Visco-plasticity stress-based solid dynamics formulation and time-stepping algorithms for stiff case

In this paper, the visco-plastic behavior of solids is formulated based on the Hellinger-Reissner variational principle. The latter provides an optimal basis to obtain an increased accuracy of computed stress by using independent space-discretizations of both displacement and stress fields. The formulation is further adapted to solid dynamics and in particular to so-called stiff case that is characterized with a large difference in stiffness and/or evolution time between different deformation modes, which presents a great challenge when integrating the dynamic response. For this class of problem, we here propose the algorithmic modifications leading to energy conserving or decaying schemes that can either preserve the total energy or dissipate the energy of higher modes, and thus control the overall stability of numerical computations with large steps over long period of time. Several numerical examples are presented to illustrate a very satisfying performance of the proposed approach and algorithm. (C) 2020 Elsevier Ltd. All rights reserved.