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In this work, we design a time-stepping scheme, which can ensure either conservation of energy or dissipation of energy of high (unresolved) modes for nonlinear dynamic analysis. The latter is needed to improve the performance in stress computation and long-term numerical stability. Finite element implementation details are given for finite-strain three-dimensional solid model with independent rotational degrees of freedom. The addition of a rotation field requires a particular choice of large strain measures, allowing one to separate large rotation and large displacement. Several numerical simulations illustrate a very satisfying performance of the proposed time-stepping scheme.

Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics