Discrete energy consistency for dynamic finite-strain frictional contact models with inelastic transformation

This paper presents a thermodynamically consistent framework for the numerical treatment of finite-strain contact problems involving frictional interaction and inelastic material transformations, with particular reference to plastic or superelastic materials. The formulation combines large-deformation continuum mechanics with dissipative constitutive behavior, including viscoelasticity, and unilateral contact constraints. We devise a time integration scheme based on the midpoint rule, combined with a semi-smooth Newton strategy for the spatial discretization of frictional contact and inelastic transformation, in such a way that continuous energy balance is reproduced at the discrete level. We carry out a theoretical analysis of the discrete energy balance based on the numerical scheme, and verify the obtained estimates by means of a numerical simulation of two nearly rigid bars compressing a hyper-visco-elasto-plastic ball. The results demonstrate that the proposed approach accurately captures complex nonlinear phenomena while maintaining robust energy behavior over long-term simulations. The study highlights the importance of discrete energy consistency for reliable and physically meaningful simulations of strongly coupled contact and inelastic processes at finite strain.