====== SGRA2 ====== Plane or axisymmetric state ===== Description ===== {{ :elements:sgra2.png?370|}} Mechanical 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. \\ \\ Type: 207 \\ \\ Implemented by: P. Besuelle, J-P. Radu (2002) ==== Files ==== Prepro: SGRA2A.F \\ Lagamine: SGRA2B.F ===== Input file ===== ^Title (A5)^^ |TITLE|"SGRA2" in the first 5 columns| ^Control data (3I5)^^ |NELEM|Number of elements| |ISPSMAS|0| |INSIG|= 0 → No initial stress \\ = 1 or 2 → Initial stresses| ^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)| ^Definition of the elements (6I5/9I5)^^ |NINTE|Number of integration points (1, 4, or 9)| |LMATM|"Classic" mechanical law| |LMATF|"Second gradient" material law| |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: $\Sigma_{111}$, $\Sigma_{112}$, $\Sigma_{121}$, $\Sigma_{122}$, $\Sigma_{211}$, $\Sigma_{212}$, $\Sigma_{221}$, $\Sigma_{222}$ \\ \\ __Internal variables__: \\ Internal variables of the "classic" mechanical law \\ Internal variables of the "second gradient" mechanical law