====== 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. ==== Files ==== Prepro: LBODAM.F \\ Lagamine: BODA2E.F, BODA2A.F, BODA3D.F ===== Availability ===== |Plane stress state| NO | |Plane strain state| YES | |Axisymmetric state| YES | |3D state| YES | |Generalized plane state| YES | ===== Input file ===== ==== Parameters defining the type of constitutive law ==== ^ Line 1 (2I5, 60A1)^^ |IL|Law number| |ITYPE| 505| |COMMNT| Any comment (up to 60 characters) that will be reproduced on the output listing| ==== Integer parameters ==== ^ Line 1 (I5) ^^ |NINTV| > 0 : Number of sub-steps used to integrate numerically the constitutive equation in a time step | |:::| = 0 : NINTV will be calculated in the law | ==== Real parameters ==== FIXME Old versions (prior to 2019) of the code and the manual indicate Line 1 & Line 2 to be one single line, which is not possible considering the format (7G10.0); old data files may not be compatible with more recent versions of the code. ^ Line 1 (7G10.0) ^^ |E| YOUNG's elastic modulus | |ANU| POISSON's ratio | |D0| Assumed limiting plastic-shear strain rate ($D_0$) | |D1| Directional hardening coefficient ($D_1$) | |RK0| Initial isotropic hardness ($K_0$) | |RK1| Maximum or limiting isotropic hardness ($K_1$) | |RK2| Minimum or stable isotropic hardness ($K_2$) | ^ Line 2 (7G10.0) ^^ |A1| Recovery coefficient of isotropic hardness ($A_1$) | |A2| Recovery coefficient of directional hardness ($A_2$) | |RM1| Hardening exponent of isotropic hardness ($m_1$) | |RM2| Hardening exponent of directional hardness ($m_2$) | |R1| Recovery exponent of isotropic hardness ($r_1$) | |R2| Recovery exponent of directional hardness ($r_2$) | |RN| Strain rate sensitivity coefficient ($n$) | ^ Line 3 (7G10.0) ^^ |A| Constant dividing the stress ($A$) | |S| Exponent of the stress function ($s$) | |THOLD| Threshold stress value ($\sigma_D$) | |R| Exponent of equivalent plastic strain rate ($r$) | |TAUCO| Ratio between deviatoric and isotropic damage ($\tau$) | |BETA| Constant in the triaxial stress function ($\beta$) | |DSMAX| Failure value of deviatoric damage | ===== Stresses ===== ==== Number of stresses ==== 6 for 3D state \\ 4 for the other cases ==== Meaning ==== The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates. \\ For the 3-D state: |SIG(1)|$\sigma_{xx}$| |SIG(2)|$\sigma_{yy}$| |SIG(3)|$\sigma_{zz}$| |SIG(4)|$\sigma_{xy}$| |SIG(5)|$\sigma_{xz}$| |SIG(6)|$\sigma_{yz}$| For the other cases: |SIG(1)|$\sigma_{xx}$| |SIG(2)|$\sigma_{yy}$| |SIG(3)|$\sigma_{xy}$| |SIG(4)|$\sigma_{zz}$| ===== State variables ===== ==== Number of state variables ==== = 22 for the 3D state \\ = 20 for the other cases ==== List of state variables ==== N = 10 for 3D state\\ N = 8 for other cases |Q(1)| Element thickness ($t$) in plane stress state | |:::| = 1 : Plane strain state | |:::| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical state | |:::| = 0 in 3D state | |:::| = Element thickness ($t$) in generalized plane state | |Q(2)| Current equivalent stress in tension | |Q(3)| Current isotropic hardness; its initial value is $K_0$ | |Q(4)| Equivalent directional hardness | |Q(5)$\rightarrow$Q(N)| Components of directional hardness | |Q(N+1)| Equivalent strain | |Q(N+2)| Deviatoric damage | |Q(N+3)| Bulk damage | |Q(N+4$\rightarrow$N+9)| Fracture criteria (not programmed) | |Q(N+10)| NINTV | |Q(N+11)| $\dot{d}$ | |Q(N+12)| = 0 if $d