Christowiak, Fabian and Kreisbeck, Carolin (2017) Homogenization of layered materials with rigid components in single-slip finite crystal plasticity. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 56 (3): 75. ISSN 0944-2669, 1432-0835
Full text not available from this repository. (Request a copy)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 Gamma-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 involvemacroscopic 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ENERGY MINIMIZATION; ELASTICITY; MICROSTRUCTURES; CONVERGENCE; F=(FFP)-F-E; CONSTRAINTS; DERIVATION; LIMIT; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Georg Dolzmann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:10 |
| Last Modified: | 18 Feb 2019 13:05 |
| URI: | https://pred.uni-regensburg.de/id/eprint/785 |
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