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

In 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.