On the existence of solutions in layered elasto-(visco-)plastic solids with negative hardening

Quasi-static strain-controlled monotonic shearing of a layered solid is considered in this study. It is shown that some hardening contrast between the layers leads to the non-existence of a solution with continuous displacement if the layers consist of elastic-plastic materials. However, it is also shown that a unique solution always exists for the regularized elasto-(visco)plastic material. The mechanical and computational significance of the analysis are discussed.