Structure‐preserving space‐time discretization of a mixed formulation for quasi‐incompressible large strain elasticity in principal stretches

Abstract

SummaryIn this paper, we propose an energy and momentum consistent time‐stepping scheme for nonlinear elastodynamics. The algorithm is based on a mixed Hu‐Washizu–type variational principle that is inspired by the concept of polyconvexity and relies on a tensor cross product of second‐order tensors. In addition, we introduce a new algorithmic stress formula in its eigenvalue representation to model the transient behavior of hyperelastic bodies of Ogden‐type materials. Finally, several numerical examples show the superior performance of the proposed formulation in terms of numerical robustness and stability.