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arXiv · 2303.10799

Isoparametric Tangled Finite Element Method for Nonlinear Elasticity

Bhagyashree Prabhune·Krishnan Suresh
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Abstract

An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric tangled finite element method (i-TFEM) was recently proposed for linear elasticity problems. It was demonstrated that i-TFEM leads to optimal convergence even for severely tangled meshes. In this paper, i-TFEM is generalized to nonlinear elasticity. Specifically, a variational formulation is proposed that leads to local modification in the tangent stiffness matrix associated with tangled elements, and an additional piece-wise compatibility constraint. i-TFEM reduces to standard FEM for tangle-free meshes. The effectiveness and convergence characteristics of i-TFEM are demonstrated through a series of numerical experiments, involving both compressible and in-compressible problems.

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Bhagyashree Prabhune, Krishnan Suresh. 2023-03-20. Isoparametric Tangled Finite Element Method for Nonlinear Elasticity. https://arxiv.org/abs/2303.10799

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