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Isoparametric Tangled Finite Element Method for Nonlinear Elasticity

by   Bhagyashree Prabhune, et al.

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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