Embedding a Micromechanical Law in the Continuum Formulation: A Multiscale Approach Applied to Discontinuous Solutions

The framework of multi scale analysis has been applied to strain localization problems. It is now extended to the case of strong discontinuities. This term describes displacement fields that possess a dis­ continuous component. The analysis of discontinuous solutions arising in one-dimensional, rate-independent plasticity is revisited. The resulting formulation is treated as a microstructural model that is sought to be embedded in the standard, macromechanical continuum framework. In a neighborhood of the discontinuity, one can identify coarse and fine scale fields such that the discontinuous component is contained in the latter. With this decomposition as a basis, multi scale analysis is used as a vehicle to effect the desired embedding. The features of the strong discontinuities model for strain-softening solids are shown to be retained in the resulting multiscale model.