Valian/linear elasticity

hog/recipes/integrands/volume/elasticity.py

+# HyTeG Operator Generator
+# Copyright (C) 2024  HyTeG Team
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+from hog.recipes.common import *
+import sympy as sp
+
+def integrand(
+    *,
+    jac_a_inv,
+    jac_a_abs_det,
+    jac_b_inv,
+    jac_b_abs_det,
+    grad_u,
+    grad_v,
+    k,
+    tabulate,
+    **_,
+):
+
+    grad_u_chain = jac_b_inv.T * tabulate(jac_a_inv.T * grad_u)
+    grad_v_chain = jac_b_inv.T * tabulate(jac_a_inv.T * grad_v)
+
+    def symm_grad(w):
+        return 0.5 * (w + w.T)
+
+    symm_grad_u = symm_grad(grad_u_chain)
+    sigma_u = k["lambda"] * grad_u_chain.trace() * sp.eye(grad_u_chain.shape[0]) + k["mu"] * 2 * symm_grad_u
+    symm_grad_v = symm_grad(grad_v_chain)
+
+    return (
+        double_contraction(sigma_u, symm_grad_v)
+        * tabulate(jac_a_abs_det)
+        * jac_b_abs_det
+    )