An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems: The three-dimensional case

Solving large deformation problems of hyperelastic materials by the finite element method is still a challenging problem due to the severe mesh distortion that occurs during the computation. In Leger et al. (2014), it was shown that combining an updated Lagrangian method with an efficient adaptive remeshing algorithm, an accurate transfer method for the deformation gradient tensor as well as an efficient continuation method leads to a very stable, efficient and accurate algorithm to solve two-dimensional very large deformation problems. In this paper, we show that this method can also be generalized to solve three-dimensional problems. A number of static problems will be presented and analyzed.