====== SGRC2 ====== Plane or axisymmetric state ===== Description ===== {{ :elements:sgra2.png?370|}} Mechanical-flow analysis, Grenoble 2nd gradient method, in large deformations. \\ \\ The element is defined by 9 nodes specified in NODES in the order indicated in the figure. \\ \\ Nodes 1, 3, 5, and 7 have 6 DoF ($u_1$, $u_2$, $v_{11}$, $v_{12}$, $v_{21}$, $v_{22}$), whereas nodes 2, 4, 6, and 8 only have 2 DoF ($u_1$, $u_2$). The central node 9 has 4 DoF ($\lambda_{11}$, $\lambda_{12}$, $\lambda_{21}$, $\lambda_{22}$), that have a different signification from ($v_{11}$, $v_{12}$, $v_{21}$, $v_{22}$) but occupy the same position. \\ \\ The flow description can be completely different from the mechanical description: the pressure can be interpolated linearly in a 4 node configuration, while the mechanical degrees of freedom are interpolated parabolically in an 8-node configuration. In that case, the flow DoF must be fixed for the nodes that are not used (2, 4, 6, and 8). \\ \\ Type: 218 \\ \\ Implemented by: J-P. Radu, F. Collin (2003)\\ The framework definition of this element can be found in Pardoen (2015)((Pardoen, B. (2015). Hydro-mechanical analysis of the fracturing induced by the excavation of nuclear waste repository galleries using shear banding. PhD thesis, University of Liège. https://orbi.uliege.be/handle/2268/188222)). ==== Files ==== Prepro: SGRC2A.F \\ Lagamine: SGRC2B.F ===== Input file ===== ^Title (A5)^^ |TITLE|"SGRC2" in the first 5 columns| ^Control data (4I5)^^ |NELEM|Number of elements| |ISPSMAS|0| |INSIG|= 0 → No initial stress \\ = 1 or 2 → Initial stresses| |INBIO|= 0 → No Biot coefficient \\ = 1 → Isotropic Biot coefficient \\ = 2 → Anisotropic Biot coefficient \\ Only for orthotropic mechanical law [[laws:orthopla|ORTHOPLA]]| ^Initial stresses - Only if INSIG > 0 (4G10.0)^^ |If INSIG=1: $\sigma_y=\sigma_{y0}+yd\sigma_{y}$ \\ If INSIG=2: $\sigma_y=min(\sigma_{y0}+yd\sigma_y,0)$|| |SIGY0| $\sigma_{y0}$ effective stress $\sigma_y$ at the axes origin| |DSIGY|Effective stress gradient along Y axis| |AK0X|$k_0$ ratio $\sigma_x/\sigma_y$| |AK0Z|$k_0$ ratio $\sigma_z/\sigma_y$ (if AK0Z=0, AK0Z=AK0X)| ^Biot coefficient - Only if INBIO > 0 (3G10.0)^^ |See [[elements:csol2|CSOL2]] for more details|| |**If INBIO = 1**|| |CBIOT|Biot coefficient| |**If INBIO = 2**|| |CBIOT1|Biot coefficient $b_{11}$| |CBIOT2|Biot coefficient $b_{22}$| |CBIOT3|Biot coefficient $b_{33}$| ^Definition of the elements (5I5/9I5)^^ |NINTE|Number of integration points (1, 4, or 9)| |LMATM|"Classic" mechanical law| |LMATSG|"Second gradient" material law| |LMATF|Fluid law| |NNODF|Number of fluid nodes (4 or 8 - Default value = 8)| |NODES(9)|List of nodes| ===== Results ===== __Stresses (in global axes)__: \\ 4 "classic" mechanical stresses: $\sigma_x$, $\sigma_y$, $\sigma_{xy}$, $\sigma_z$ \\ 8 "second gradient" mechanical stresses: $\Sigma_{111}$, $\Sigma_{112}$, $\Sigma_{121}$, $\Sigma_{122}$, $\Sigma_{211}$, $\Sigma_{212}$, $\Sigma_{221}$, $\Sigma_{222}$ \\ 4 flow stresses: $f_x$, $f_y$, $f_{emmagasiné}$, $0$ \\ \\ __Internal variables__: \\ Internal variables of the "classic" mechanical law \\ Internal variables of the "second gradient" mechanical law \\ Internal variables of the fluid law