A mixed variational framework for the design of energy-momentum schemes inspired by the structure of polyconvex stored energy functions

A new approach to the design of energy-momentum (EM) consistent algorithms for nonlinear elastodynamics is proposed. The underlying mixed variational formulation is motivated by the structure of polyconvex stored energy functions and benefits from the notion of a tensor cross product for second-order tensors. The structure-preserving discretization in time of the mixed variational formulation yields an EM consistent semi-discrete formulation. The semi-discrete formulation offers several options for the discretization in space. In the special case of a purely displacement-based method a new form of the algorithmic stress formula is obtained. Several numerical examples are presented to evaluate the performance of the newly developed schemes.