Variational based effective models for inelastic materials

Abstract

AbstractMechanical systems with inelastic materials and given boundary conditions can be generally defined and solved. However, for large systems, this problem becomes non trivial and computationally costly, especially when microstructures occure. Therefore, multi‐scale modeling is used to capture the behavior of the system.In this study, we present a methodology to provide such models for inelastic materials starting from the variational scheme. Using the variational principle we define the material strain energy and dissipation potential at the coarse scale (macro scale) starting from their counterparts on the fine scale, through the homogenization scheme. Then we solve the material model at the macro level instead of solving the fine scale model or the whole combination of scales. This multi‐scale model offers a reduced number of degrees of freedom and can generally provide the behavior of the system. Moreover, the macro scale model preserves the mathematical structure of the micro scale one. Nevertheless, for this effective model, special care needs to be given to the selection of the inelastic variables solved on the macro scale. This model is illustrated by the application to problems in classical plasticity.