185&do=diff ARBTHMET Description Elasto-plastic constitutive law coupled with thermal and metallurgical effects in solids The model This law is only used for coupled thermal, metallurgical, mechanical analysis of solids submitted to heat flow, metallurgical phase changes and mechanical stresses and strains.$=R_{eo}$$=E_{to}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon_{\theta}}$$=R_{eo}$$\bar{\varepsi… text/html 2026-03-17T08:48:41+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/bbm?rev=1773733721&do=diff BBM Barcelona Basic Model Description Full law name : ALONSO-GENS BBM An elasto-plastic constitutive law for saturated or partially saturated soils based on the CAMCLAY-type model. It can take into account: * the influence of the LODE angle;\[\kappa=\kappa_0\]$\kappa_0$\[\kappa = \kappa_0\left[1+\alpha_1.s+\alpha_2.\ln\left(\frac{s+u_{atm}}{u_{atm}}\right)\right]\]$\kappa_0$$\alpha_1$$\alpha_2$\[\kappa_{s0}=\kappa_{s0,ref}\left(\frac{\rho_d}{\rho_{d,ref}}\right)^{N_{\kappa_{s}}}\]$\ka… text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/binds?rev=1598363185&do=diff BINDS Description Constitutive law for BINDS elements. The model This law is used to enforce non-linear constraints between several degrees of freedom of the discretized structure. Files Prepro: LBINDS.F Availability Plane stress state YES Plane strain state text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/bocha?rev=1598363185&do=diff BOCHA Description Constitutive law for BOCHA element in plane state The model Used to model a ferrostatic pressure as function of the depth of the studied slice under the meniscus. Files Prepro: LBOCHA.F Availability Plane stress stateNO Plane strain state text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/bodam?rev=1598363185&do=diff BODAM Description Elastic-visco-plastic constitutive law for solid elements at constant temperature (Bodner model) with damage. The model This law is used for mechanical analysis of elastic-visco-plastic isotropic solids undergoing large strains. Strain rate effects and isotropic and directional hardening or recovery are included.$D_0$$D_1$$K_0$$K_1$$K_2$$A_1$$A_2$$m_1$$m_2$$r_1$$r_2$$n$$A$$s$$\sigma_D$$r$$\tau$$\beta$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{… text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/bodath?rev=1598363185&do=diff BODATH Description Bodner elastic-visco-plastic constitutive damage law with thermal effects for solid elements at variable temperature. The model Coupled thermo-mechanical analysis with damage of elastic-visco-plastic solids undergoing large strains.$\alpha$$K_o$$K_o$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{ZZ}$$\sigma_{XY}$$\sigma_{XZ}$$\sigma_{YZ}$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{XY}$$\sigma_{ZZ}$$\dot{\varepsilon_\theta}$ text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/cazacu?rev=1598363185&do=diff CAZACU Description 3D constitutive law with an orthotropic yield criterion for hexagonal closed packed materials The model Mechanical analysis of elasto-plastic HCP materials undergoing large strains. Files Prepro: LCAZAC2.F Lagamine : CAZACU2.F$E_{1}$$E_{2}$$E_{3}$$\mbox{ANU}_{12}$$\mbox{ANU}_{13}$$\mbox{ANU}_{23}$$G_{12}$$G_{13}$$G_{23}$$$\begin{pmatrix} \varepsilon_{11} \\ \varepsilon_{22}\\ \varepsilon_{33}\\ \varepsilon_{12} \\ \varepsilon_{13} \\ \varepsilon_{23} \end{pmatrix… text/html 2022-10-14T15:52:20+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/cazacutn?rev=1665755540&do=diff CAZACUTN Description 3D Coupled damage law for porous hexagonal closed packed (HCP) materials exhibiting orthotropy and strength differential effect. The model The mathematical model was developed by (J. Stewart & O. Cazacu, 2011),following a Gurson-type approach where the material yield stress is determined by the \[\begin{pmatrix} \varepsilon_{11} \\ \varepsilon_{22} \\ \varepsilon_{33} \\ \varepsilon_{12} \\ \varepsilon_{13} \\ \varepsilon_{23} \end{pmatrix} = \begin{pmatrix} \fr… text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/cazacuw?rev=1598363185&do=diff CAZACUW Description 3D constitutive law with an orthotropic yield criterion for hexagonal closed packed materials The model Mechanical analysis of elasto-plastic HCP materials undergoing large strains. Files Prepro: LCAZACW.F Lagamine: CAZACUW.F$E_{1}$$E_{2}$$E_{3}$$\mbox{ANU}_{12}$$\mbox{ANU}_{13}$$\mbox{ANU}_{23}$$G_{12}$$G_{13}$$G_{23}$\[\begin{pmatrix} \varepsilon_{11} \\ \varepsilon_{22} \\ \varepsilon_{33} \\ \varepsilon_{12} \\ \varepsilon_{13} \\ \varepsilon_{23} \end{pmatrix… text/html 2022-09-28T16:23:57+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/chab?rev=1664375037&do=diff CHAB Description Chaboche elasto-visco-plastic constitutive model with thermal and cyclic effects for solid elements at constant or variable temperatures with damage computation. The model is highly adjustable and can be used for very simple laws (elastic, bilinear plasticity) as well as for more complex behaviors (visco-plasticity, isotropic hardening, kinematic hardening, cyclic hardening, $\underline{\varepsilon}^{th}$$\underline{\varepsilon}^{e}$$\underline{\varepsilon}^{p}$\[\underline… text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/cloe?rev=1598363185&do=diff CLOE Description Rate type constitutive law for sands. The model Rate type law (incremental non-linear) for mechanical analysis of soil like media, and especially of sands. Two tangent stiffness matrix, one obtained by directional linearisation and the other by numerical perturbations.$10^{-4}$$\alpha_2$$\alpha_2$$\alpha_3$$\alpha_3$$\alpha_4$$\alpha_4$$\alpha_1$$\alpha_1$$\alpha_2$$\alpha_2$$\alpha_3$$\alpha_3$$\alpha_4$$\alpha_4$$\alpha_5$$\alpha_5$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\… text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/cntcq?rev=1598363185&do=diff CNTCQ Description Constitutive law for unilateral contact with friction, for thin 3D shell elements. The model This law is used for mechanical analysis of unilateral contact with friction in 3D state for shells. Contact can occur on both sides of shell.$K_p$$K_{\tau}$$\Phi$$\tau$$\tau$$\rvert\rvert\tau\rvert\rvert$$p$ text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/cntsh?rev=1598363185&do=diff CNTSH Description Constitutive law for unilateral contact with friction for: * Plane membrane elements (MEM2D); * Thin plane shell elements (KIRSH); * Thick plane shell elements (MINDS). The model This law is used for mechanical analysis of unilateral contact with friction in generalized plane state for shells and membranes.$\tau$\[2\times N + 2 \leq MPARA\]$K_p$$K_{\theta}$$\tau$$\xi$$\xi$ text/html 2020-08-25T15:46:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/copo1?rev=1598363185&do=diff COPO1 Description Constitutive law for boundary condition inpollutant transport analysis The model This law is only used for linear thermal analysis of pollutant transport. This constitutive law takes account of transfer between the solid and the external world by convection. The coefficients of convection are constant. Those coefficients induce a mix boundary condition on the diffusive flux. $(=T_a)$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/couc?rev=1598363186&do=diff COU2DC/3DC Description Constitutive law for unilateral thermo-mechanical contact The model Thermo-mechanical analysis of problems involving unilateral contact between two bodies. Coulomb dry friction law is used. The contact condition is enforced via a penalty method or augmented Lagrangian method according to ISTRA(4). Heat transfer between the bodies depends upon the contact state. $\neq$$K_p$$K_{\tau}$$tg \phi $$10^{20}$$\sigma_0$$\varepsilon$$\sigma_0$$\varepsilon$$\Rightarrow$$\in$$\Rig… text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/coul2d?rev=1598363186&do=diff COUL2D Description Constitutive law for unilateral contact Available for CNTCP See coupled law COU2DC/COU3DC The model This law is only used for mechanical analysis of problems involving unilateral contact between two bodies. COULOMB dry friction law is used. The contact condition in enforced via a penalty method.$=K_P$$=K_\tau$$=\tan\phi$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/credam?rev=1598363186&do=diff CREDAM Description Constitutive law for unilateral mechanical contact with creep damage The model Creep damage analysis for polycrystalline materials. The contact and damage evolution conditions at the grain boundary are enforced via a penalty method. A threshold value is defined for crack propagation. When this value is reached, the interface and its foundation are no longer in contact$\dot{\varepsilon}_{c}^{e}/\varepsilon_{B}$$K_P$$K_{\tau}$$K_P$$K_{\tau}$$\delta$$\dot{V}$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/dafa2?rev=1598363186&do=diff DAFA2 Description Full law name : EVP-DAFALIAS-KALIAKIN DAFALIAS-KALIAKIN elasto-visco-plastic constitutive law for isotropic cohesive soils. The model This law is used for mechanical analysis of elasto-visco-plastic isotropic porous media undergoing large strains according to DAFALIAS-KALIAKIN $\neq$$\lambda$$e$$\ln(p)$$\kappa$$e$$\ln(p)$$\phi_c$$\phi_e$$\nu > 0$$\gamma$$I_l$$I$$I_0$$I$$I_0$$I_l$$P_a$$P_a$$R_c$$1.0\leq R\leq\infty$$A_c$$0$$A_c<\infty$$0.05\leq t\leq 0.95$$R_e/R_c$$R_e$$R… text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/dvree?rev=1598363186&do=diff DVREE Description Simple damage constitutive law. The model This law is used for mechanical analysis for solids. Files Prepro: LDVREE.F Lagamine: DVREE.F Availability Plane stress state NO Plane strain state YES Axisymmetric state NO 3D state$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/e2gdp?rev=1598363186&do=diff E2GDP Description Elastic constitutive law for solid elements at constant temperature. Second gradient-plane deformation (for second gradient method from Grenoble). The model This law is used for mechanical analysis of elastic isotropic solids undergoing large strains. $\neq$$^{nd}$$\Sigma_{111}$$\Sigma_{112}$$\Sigma_{121}$$\Sigma_{122}$$\Sigma_{211}$$\Sigma_{212}$$\Sigma_{221}$$\Sigma_{222}$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/echra?rev=1598363186&do=diff ECHRA Description Constitutive law for the heat exchange by mutual radiation between surface elements of solids (for element RAYON) The model This law is only used for non linear thermal analysis of solids. This constitutive law allows to consider heat exchange by radiation between elements pertaining to the surface of a solid. $(=T_1)$$(=T_2)$$\sigma* \left( T_1^3 + T_1^2 T_2 + T_1 T_2^2 + T_2^3\right)$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ecoup?rev=1598363186&do=diff ECOU-P Description Constitutive law of flow in porous media for a pipe element The model This law is only used for non linear analysis of seepage in porous media. The case of free surface seepage is also treated. This law is used for one‑dimensional flow.$k$$\left(\left[L^2\right]\right)$\[k_{intrinsic}=K\frac{\mu_f}{\rho_fg} \\ [L^2]=[LT^{-1}]\frac{[ML^{-1}T^{-1}]}{[ML^{-3}][LT^{-2}]} \]$K$$(\left[LT^{-1}\right])$$k$$\rho_f$$n_0$$C_p$$\alpha$$\beta$$\theta = \theta(p)$$\mu_f=10^{-3}$$\th… text/html 2025-11-28T20:44:58+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ecous?rev=1764359098&do=diff ECOU-S Description Constitutive law of flow in porous media for solid elements. The model This law is used for non linear analysis of seepage in porous media. The case of free surface seepage is also treated. This law is used in two or three dimensional flow. \[\frac{\partial}{\partial t}(\rho_f.\theta)+div(\rho_f.\underline{q})=0\]\[\underline{q} = \frac{-k}{\mu}\left(\underline{grad}(p)+\rho_f.g.\underline{grad}(z)\right)\]$K=f(n)$$K=f(n)$$S_w$$k_w$$k$$L^2$$K$$LT^{-1}$\[k_{intrinsic} = K\f… text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ela?rev=1598363186&do=diff ELA Description Elastic constitutive law for solid elements at constant temperature The model This law is used for a mechanical analysis of elastic isotropic solids undergoing large strains. Files Prepro: LELA.F Lagamine: * ELA2S.F (Plane stress state)$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\varepsilon_{r}$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/elamet?rev=1598363186&do=diff ELAMET Description Elastic constitutive law coupled with metallurgical effects for solid at variable temperature The model Non-linear analysis of elastic solids coupled with thermal and metallurgical analysis. The phase transformations induce modifications of the elastic moduli, volume changes. The temperature changes induce thermal expansion. $\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/elath?rev=1598363186&do=diff ELATH Description Elastic constitutive law with thermal effects for solid elements at variable temperature. The model This law is used for a coupled thermo-mechanical analysis of elastic solids undergoing large strains. Files Prepro: LELATH.F $\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon}_{\theta}$ text/html 2020-08-25T15:46:26+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/elatr?rev=1598363186&do=diff ELA-TR Description Elastic constitutive law for solid elements at constant temperature The model This law is only used by TRUSS elements Files Prepro: LELATR.F Availability Plane stress state YES Plane strain state YES Axisymmetric state NO $N_{PK2}$$N_{PK2}$ text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/endc?rev=1598363187&do=diff ENDC Description Endochronic (internal time) model coupled with damage for elasto-plastic cyclic loading analysis in plane state at constant temperature. The model This law is used for mechanical analysis of 2-D continuum element undergone large deformation by using endochronic (internal time) theory coupled with damage model for elasto-plastic cyclic loading.\[\rho(\zeta)=\rho_0+\rho_1(\zeta)\]\[\rho_1(\zeta)=\frac{E_1}{E}\;e^{-\alpha_1.\zeta}+\frac{E_2}{E}\]\[\rho(\zeta)=\rho_0+\rho_1(\zet… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ep1gdp?rev=1598363187&do=diff EP1GDP Description Elasto-plastic constitutive law for solid elements at constant temperature First gradient – plane deformation → for second gradient method from grenoble Implemented by: P. Besuelle, 2002 The model This law is only used for mechanical analysis of elastic isotropic solids undergoing large strains.$\neq$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$F_{11}$$F_{12}$$F_{21}$$F_{22}$ text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epani?rev=1598363187&do=diff EP-ANI Description Elasto-plastic constitutive law of anisotropic materials for solid elements at constant temperature (Zhu) The model Mechanical analysis of orthotropic elasto-plastic solids (Hill's model) undergoing large strains. Mixed hardening is assumed. $\nu_{12}$$\leq$$\nu_{23}$$\leq$$\nu_{23}$$\nu_{12}$$\leq$$\leq$$\nu_{13}$$\leq$$\nu_{13}$$\nu_{23}$$\leq$$\leq$$<_{12}$$\leq$$\frac{SIG1Y}{\sqrt{3}}$$\nu$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\epsilon_{\theta}$$\rightar… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/eparb?rev=1598363187&do=diff EP-ARB Description Elasto-plastic constitutive law for solid elements at constant temperature. The model This law is used for a mechanical analysis of elasto-plastic isotropic solids undergoing large strains. Mixed hardening is assumed. Files Prepro: LARB.F $\sigma=C.\varepsilon^n$$\neq$$\geq$$\sigma_{y1}$$\sigma_{y2}$$\leq$$\varepsilon_2$$\in$$\in$$\in$$\sigma=C.\varepsilon^n$$\sigma=C.\varepsilon^n$$\bar{\sigma},\bar{\varepsilon}$$\neq$$i^{th}$$N_i$$N_F$$\sigma_{xx}$$\sigma_{yy}$$\sigma_… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epcapsol?rev=1598363187&do=diff EP-CAPSOL Description CAP MODEL : Elasto-plastic constitutive law for solid elements at constant temperature. The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains. Files Prepro: LCAP.F $5.10^{-3}$$\neq$$\psi$$\psi$$I_\sigma$$n_0$$dp_0$$p_0\varepsilon_v^p$$ECRO=\frac{1+e_0}{\lambda - \kappa}$$ECRO=\frac{1+e_0}{\lambda - \kappa}$$ECRO=\frac{1+e_0}{\lambda - \kappa}$$\nu$$p_0 = PCONS0$$p_0 = \sigma_v . OCR$$p_0 = p_0(\sigma,\te… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epchemsol?rev=1598363187&do=diff EP-CHEMSOL Description Cap model : elasto-plastic constitutive law for solid elements at constant temperature with effect of contaminant concentration. The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.$5.10^{-3}$$\neq$$\neq$$\psi$$\psi$$\neq$$I_{\sigma}$$\neq$$n_o$$c(c) = c(0) + k.c$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsi… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epdam?rev=1598363187&do=diff EP-DAM Description Elasto-plastic isotropic constitutive law with damage for solid elements at constant temperature endochronic The model This law is used for mechanical analysis of elasto‑plastic isotropic solids undergoing large strains, taking account of internal damage generated by plastic strains. Plastic isotropic hardening is assumed.$(=\tau)$$(=a_G)$$(=R_e)$$(=k)$$(=n)$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epell?rev=1598363187&do=diff EP-ELL Description Elliptic elasto-plastic constitutive law for solid elements at constant temperature The model Mechanical analysis of elasto-plastic isotropic porous media undergoing large strains. Dilatancy is included through an elliptic yield surface relating the mean stress and the von MISES equivalent stress. Isotropic hardening is assumed.$5*10^{-3}$$\neq$$a_{0}$$n_{0}$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{ZZ}$$\sigma_{XY}$$\sigma_{XZ}$$\sigma_{YZ}$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{… text/html 2026-01-19T11:06:43+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epelli?rev=1768817203&do=diff EP-ELLI Description Elliptic elasto-plastic constitutive law for solid elements at constant temperature The model Mechanical analysis of elasto-plastic isotropic porous media undergoing large strains. Dilatancy is included through an elliptic yield surface relating the mean stress and the von MISES equivalent stress. Isotropic hardening is assumed.$5*10^{-3}$$I_{\sigma}$$n_{0}$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{XY}$$\sigma_{ZZ}$$\dot{\varepsilon}_{\theta}$$W^{p}$$\circ$$\varepsilon_{eq1} … text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epgtnb?rev=1598363187&do=diff EP-GTNB Description 3D elasto-plastic constitutive combining isotropic and kinematic hardening, anisotropic yield locus and growth of voids. Rupture criterion applied on porous ductile materials (GURSON model). The model * Mixed hardening and plastic anisotropy.$\sigma_Y = K(\varepsilon_0+\bar{\varepsilon}^p)^n$$\sigma_Y = \sigma_0 + K[1-\exp(-n.\bar{\varepsilon}^p)]$$\sigma_Y = \sigma_0 + K(\bar{\varepsilon}^p)^n$$K$$n$$\varepsilon_0$$\sigma_0$$C_X.X_{sat}$$C_X$\[\dot{\underline{X}} = C_X… text/html 2020-08-25T15:46:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epgtnb2?rev=1598363187&do=diff EP-GTNB2 Description 3D elasto-plastic constitutive combining isotropic and kinematic hardening, anisotropic yield locus, nucleation and growth of voids. Rupture criterion applied on porous ductile materials (GURSON model). The model * Mixed hardening and plastic anisotropy.$\sigma_Y = K(\varepsilon_0+\bar{\varepsilon}^p)^n$$\sigma_Y = \sigma_0 + K[1-\exp(-n.\bar{\varepsilon}^p)]$$\sigma_Y = \sigma_0 + K(\bar{\varepsilon}^p)^n$$K$$n$$\varepsilon_0$$\sigma_0$$C_X.X_{sat}$$C_X$\[\dot{\underl… text/html 2020-08-25T15:46:28+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epgtnphy?rev=1598363188&do=diff EP-GTNPHY Description 3D elasto-plastic constitutive combining isotropic and kinematic hardening, anisotropic yield locus, nucleation growth and coalescence of voids. Physically-based models. Applied on porous ductile materials. The model * Mixed hardening and plastic anisotropy.$q_2$$\sigma_Y = K(\varepsilon_0+\bar{\varepsilon}^p)^n$$\sigma_Y = \sigma_0 + K[1-\exp(-n.\bar{\varepsilon}^p)]$$\sigma_Y = \sigma_0 + K(\bar{\varepsilon}^p)^n$$K$$n$$\varepsilon_0$$\sigma_0$$C_X.X_{sat}$$C_X$\[\d… text/html 2020-08-25T15:46:28+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epgur?rev=1598363188&do=diff EP-GUR Description Elasto-plastic constitutive law for porous ductile metals at constant temperature, using the GURSON model. The model This law is used for mechanical analysis of elasto-plastic isotropic porous ductile solids undergoing large strains. Combined isotropic and kinematic hardening is assumed.$\sigma_{y1}$$\leq$$\leq$$n$$\leq$$-E_t$$f_C$$f_F$$f_F^*/f_F$$Q_{UN}$$Q_1$$Q_{DEUX}$$Q_2$$Q_{TR}$$Q_3$$\alpha_n$$\alpha_n$$1.0\times10^{-4}$$\varepsilon_N$$\sigma_N$$f_N$$S_{\varepsilon}$$S… text/html 2020-08-25T15:46:28+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epgurshear?rev=1598363188&do=diff EP-GURSHEAR Description Law name : GTNB 3D elasto-plastic constitutive combining isotropic and kinematic hardening, anisotropic yield locus and nucleation, growth and coalescence of voids. Extended to shear loads. Applied on porous ductile materials.$\sigma_Y = K(\varepsilon_0+\varepsilon_M^P)^n$$\sigma_Y = \sigma_0 + K[1-\exp(-n.\varepsilon_M^P)]$$\sigma_Y = \sigma_0 + K(\varepsilon_M^P)^n$$K$$\varepsilon_0$$\sigma_0$$n$$C_X$\[\dot{\underline{X}} = C_X\left(X_{sat}\;\dot{\underline{\vareps… text/html 2020-08-25T15:46:28+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epjet?rev=1598363188&do=diff EP-JET Description Elasto-plastic constitutive law for solid elements at constant temperature The model This law is used for mechanical analysis of elastoplastic isotropic element undergone large deformation. Isotropic hardening is assumed. Files $\nu$$(R_e)$$(E_t)$$\nu$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$R_e$$(\bar{\varepsilon}^p)$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{1}$$… text/html 2020-08-25T15:46:28+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/eplev?rev=1598363188&do=diff EP-LEV Description An elasto-viscoplastic simplified law The model Mechanical analysis of visco-plastic isotropic solids undergoing large strains. Isotropic hardening is assumed. Files Prepro: LLEV.F Availability Plane stress state YES Plane strain state$\rightarrow$$\rightarrow$$\rightarrow$$\rightarrow$$\dot{\lambda} = 0$$\rightarrow$$\dot{\lambda}_{eq}$$\Rightarrow$$\dot{\sigma}_{eq}$$\rightarrow$$\dot{\lambda}_{eq}$$\Rightarrow$$\dot{\varepsilon}_{eq}$$\rightarrow$$ \rightarrow$$… text/html 2020-08-25T15:46:28+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epmohr?rev=1598363188&do=diff EP-MOHR Description Elasto-plastic constitutive law for solid elements at constant temperature (non-associated) with linear elasticity. Isotropic hardening/softening of friction angle and cohesion is possible and the Mohr Coulomb yield surface is represented.$g$$p-q$$$ I_{\sigma} = \sigma_{ij} \quad ; \quad \hat{\sigma}_{ij}=\sigma_{ij}-\frac{I_{\sigma}}{3}\delta_{ij} $$$$ II_{\sigma} = \sqrt{\frac{1}{2}\hat{\sigma}_{ij}\hat{\sigma}_{ij}} \quad ; \quad III_{\sigma} = \frac{1}{3}\hat{\sigma}_{i… text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epmomas?rev=1598363189&do=diff EP-MOMAS Description Elasto-plastic constitutive law for solid elements at constant temperature (non-associated) with linear elasticity. Isotropic softening of cohesion is possible. The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains. $\psi$$\psi$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon}_{\theta}$$W^p$$\varepsilon_{eq1}=\i… text/html 2023-11-21T13:12:07+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epplasol?rev=1700568727&do=diff EP-PLASOL Description Elasto-plastic constitutive law for solid elements at constant temperature (non-associated) with linear elasticity. Isotropic hardening/softening of friction angle and cohesion is possible. Integration is performed using an implicit backward Euler scheme with a return mapping normal to the flow surface g. This law can take into account the influence of:\[ I_{\sigma} = \sigma_{ij}\delta_{ij} = \sigma_{ii}; \widehat{\sigma}_{ij} = \sigma_{ij} - \frac{I_\sigma}{3}\delta_… text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/eprock?rev=1598363189&do=diff EP-ROCK Description Constitutive law for layered rocks at constant temperature The model This law is only used for elasto‑plastic constitutive law for mechanical analysis of layered rocks, with only one family of parallel joints. Rocks are elastic and joints have a COULOMB rigid plastic behaviour.$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon}_\theta$ text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epsucsol?rev=1598363189&do=diff EP-SUCSOL Description Cap model : elasto-plastic constitutive law for solid elements at constant temperature with effect of suction. The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.$\geq 0$$=5.10^{-3}$$\neq 0$$\Psi$$\Psi$$I_{\sigma}$$n_0$$c(s) = c(0)+k.s$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon}_{\theta}$$W^p$$\varepsi… text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/epsuctsol?rev=1598363189&do=diff EP-SUCTSOL Description Cap model : élastomère-plastic constitutive law for solid elements at constant temperature with effect of suction and temperature. The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.$5.10^{-3}$$\neq$$\neq$$\Psi$$\Psi$$\neq$$\neq$$_{sigma}$$\neq$$n_0$\[p_0^*\left(\varepsilon_{\nu}^p\;,\;\Delta T\right) = p_0^*\left(\varepsilon_{\nu}^p\right)+A(\Delta T)\]\[A(\Delta T) = a_1\; \Delta T + a_2\;\Delta T\;\rv… text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/eptsoil?rev=1598363189&do=diff EP-TSOIL Description Cap model : elasto-plastic constitutive law for solid elements at constant temperature with thermoplasticity (A thermomechanical model of clays, CUI et al., 2000). The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains.$1.10^{-5}$$\neq$$\Psi$$\Psi$\[p'_{cT} = p'_{c_0T_0}\exp(-\alpha_0\Delta T)\]\[p'_{cT} = p'_{c_0T_0}\left[1-\gamma_T\log\left(\frac{T}{T_0}\right)\right]\]$\neq$$_{sigma}$$\neq$$n_0$\[TY \equiv … text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/evp-nh?rev=1598363189&do=diff EVP-NH Description ELASTO VISCO PLASTIC CONSTITUTIVE LAW FOR SOLID ELEMENTS AT VARIABLE TEMPERATURE (Norton-Hoff) Implemented by: Pascon F (1998), Charles JF (1997 - 1999) Project: continuous casting research for ARBED (RW2748) The model Coupled dynamic recrystallisation-thermo-mechanical analysis of elasto-visco-plastic solids undergoing large strains.$K_0, P_1, P_2, P_3, P_4$$K_0, P_1, P_2, P_3, P_4$$P_2= e^{-(\frac{T-C_4}{C_5})}.T^{C_6}$$P_2= (\frac{C_4}{T})^2 - \frac{C_5}{T} + C_6$$K_… text/html 2020-08-25T15:46:29+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/evpbonz?rev=1598363189&do=diff EVP-BONZ FIXME This page does not match the code. The law corresponding to ITYPE = 36 is law KOLYM; in addition, LBONZ.F does not exist in Prepro. Description Elastic-visco-plastic constitutive law for solid elements at constant temperature (Bodner model)$D_0$$D_1$$K_0$$K_1$$K_2$$A_1$$A_2$$m_1$$m_2$$r_1$$r_2$$n$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{\varepsilon}_{\theta}$$K_0$$\rightarrow$$\righta… text/html 2020-08-25T15:46:30+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/evpgrob?rev=1598363190&do=diff EVP-GROB Description Elastic‑visco‑plastic constitutive law for solid elements at variable temperature The model This law is used for a mechanical analysis of elastic‑visco‑plastic isotropic solids undergoing large strains. Strain‑rate effects and isotropic hardening are included.$E_o$$b_E$$\nu$$b_{<}$$n_o$$B_o$$Q$$m_o$$K_{so}$$\gamma_o$$\theta_o$$b_{\theta}$$K_{oo}$$b_K$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\si… text/html 2020-08-25T15:46:30+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/evpirs?rev=1598363190&do=diff EVP-IRS Description Elastic‑visco‑plastic constitutive law for solid elements at constant temperature The model This law is used for a mechanical analysis of elastic‑visco‑plastic isotropic solids undergoing large strains. Strain‑rate effects and isotropic hardening or recovery are included.$n$$B$$m$$H_1$$q$$H_2$$K_o$$(\bar{\sigma} = C \bar{\varepsilon}^n)$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$\dot{… text/html 2020-08-25T15:46:30+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/fczm?rev=1598363190&do=diff FCZM Description Constitutive law for Xu and Needleman’s cohesive zone model with fatigue. En cours de développement – dernière mise à jour décembre 2005 (C.Lequesne) The model The model is Cohesive Zone Model of Xu and Needleman. The normal and shear stresses are computed. The fatigue damage variable is computed by ARB law in the BLZ element and imported. $\sigma_n$$\sigma_t$ text/html 2020-08-25T15:46:30+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/fczml?rev=1598363190&do=diff FCZML Description Constitutive law for bilinear Crisfield’s cohesive zone model coupled with fatigue The model The model is a bilinear Cohesive Zone Model of Crisfield. The normal and shear stresses are computed. Files Prepro: LFCZML.F Lagamine: FCZML.F, FCZML3.F text/html 2020-08-25T15:46:30+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/fmilc?rev=1598363190&do=diff FMILC Description Constitutive law for mixed limit condition for element FMILC The model This law is only used for non linear thermal analysis of solids. This constitutive law allows to impose a mixed limit condition on a boundary, with a classical penalty method.$V_S < V_0$$q=0$$V_S > V_0$$q=K\left( V_0 - V_S \right) $$V$$V_0$$V$$V_S$$V_S$$V_0$$q$ text/html 2020-08-25T15:46:30+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/fmivp?rev=1598363190&do=diff FMIVP Description Constitutive law for mixed limit condition for element FMIVP (seepage and evaporation) The model This law is only used for non linear analysis of solids. This constitutive law allows to impose a mixed limit condition on a boundary, with a classical penalty method, combining with an evaporation boundary condition.$S_{rw}$$\left[m/s\right]$$\left[Pa\right]$$\left[ K\right]$$\left[ J/kg\right]$$S_{rw}$$S_{rw}$$S_{rw}$$S_{rw}$$S_{res}$$S_{r,field}$$\left[Pa\right]$\[ \vec{q} = … text/html 2020-08-25T15:46:31+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/hiljet?rev=1598363191&do=diff HIL-JET Description Elasto isotrop-plastic anisotropic constitutive law for solid elements at constant temperature for element jet. The model Mechanical analysis of elasto isotropic-plastic anisotropic element undergone large deformation. Isotropic hardening is assumed. $\sigma_{11}^{y}$$E_{11}^{t}$$\sigma_{22}^{y}$$E_{22}^{t}$$\sigma_{33}^{y}$$E_{33}^{t}$$\sigma_{12}^{y}$$E_{12}^{t}$$\sigma_{13}^{y}$$E_{13}^{t}$$\sigma_{23}^{y}$$E_{23}^{t}$$\sigma_{xx}^{y}$$\sigma_{yy}^{y}$$\sigma_{zz}^{y}… text/html 2020-08-25T15:46:31+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/hill3d?rev=1598363191&do=diff HILL3D Description Anisotropic elasto-plastic law based on HILL48 yield locus for solid elements at constant temperature. The model Mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.$\Rightarrow$$E_{1}$$E_{2}$$E_{3}$$\mbox{ANU}_{12}$$\mbox{ANU}_{13}$$\mbox{ANU}_{23}$$$ \begin{pmatrix} \varepsilon_{11} \\ \varepsilon_{22}\\ \varepsilon_{33}\\ \varepsilon_{12} \\ \varepsilon_{13} \\ \varepsilon_{23} \end{pmatrix} = \begin… text/html 2023-03-28T18:12:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/hill3d_ki?rev=1680019947&do=diff HILL3D_KI Description Anisotropic elasto-plastic law based on HILL48 yield locus for solid elements at constant temperature. The model Mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Classic isotropic and kinematic hardening is available. $\Rightarrow$$|\Delta\mathbf{\hat{\varepsilon}}_{n+1}^{p} - \Delta\mathbf{\hat{\varepsilon}}_{n}^{p}| \geq$$\Delta\mathbf{\hat{\varepsilon}}^{p}$$E_{1}$$E_{2}$$E_{3}$$\mbox{ANU}_{12}$$\mbox{ANU}_{13}$$\mbox{ANU}_{23}$$$ \… text/html 2020-08-25T15:46:31+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/hilsh?rev=1598363191&do=diff HILSH Description Anisotropic elastoplastic constitutive law, numerically integrated on thickness For: * membrane elements (MEM2D) * thin shell elements (KIRSH) * thick shell elements (MINDS) in generalized plane state Implemented by: L. Grisard (1991)$\sigma_x$$\sigma_z$\[ \sqrt{\alpha_1 \sigma_x^2 + \alpha_2 \sigma_z^2 - \alpha_{12} \sigma_x \sigma_z + 3 \alpha_z \tau^2} \leq \sigma_0 \]$\alpha_1 = 1$$\alpha_3 = 1$$R_x = \frac{1 + r_x}{2 r_x}$$\alpha_2 = R_z / R_X$$\alpha_{1… text/html 2023-12-12T16:03:58+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/hmic?rev=1702393438&do=diff HMIC Description 2D hydraulic microscopic law for solid elements. Can be parallelised in ELEMB (at the macro-scale) or in the perturbation loop (at the micro-scale). The law definition and typical values of parameters for clays can be found in Corman (2024)$w$\[ \underbrace{\frac{\partial}{\partial t} (\rho_s . n . S_{r,w}) + div(\rho_w \vec{q_l})}_{\text{Liquid water}} = 0 \]\[ \vec{q_l} = - \frac{k_{r_w}}{\mu_w}\frac{1}{A}\kappa\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\]\[… text/html 2025-09-10T14:39:49+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/hypofe2?rev=1757507989&do=diff HYPOFE2 Description Multiscale law for water-air seepage, pollutant diffusion and advection. Inspired from WAVAT and ADVEC. Can be parallelized with ELEMB (macroscale) or at the perturbation loop (microscale). Takes into account the hysteresis in the water retention law when used with FKRSAT. Can also be used with osmotic suction (under development).\[ \underbrace{\frac{\partial}{\partial t} (\rho_s . n . S_{r,w}) + div(\rho_w . \vec{q_l})}_{\text{Liquide}} + \underbrace{\frac{\partial}{\par… text/html 2020-08-25T15:46:31+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ilysh?rev=1598363191&do=diff ILYSH Description Anisotropic elastoplastic constitutive law, analytically integrated on thickness For: * membrane elements (MEM2D) * thin shell elements (KIRSH) * thick shell elements (MINDS) in generalized plane state The model This law is only used for mechanical analysis of anisotropic elastoplastic thin bodies (membranes and shells) in generalized plane state. This law deals with reduced stresses, analytically integrated on thickness. The anisotropic ILYUSHIN criteria i… text/html 2020-08-25T15:46:31+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/intec2?rev=1598363191&do=diff INTEC2 Description Constitutive law of longitudinal and transversal flow in porous media for a interface element (FAIL2B or FAIN2B) The model This law is only used for non linear analysis of longitudinal seepage in porous media interface element. The case of free surface seepage is also treated.$T_{t\_c}$$T_{t\_nc}$$k_l = k_{l0}$$k_l = f(d) = \frac{\left(D_0 + V\right)^{exp}}{12} = \frac{d^{exp}}{12}$$\neq$$k$$\left(\left[L^2\right]\right)$$K_l$$(\left[LT^{-1}\right])$\[ k_{f,intrinsic} = … text/html 2020-08-25T15:46:31+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/intec3?rev=1598363191&do=diff INTEC3 Description Constitutive law of longitudinal flow in porous media for a 3d interface element (FAIL3B) The model This law is only used for non linear analysis of longitudinal seepage in porous media 3d interface element. The case of free surface seepage is also treated.$T_{t\_c}$$T_{t\_nc}$\[ \frac{\partial}{\partial t}(\rho_f \theta) + div (\rho_f \vec{q}) = 0\]\[\vec{q} = \frac{-k}{\mu} \left( \vec{grad}(p)+\rho_f g \vec{grad}(z)\right)\]$\neq$$S_W$$\neq$$k_W$$k_l = k_{l0}$$k_l = … text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/intfl?rev=1598363192&do=diff INTFL2/INTFL3 Description Constitutive law of longitudinal and transversal flows (water, gas and thermal) in porous media for an interface element 2D (FAIF2B) or 3D (FAIF3B). Implemented by: J.P. Radu, 2007-2008 The model This law is used for non-linear analysis of longitudinal seepage (water, gas and thermal) in porous media interface element. $T_{t_c}$$T_{t_{nc}}$$k_w$$k_a$$S_w$$\Gamma_T$\[ \left\{\begin{array}f_{we}=\dot{M}_w=\left(\dot{\varepsilon}_v.S_w+n.S_w.\frac{\dot{\rho}_w}{\xi… text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/intme?rev=1598363192&do=diff INTME2/INTME3 Description Constitutive law for mechanical contact for interface elements (FAIL2B/FAIN2B/FAIF2B or FAIL3B/FAIN3B/FAIF3B). The model This law is similar to the Coulomb's Law in 2D/3D and is used in mechanical analysis of problems involving unilateral contact between two bodies. Coulomb dry friction law is used. The contact condition is enforced via a penalty method or augmented Lagrangian method according to ISTRA(4). \[\Delta \sigma = K_p\;\Delta V\]\[\Delta\sigma = \frac{K_p}… text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/irsth?rev=1598363192&do=diff IRSTH Description Elastic-visco-plastic constitutive law with thermal effects for solid elements at variable temperature (to check before use, A-M. HABRAKEN, june 91). The model Coupled thermo-mechanical analysis of elastic-visco-plastic solids undergoing large strains$\alpha$$H_1$$H_2$$K_o$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{ZZ}$$\sigma_{XY}$$\sigma_{XZ}$$\sigma_{YZ}$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{XY}$$\sigma_{ZZ}$$\dot{\varepsilon_\theta}$$K_o$$\sigma_m$ text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/lblzt?rev=1598363192&do=diff LBLZT Description Thermal conduction constitutive law for solid elements at constant temperature (only suited for BLZ2T and BLZ3T). The model This law is only used for non linear thermal analysis of isotropic solids. This constitutive law takes account of heat transfer by conduction and heat accumulation in solids, the conductivity and heat capacity of which depend on temperature. This law is used for two or three dimensional heat flow.$\vec{q} = \lambda (1-\alpha T) \vec{grad}(T)$$(=q_X)$$… text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/levjet?rev=1598363192&do=diff LEV-JET Description An elasto‑viscoplastic constitutive law for solid elements at constant temperature ‑ Levi model. The model This law is used for mechanical analysis of elastoplastic isotropic element undergone large deformation. Files Prepro: LJETV.F $\dot{\omega} = 0$$\dot{\sigma}_{eq} = \dot{\sigma}_{eq}^{Trial}$$\dot{\sigma}_{eq} \Rightarrow \dot{\varepsilon}_{eq}$$\dot{\lambda}_{vp} = 0$$\dot{\lambda}_{vp} \Rightarrow \dot{\sigma}_{eq}$$\dot{\lambda}_{vp} \Rightarrow \dot{\varepsil… text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/levt?rev=1598363192&do=diff LEV-T Description Elasto-viscoplastic constitutive law with thermal effects for solid elements at variable temperature The model Coupled thermo-mechanical analysis of elasto-viscoplastic isotropic element undergoing large strains. Files Prepro: LLEVT.F $\alpha$$\int{\alpha dT}$$\dot{\lambda}$$\hat{D}_{eq}$$\alpha$$\int{\alpha dT}$$A_{c}$$\sigma- \dot{\varepsilon}_{\theta}$$A_{m}$$\sigma- \dot{\varepsilon}_{\theta}$$\hat{\sigma}_{eq} = A_{c} \hat{D}_{eq}^{A_{m}}$$E_{0}$$E_{0}(1-exp(-B_{E}*… text/html 2020-08-25T15:46:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/lhilcq?rev=1598363192&do=diff LHILCQ Description Hill's type constitutive law for 3D shell (COQJ4) element, numerically integrated on the thickness. This element uses the Green-Lagrance strain tensor and the Piola-Kirkhoff stress tensor for the plastic deformation but it uses the true strain and Cauchy stress tensor for the elastic deformation. $\leq$$\geq$$\geq$$\sigma = K ( \varepsilon_0 + \varepsilon^{pl})^n$$K$$n$$\varepsilon_0$$\varepsilon_0 = \left( SY11/K \right)^{1/n}$$\sigma = K ( \varepsilon_0 + \varepsilon^{pl}… text/html 2021-07-28T16:44:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/licha?rev=1627483477&do=diff LICHA Description Constitutive law defining distributed loads on a line or a surface. Implemented by: S. Cescotto - mai 1986 The model Definition of a uniformly distributed load (whether normal or tangent, whether in global axis) on a line (LICHA element) or on a surface ($F_n(y).F_n(y=0) \leq 0$$F_n= 0$$F_r= 0$$F_n(y).F_n(y=0) > 0$$F_n= 0$$F_r= 0$$F_n(y).F_n(y=0) < 0$$F_n= 0$$F_r= 0$$F_n(y).F_n(y=0) > 0$$F_n= 0$$F_r= 0$$\rho_s.g$$\rho_w.g$$\rho g$$\rho g= (1-n) \rho_s*g+S_r*n*\rho_w *g$ text/html 2022-01-21T16:38:54+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/licht?rev=1642779534&do=diff LICHT Description Constitutive law defining distributed flow on a line, on a surface, or in volume Last revision: L. Grisard - sept 1990 The model Definition of uniformly distributed flow on a line or on a surface, or in volume. This can be used in thermal analysis or in the analysis of flow in porous media. text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/lilycq?rev=1598363193&do=diff LILYCQ Description Ilyushin's type constitutive law for 3d shell (COQJ4) element. Use the resultant stresses directly. The model This law is only used for mechanical analysis of elasto-anisotropic plastic with linear anisotropic or non-linear isotropic hardening. The resultants stresses are used directly.$\geq$$\geq$$D_{NM}$\[ f = \frac{1}{h^2}Q_{NN} + D_{NM} \frac{4}{\sqrt{3}h^3}Q_{NM} + \frac{16}{h^4}Q_{MM} - \sigma_y^2 \]\[ Q_NN = \alpha_{11}N_x^2 + \alpha_{22}N_y^2 + \alpha_{33}N_{xy}^2 … text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/linadc?rev=1598363193&do=diff LINADC Description Law for linear heat advection diffusion 1D element (only for HEATX element) The model This law is used in combination with the finite element HEATX. The purpose is the modeling of simplified equations of advection-diffusion of heat in a pipe. A lateral heat flow with the surrounding medium is also taken into account. See GEOTHERWAL reports or more information on the formulation.$Q_P$$\left[kg/m^3\right]$$\left[W/m/K\right]$$\left[J/kg/K\right]$$\left[m/s\right]$$\left[K\ri… text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/llevcq?rev=1598363193&do=diff LLEVCQ Description An elasto-viscoplastic simplified constitutive law - LEV for 3D shell (COQJ4) element, numerically integrated on the thickness. The model This law is only used for mechanical analysis of elasto-viscoplastic with numerical integrations on the thickness.$\leq$$\dot{\lambda} = 0$$\dot{\lambda}_{eq} \Rightarrow \dot{\sigma}_{eq}$$\dot{\lambda}_{eq} \Rightarrow \dot{\varepsilon}_{eq}$$\sigma-\varepsilon$\[ \sigma_{eq} = c \left( \dot{\varepsilon}_{eq}\right)^m \]$N_x$$N_y$$N_{x… text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/llien?rev=1598363193&do=diff LLIEN Description Penalty law for shell/solids link element LIEN3 The model This law is only used for mechanical analysis of shell models, using shell elements linked to solid elements with the link element LIEN3. Files Prepro: LLIEN.F Availability Plane stress state$K$\[ = \frac{1}{N+1} \sum_{k=0}^N \sqrt{\Delta X_k^2 + \Delta Y_k^2 + \Delta Z_k^2} \]$n_1$$n_2$$n_3$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/loacq?rev=1598363193&do=diff LOACQ Description Constitutive law for loading (thin) 3D shell elements. The model This law is used for mechanical analysis of shells, loaded by uniform pressure and shear, normal and tangential to the mid-line $\xi$ at any moment, or in the global axes.$p_o$$\tau_r$$\tau_s$$p_o$$\tau_r$$\tau_s$$p_o$$\tau$$\tau_r$$\tau$$\tau_s$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/loash?rev=1598363193&do=diff LOASH Description Constitutive law for loading plane membrane and shell elements: * Plane membrane element (MEM2D) ; * Thin plane shell elements (KIRSH) ; * Thick plane shell elements (MINDS). The model This law is used for mechanical analysis of membranes and shells, loaded by uniform pressure and shear, normal and tangential to the mid line $\xi$$p_o$$\tau_o$$p_o$$\tau_o$$p$$p_o$$\eta$$\tau$$\tau_o$$\xi$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/lstiff?rev=1598363193&do=diff LSTIFF Description Constitutive law defining a concentrated stiffness at one node, onde degree of freedom, possible use as a linear spring. The model Definition of a stiffness at one DOF, useful in case of contact solid-solid where one solid has only the stiffness issued from the contact elements.$\alpha$$\beta$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/lvmcq4?rev=1598363193&do=diff LVMCQ4 Description Von Mises type constitutive law for 3D shell (COQJ4) element numerically integrated on the thickness. The model This law is only used for mechanical analysis of elastoplastic isotropic hardening. Numerical integration on the thickness is used.$\leq$$\geq$$\sigma_i$$\varepsilon$$N_x$$N_y$$N_{xy}$$M_x$$M_y$$M_{xy}$$\sigma_y^e$$K = 3 + (IPI-1)*6$$\sigma_y$$\varepsilon_{ep}^p$$\sigma_{11}$$\sigma_{22}$$\sigma_{12}$$3 + NPI*6$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/mazar?rev=1598363193&do=diff MAZAR Description Mazars damage mechanics constitutive law for concrete The model This law is only used for mechanical analysis for concrete solids undergoing large strains. Files Prepro: LMAZAR.F Availability Plane stress state YES Plane strain state$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/meso2?rev=1598363193&do=diff MESO2 DELETEME This law does not seem to exist in the code. LMESO2.F does not exist. ITYPE = 295 corresponds to law FCZM Description Elastic visco-plastic constitutive law for solidification problem (continuous casting) (always used with THSOL2) The model $E_o$$b_E$$\nu_0$$b_\nu$$n_o$$E_o$$-b_o T$$\nu = \nu_o exp(\nu_K T$$B_o$$m_o$$K_{so}$$\gamma_o$$\theta_o$$b_\theta$$K_{oo}$$b_K$$\sigma(8)$$\sigma_{11}$$\sigma_{22}$$\sigma_{12}$$\sigma_{33}$$K_o$$b_K$$\varepsilon^{P}$ text/html 2020-08-25T15:46:33+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/meta?rev=1598363193&do=diff META Description Constitutive law of metallurgical phase transformations in solids without mechanical interaction (law called directly by PL8TM in Lagamine). The model Prediction of metallurgical phase transformations for a given evolution of the temperature field.$\lambda_o$$\rho c_o$$\lambda$$\lambda_o$$\rho_o$$\rho c_o$ text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/metamec?rev=1598363194&do=diff METAMEC Description Constitutive law for metallurgical phase transformations with mechanical interaction in solids. The model This law is used for prediction of metallurgical phase transformations for a given evolution of the temperature field and of the mechanical field.$\sigma_{max}$$\sigma$$\sigma$$\lambda_0$$\rho c_0$$q$$\lambda$$\lambda_0$$\rho c$$\rho c_0$ text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/minty3?rev=1598363194&do=diff MINTY3 Description Anisotropic elasto-plastic law based on texture for solid elements at constant temperature. Microscopic INTerpolated Yield locus 3D The model This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.$\phi$$\phi$$\Gamma^{\circ}$$\phi$$m$$m$$\alpha_{12}$$\alpha_{13}$$\alpha_{23}$$\alpha_{44}$$\alpha_{55}$$\alpha_{66}$$\phi$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/minty3_ki?rev=1598363194&do=diff MINTY3_KI Description Anisotropic elasto-plastic law based on texture for solid elements at constant temperature combined with the microstructure hardening model of C. TEODOSIU. Microscopic INTerpolated Yield locus 3D KInematic The model This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic or Isotropic & Kinematic (Teodosiu) hardening are assumed.$S_L$$S_L$$S_L$$\rvert\Delta\hat{\varepsilon}_{n+1}^p-\Delta\hat{\varepsilon}_n^p\rv… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/mipay3?rev=1598363194&do=diff MIPAY3 Description Anisotropic elasto-plastic law based on texture for solid elements at constant temperature. MIcroscopic PArt Yield law 3D The model This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.$\phi$$\phi$$\Gamma^{\circ}$$\phi$$\alpha_{12}$$\alpha_{13}$$\alpha_{23}$$\alpha_{44}$$\alpha_{55}$$\alpha_{66}$$\phi$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\Gamma$$\ne… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/multidam23d?rev=1598363194&do=diff MULTIDAM23D Description Elasto(-visco)-plastic damage law of anisotropic materials for solid elements at constant temperature. The model This law is used for mechanical analysis of elasto(-visco)-plastic damage orthotropic solids undergoing large strains, plastic mixed hardening and damage anisotropic hardening are assumed.$\rightarrow$$\rightarrow$$\rightarrow$$\in$$\in$$\rightarrow$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sig… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ortho3d?rev=1598363194&do=diff ORTHO3D Description Orthotropic elastic constitutive law for solid elements at constant temperature. The model This law is used for mechanical analysis of orthotropic elasticity undergoing large strains. Orthotropic elasticity There are 9 independent parameters : $E_1$$E_2$$E_3$$\nu_{12}$$\nu_{13}$$\nu_{23}$$G_{12}$$G_{13}$$G_{23}$\[D^e_{ijkl} = \begin{bmatrix} \frac{1}{E_1} & \frac{-\nu_{21}}{E_2} & \frac{-\nu_{31}}{E_3} & & & \\ \frac{-\nu_{12}}{E_1} & \frac{1}{E_2} & \frac{-\nu_{32}}{E… text/html 2025-10-21T10:06:27+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/orthopla?rev=1761033987&do=diff ORTHOPLA Description Elasto‑plastic constitutive law for solid elements at constant temperature (non-associated) with linear anisotropic elasticity. Isotropic hardening/softening of friction angle and cohesion is possible. This law is a combination of $\alpha_{\sigma_1}$$\vec{\sigma_1}$$\vec{e_3}$\[ \alpha_{\sigma_1} = \arccos\left( \frac{\vec{e_3}\vec{\sigma_{1}}'}{||\vec{e_3}||\ ||\vec{\sigma_1}'||} \right) \]$c_{0^{\circ}}, c_{min}, c_{90^{\circ}}$$\alpha_{\sigma_1} = 0^{\circ}$$\alpha_{\… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/orthoplatra?rev=1598363194&do=diff ORTHOPLATRA Description Elasto-plastic constitutive law for solid elements at constant temperature (non-associated) with non-linear anisotropic elasticity. Isotropic hardening/softening of friction angle and cohesion is possible. Tensile criterion for desiccation cracking included. Isotropic hardening/softening of tensile strength is possible. \[f = II_2 +\frac{1}{(3.\cos\beta-\sqrt{3}\sin\beta)}.(I_1-3.\sigma'_t)\]$I_1$$II_2$$\beta$$\sigma_t$\[\sigma_t'=\sigma_t'^{sat}-\left(k_2*\left(1-\exp\… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/persol?rev=1598363194&do=diff PERSOL Description Non-associated PERZYNA type visco-plastic constitutive law with non-linear elasticity. Isotropic hardening/softening for friction angle, cohesion and pre-consolidation pressure. For solid elements at constant temperature. The model $\sigma_1 ; \sigma_2 ; \sigma_3$$\sigma_1 ; \sigma_2 ; \sigma_3$$\Psi$$\Psi$$\phi_C-\Psi_C=\phi_E-\Psi_E$$I_{\sigma}$$\psi_C$$\psi_E$$\phi_{C0}$$\phi_{C}$$\phi_{Cf}$$\phi_{C}$$B_p$$\phi_{E0}$$\phi_{E}$$\phi_{Ef}$$\phi_{E}$$c_0$$c_f$$B_c$$n_o$$\Ph… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/prevost?rev=1598363194&do=diff PREVOST Description Nested surface model. The model This law is used for mechanical analysis of the cyclic behaviour of soils, with or without cohesion. Files Prepro: LPREVO.F Lagamine: PREVOST.F Availability Plane stress state NO Plane strain state$\neq$$p'_0$$p$$n$$\alpha_{11}$$\alpha_{22}$$\alpha_{33}$$\alpha_{12}$$\alpha_{11}$$\alpha_{22}$$\alpha_{33}$$\alpha_{12}$$\alpha_{13}$$\alpha_{23}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\s… text/html 2020-08-25T15:46:34+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/ptrns?rev=1598363194&do=diff PTRNS Description Advection‑diffusion constitutive law in saturated-unsaturated porous media for solid eulerian elements (element TRPO2) (Pollutant TRansport in Non Saturated conditions) The model This law is only used for linear pollutant transport in isotropic solids by upwind methods in saturated-non saturated porous media. $a_T, a_L, D_m, R_{dm}, R_{dim}, A_m, A_{im}, \alpha_m, \alpha_{im}$$(a_T)$$(a_L)$$(D_m)$$(R_{dm})$$(R_{dim})$$(A_{m})$$(A_{im})$$(\alpha_{m})$$(\alpha_{im})$$a_T(S_… text/html 2020-08-25T15:46:35+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/qmlc?rev=1598363195&do=diff QMLC Description Constitutive law for flow mixed limit condition for element Q2MLC The model This law is only used for non linear flow analysis of solids. This constitutive law allows to impose a uniform flow mixed limit condition on a boundary. The retention curve allows to divide the imposed total flow among a water flow and a gas flow, according the saturation degree.$S_w$$\neq$$S_W$$S_W$$S_W$$S_W$$(=S_{res})$$(=S_{rfiled})$$\left[Pa\right]$$\left[kg/s\right]$$\left[kg/s\right]$ text/html 2022-01-21T16:42:57+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/raco?rev=1642779777&do=diff RACO Description Constitutive law for convection and radiation for elements CONRA and CORA3. Last revision: L. Grisard - sept 1990 The model Non linear thermal analysis of solids. This constitutive law takes account of heat transfer between the solid and the external world by convection and radiation. The coefficients of convection and radiation may be defined as functions of temperature.$\sigma\varepsilon$$\varepsilon \rightarrow 1-\varepsilon$\[\frac{2\varepsilon}{2-\varepsilon}\]$\varep… text/html 2024-04-22T16:59:24+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/rchim?rev=1713797964&do=diff RCHIM Description Biochemical law for chemical reaction, whose PREPRO is LRCHIM.F and the law is implicit in the REACT element. The model IF ICOAL = 1: If ICOAL=1, the reaction modelled is the burning of coal. Several chemical species are of interest: the $O_2$$CO_2$$O_2$$\tau_{O_2}$\[\tau_{O_2}= \frac{1089}{26 * 32}\left[C_{coal}*AK0*\exp{\left(\frac{-EDR}{TEMP}\right)}\right]^{-1}\]$\Delta t_{ch} = 0.1*\tau_{O_2}$$\Delta t$\[AQF = C_{COAL} * C_{O_2} * AK0 * \exp{\left(\frac{-EDR}{TEMP}\ri… text/html 2024-04-19T10:43:32+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/react?rev=1713516212&do=diff RCHIM FIXME THIS PAGE IS FALSE, PLEASE SEE RCHIM. Description Biochemical law for chemical reaction, whose PREPRO is LRCHIM.F and the law is implicit in the REACT element. The model This constitutive law is used to take into account the degradation of organic matter and the following production of Volatil Fatty Acid (VFA). Those VFA are then consumed to produce methanogen biomass. \[r_g = b \times \theta_e \times \phi \times P\]$b$\[\theta_e = \frac{\theta - \theta_{res}}{\theta_{sat} - \th… text/html 2020-08-25T15:46:35+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/respla?rev=1598363195&do=diff RESPLA Description Elasto-plastic constitutive law for RESSO bound elements. The model This law is used for mechanical analysis of elasto-plastic isotropic porous media undergoing large strains. Files Prepro: LRESPL.F Availability Plane stress state$\sigma_{\text{horizontal}}$$\sigma_h$$K_a < K_{eff} < K_p$$K_{eff} = K_a$$K_{eff} = K_p$$K_a < K_{eff} < K_p$ text/html 2020-08-25T15:46:35+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/rubb?rev=1598363195&do=diff RUBB Description Hyperelastic constitutive law for solid elements at constant temperature The model This law is only used for large strains analysis of rubber-like materials Files Prepro: LRUBB.F Lagamine: RUBB2S.F, RUBB2E.F, RUBB2A.F, RUBB3D.F$ln I_3$$I_3 - l$\[ W = C_l (I_l - 3) + C_2 (I_2 - 3) \]\[ W = G \{ 2 D_m \left[ \ln\left( l \frac{D_l}{D_m}\right) + \frac{D_l}{D_m} \right] + \frac{2}{3} a D_l^{\frac{2}{3}} \} \]\[ D_l = 0.5 (I_l - 3 ) \]$I_1, I_2, I_3$$C_1$$C_2$$G$$D_m$$0.489 <… text/html 2021-06-30T11:03:18+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/sgcp?rev=1625043798&do=diff SGCP Description STRAIN GRADIENT CRYSTAL PLASTICITY CONSTITUTIVE LAW Implemented by S. Yuan, L. Duchêne, 2017 The model Mechanical analysis of strain gradient crystal plasticity problem Evers, L.P., Brekelmans, W.A.M., Geers, M.G.D., 2004, J. Mech. Phys. Solids. 52, 2379-2401. doi: 10.1016/j.jmps.2004.03.007 $h_k$$\nu(NS)$$C_{11}$$4^{th}$$C_{12}$$4^{th}$$C_{44}$$4^{th}$$\dot{\gamma}_{0}$$m$$G_{0}$$k$$T$$c$$\mu$$b$$a_{0}$$a_{1}$$a_{2}$$a_{3}$$a_{4}$$a_{5}$$y_{c}$$\rho_{{SSD}_{0}}$$K$$h_{… text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/silcoetc?rev=1598363196&do=diff SILCOETC Description Full law name : SILCOETC3D Coupled plastic-damage multiracial constitutive law for concrete behaviour. For further details see PhD thesis of Thomas Gernay or Andra report by B. Cerfontaine. The model Files Prepro: LSILCOETC3D.F $n$$\varepsilon_{peak}$$\alpha$$^2$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{zz}$$\sigma_{xy}$$\sigma_{xz}$$\sigma_{yz}$$\sigma_{xx}$$\sigma_{yy}$$\sigma_{xy}$$\sigma_{zz}$$t$$\varepsilon_r$$t$ text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/solcp1?rev=1598363196&do=diff SOLCP1 Description Linear constitutive law of flow and deformation in porous media for a pipe element The model This law is used for linear analysis of coupled seepage and compaction in porous media. This law is used for one‑dimensional problems.$=n_0$ text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/solnl1?rev=1598363196&do=diff SOLNL1 Description Constitutive law of flow and deformation in porous media for a pipe element The model Elasto-plastic nonlinear analysis of coupled seepage and compaction in porous media. This law is used for one-dimensional problems Files Prepro: LSONL1.F $\rightarrow$$\alpha e + \beta$$\rightarrow$$\alpha (e-\beta )^{\delta} \cdot (1+e$$\gamma$$\alpha$$\beta$$\delta$$\Omega$$e_0$$\sigma_{p’}$$v_v/v_m$$\sigma_{p’r}$ text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/thmet?rev=1598363196&do=diff THMET Description Constitutive law of thermal conduction coupled with the effects of the metallurgical phase transformations The model This law is only used for non linear thermal analysis coupled with metallurgical analysis of isotropic solids. $=q_X$$=q_Y$ text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/thnlp?rev=1598363196&do=diff THNL-P Description Thermal conduction constitutive law for a bar element at variable temperature The model This law is only used for non linear thermal analysis of isotropic solids. This constitutive law takes account of heat transfer by conduction and heat accumulation in solids, the conductivity and heat capacity of which depend on temperature. text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/thnls?rev=1598363196&do=diff THNL-S Description Thermal conduction constitutive law for solid elements at variable temperature. The model Non linear thermal analysis of isotropic solids. This constitutive law takes account of heat transfer by conduction and heat accumulation in solids, the conductivity and heat capacity of which depend on temperature. This law is used for two or three dimensional heat flow.$\rho c(T)$$\int \rho cdT$$\rho C_p = a_{CAP}T^2+b_{CAP}T+c_{CAP}$$\int{\rho C_p} = a_{CAP}T^2+b_{CAP}T+c_{CAP}… text/html 2020-08-25T15:46:36+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/thsol2?rev=1598363196&do=diff THSOL2 DELETEME This law does not seem to exist in Lagamine anymore. LTSOL2.F does not exist in Prepro Description Thermal conduction constitutive law for solidification problem The model Non-linear thermal analysis of isotropic solids. This constitutive law takes account of heat transfer by conduction, heat accumulation and latent heat production during liquid to solid transformation$\lambda$$\rho$$T_S$$T_L$$\int_{T_l}^{T} {(RHO*CP) dT}$$\rho$$\Delta$$\sigma \dot{\varepsilon}^{p}$ text/html 2020-08-25T15:46:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/visu?rev=1598363197&do=diff VISU Description Cap model : elasto‑viscoplastic constitutive law for solid elements at constant temperature with effect of suction The model This law is used for mechanical analysis of elasto‑viscoplastic isotropic porous media undergoing large strains. $5.10^{-3}$$\psi$$\psi$$\neq$$I_\sigma$$n_o$$c(s) = c(0) + k.s$$\Phi_C = ( f_c /p())* * \alpha_c$$\gamma_c$$\gamma_c$$\alpha_d$$\Phi_d = \left( \frac{f_d}{p_0} \right)^{\alpha_d}$$\alpha_d$$\gamma_d = a_2 \gamma_c$$\sigma_{xx}$$\sigma_{yy}$$… text/html 2024-11-29T15:53:49+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/vmvp?rev=1732892029&do=diff VMVP Von Mises Visco-Plastic. Description 3D isotropic viscoplastic damage law that enables the modeling of non-classical creep responses via Graham-Walles and a modified activation function-Norton viscosity function. Overview This law was implemented in the context of C.Rojas-Ulloa's PhD. project (01/2021-12/2025) on the modeling of the non-classical long-term creep response of Incoloy 800H (see $f(T)$$J_{2}$$J_{2}(\underline{\tilde{\sigma}}-\underline{\mathbb{X}})=\Bigl[\frac{3}{2}(\under… text/html 2020-08-25T15:46:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/wapet?rev=1598363197&do=diff WAPET / WAPET3 Description Water-oil seepage-thermal coupled 2D-3D constitutive law for solid elements. Implemented by: F. Collin, J.P. Radu, R. Charlier, 2000 The model This law is used for water seepage - oil seepage - thermal coupled for non-linear analysis in 2D/3D porous media.$k_w$$k_p$$S_w$$\Gamma_T$\[\left\{\begin{array}{l} f_{we} = \dot{M}_w=\left(\dot{\varepsilon}_v.S_w+n.S_w.\frac{\dot{\rho}_w}{\xi_w}+n.\dot{S}_w\right)\rho_w \\ f_{pe} = \dot{M}_p=\left(\dot{\varepsilon}_v.S_p… text/html 2023-12-12T16:47:25+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/wavat?rev=1702396045&do=diff WAVAT/WAVAT3 Description Water - air seepage - thermal coupled – vapour diffusion 2D/3D constitutive law for solid elements The model This law is only used for water seepage - air seepage-thermal coupled and vapour diffusion for non linear analysis in 2D/3D porous media.\[ \underbrace{\frac{\partial}{\partial t} (\rho_s . n . S_{r,w}) + div(\rho_w \vec{q_l})}_{\text{Liquide}} + \underbrace{\frac{\partial}{\partial t} (\rho_v . n . S_{r,g}) + div(\rho_v \vec{q_g})}_{Vapeur} = 0 \]\[ \vec{q_l… text/html 2023-12-12T16:07:51+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/wavat2?rev=1702393671&do=diff Corman, G. (2024). Hydro-mechanical modelling of gas transport processes in clay host rocks in the context of a nuclear waste repository. PhD thesis, University of Liège. \[ \underbrace{\frac{\partial}{\partial t} (\rho_s . n . S_{r,w}) + div(\rho_w \vec{q_l})}_{\text{Liquide}} + \underbrace{\frac{\partial}{\partial t} (\rho_v . n . S_{r,g}) + div(\rho_v \vec{q_g})}_{Vapeur} = 0 \]\[ \vec{q_l} = - \frac{k_w}{\mu_w}\left[ \vec{grad}(p_w) + g \rho_w \vec{grad}(y)\right]\ \text{où}\ k_w = K_w \frac… text/html 2020-08-25T15:46:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/wpro?rev=1598363197&do=diff WPRO Description Constitutive law for well limit condition for element WEPRO Implemented by: F. Collin, 2001 The model This constitutive law is used for non-linear flow analysis of solids and allows to model fluids exchanges between a well and the reservoir.$S_w$$k_{r,w}$$k_{r,p}$$S_w$$S_w$$S_w$$S_w$$S_{res}$$S_{r,field}$$k_{r,w}$$k_{r,w}$$k_{r,w}$$k_{r,p}$$k_{r,p}$$k_r$\[SIG(1) = f_w=T^{well}.\frac{k_{rw}}{\mu_w}(p_w-p_{well})\]\[SIG(2) = f_o=T^{well}.\frac{k_{ro}}{\mu_o}(p_o-p_{well})\… text/html 2020-08-25T15:46:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/zdmg?rev=1598363197&do=diff ZDMG Description Elastic(-visco)-plastic constitutive law fully coupled with damage for solid elements at constatnt temperature. Implemented by: Zhu Yongui, 1992 Improved by: Sylvie Castagne, 1997 Ehssen Betaieb, 2019 The model The Lemaitre model is a fully coupled elastoplastic damage model based on energy equivalence. In this approach, damage is defined phenomenologically or experimentally instead of analytically or microscopically. The constitutive equations of the damaged material fo… text/html 2020-08-25T15:46:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/zdmgc?rev=1598363197&do=diff DAM-EP-TH Description Elastic-(visco)-plastic constitutive law fully coupled with damage for solid elements at variable temperature The model Mechanical analysis of thermo-elasto-(visco)-plastic-damage isotropic solids undergoing large strains, plastic mixed hardening and damage isotropic hardening are assumed.$\rightarrow$$\rightarrow$$\rightarrow$$rightarrow$$\rightarrow$$\rightarrow$$\alpha$$\Phi$$\sigma_0$$E_t$$\Phi$$\sigma_{XX}$$\sigma_{YY}$$\sigma_{ZZ}$$\sigma_{XY}$$\sigma_{XZ}$$\sigma… text/html 2020-08-25T15:46:37+0200 Anonymous (anonymous@undisclosed.example.com) http://www.lagamine.uliege.be/dokuwiki/doku.php/laws/zizou?rev=1598363197&do=diff ZIZOU Description Cap-model elasto-plastic + cap-model visco-plastic constitutive laws for solid elements at constant temperature with influence of lode angle and suction The model This law is used for mechanical analysis of elastoplastic‑viscoplastic isotropic porous media undergoing large strains. $5.10^{-3}$$\psi$$\psi$$I_\sigma$$n_o$$c(s) = c(0) + k.s$$I_\sigma$$n_o$$c(s) = c(0) + k.s$$\Phi_C = ( f_c /p())* * \alpha_c$$\gamma_c$$\gamma_c$$\alpha_d$$\Phi_d = \left( \frac{f_d}{p_0} \right)…