Homogenization of layered materials with rigid components in single-slip finite crystal plasticity

C.C. Kreisbeck, Fabian Christowiak

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense that it admits only local rotations, the other one is softer featuring a single active slip system with linear self-hardening. As a main result, we obtain explicit homogenization formulas by means of Γ-convergence. Due to the anisotropic nature of the problem, the findings depend critically on the orientation of the slip direction relative to the layers, leading to three qualitatively different regimes that involve macroscopic shearing and blocking effects. The technical difficulties in the proofs are rooted in the intrinsic rigidity of the model, which translates into a non-standard variational problem constraint by non-convex partial differential inclusions. The proof of the lower bound requires a careful analysis of the admissible microstructures and a new asymptotic rigidity result, whereas the construction of recovery sequences relies on nested laminates.
Original languageEnglish
Article number75
Journal Calculus of Variations and Partial Differential Equations
Volume56
Issue number3
DOIs
Publication statusPublished - 2017

Keywords

  • 49J45 (primary)
  • 74Q05
  • 74C15

Fingerprint

Dive into the research topics of 'Homogenization of layered materials with rigid components in single-slip finite crystal plasticity'. Together they form a unique fingerprint.

Cite this