  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.

Numerical Analysis;Numerical Analysis