Abstract
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.
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