Micro-Slip-Induced Multiplicative Plasticity: Existence of Energy Minimizers

To account for material slips at microscopic scale, we take deformation mappings as SBV functions., which are orientation-preserving outside a jumpset taken to be two-dimensional and rectifiable. For their distributional derivative F = D-phi we examine the common multiplicative decomposition F = (FFp)-F-e into so-called elastic and plastic factors, the latter a measure. Then, we consider a polyconvex energy with respect to F-e, augmented by the measure |curl F-p|. For this type of energy we prove the existence of minimizers in the space of SBV maps. We avoid self-penetration of matter. Our analysis rests on a representation of the slip system in terms of currents (in the sense of geometric measure theory) with both Z(3) and R-3 valued multiplicity. The two choices make sense at different spatial scales; they describe separate but not alternative modeling options. The first one is particularly significant for periodic crystalline materials at a lattice level. The latter covers a more general setting and requires to account for an energy extra term involving the slip boundary size. We include a generalized (and weak) tangency condition; the resulting setting embraces gliding and cross-slip mechanisms. The possible highly articulate structure of the jump set allows one to consider also the resulting setting even as an approximation of climbing mechanisms.

Automated summary

This study explains material slips at a microscopic scale using deformation mappings as SBV functions. It examines the existence of energy minimizers and avoids self-penetration of matter through a decomposition of elastic and plastic factors. The study also presents a representation of the slip system in terms of currents with different multiplicity choices.