COUPLED 2025

A Petrov-Galerkin EAS Formulation for the FE-Simulation of Thermo-Elastomechanical Problems

  • Zähringer, Felix (Karlsruhe Institute of Technology)
  • Betsch, Peter (Karlsruhe Institute of Technology)

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The quality of the results of finite element (FE) simulations is highly dependent on the chosen mesh. Especially in the case of highly distorted meshes, large discrepancies between the numerical and the analytical solution can be observed (see, e.g., [1]). This mesh-sensitive behavior is not only prevalent in simulations of purely mechanical problems, but also in multiphysics simulations. In this contribution, we investigate to what extent the Petrov-Galerkin FEM provides a remedy to this problem. In contrast to the Bubnov-Galerkin method, which is used for most FE formulations, the Petrov-Galerkin method employs different ansatz spaces for the test and trial functions. For purely mechanical problems, several Petrov-Galerkin elements have already been developed, which demonstrate significantly improved properties in terms of mesh sensitivity (see, e.g., [2, 3, 4]). In this contribution, we demonstrate how a Petrov-Galerkin FE formulation, originally developed for the simulation of purely mechanical problems using the Enhanced Assumed Strain (EAS) method (cf. [3, 4]), can be extended to enable the simulation of thermo-elastomechanical problems. The properties of the proposed formulation are illustrated through numerical examples. REFERENCES [1] Lee, N.-S. and Bathe, K.-J. Effects of element distortions on the performance of isoparametric elements. Int. J. Numer. Meth. Engng. 36, 3553-3576, (1993). [2] Xie, Q., Sze, K. Y. and Zhou, Y. X. Modified and Trefftz unsymmetric finite element models. Int. J. Mech. Mater. Des. 12, 53-70, (2016). [3] Pfefferkorn, R. and Betsch, P. Mesh distortion insensitive and locking-free Petrov-Galerkin low-order EAS elements for linear elasticity. Int. J. Numer. Meth. Engng. 122(23), 6924-6954, (2021). [4] Pfefferkorn, R. and Betsch, P. Hourglassing- and locking-free mesh distortion insensitive Petrov–Galerkin EAS element for large deformation solid mechanics. Int. J. Numer. Meth. Engng. 124(6), 1307-1343, (2022).