Variational Modeling of Slip: From Crystal Plasticity to Geological Strata

Slip processes are soft modes of deformation, characteristic of a variety of layered materials. The layers can be at the atomic scale, as in the plastic deformation of crystalline lattices, or on a macroscopic scale, as in stacks of cards or sheets of paper and geological strata. The characteristic deformation processes involve sliding of the layers over one another, leading to a shear deformation with a specific orientation. If the forcing is not parallel to the layers, complex microstructures may form, which have a remarkable similarity over different systems and often consist of alternating shears of different sign. We review here recent results on the detailed analysis of slip processes in crystal plasticity based on the theory of relaxation, discuss the general variational framework for these microstructures, and compare with available experimental results in different systems. We then address the situation in which slip in several different directions may coexist in the same system, as frequently observed in plastically deformed crystals.