Schubert, Tobias (2015) Scaling relation for low energy states in a single-slip model in finite crystal plasticity. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 95 (11). pp. 1174-1189. ISSN 0044-2267, 1521-4001
Full text not available from this repository. (Request a copy)Abstract
We derive a scaling-relation, for the infimum of the energy J(epsilon,delta)(u, gamma) = integral(Omega) 1/epsilon dist(q) (del u(1 - gamma(e) over arrow(1) circle times (e) over arrow(2)) , SO(2)) + vertical bar gamma vertical bar(p) d lambda(2) (x, y) + delta V-y (chi({gamma = 0}), Omega) , for small epsilon, delta > 0, where p, q >= 1, u : Omega -> R-2 is a deformation with suitable affine boundary conditions and gamma : Omega -> R is a suitable slip variable. This model is motivated by a two-dimensional single-slip model in finite crystal plasticity. We show that the infimum of the energy J(epsilon,delta) scales as delta(q/q+1)/epsilon(1/q+1). This scaling-relation is attained by an asymptotically self-similar branching construction. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DISLOCATION-STRUCTURES; MICROSTRUCTURES; DEFORMATION; STRAINS; Branching; single-crystal plasticity; microstructure |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 May 2019 13:53 |
| Last Modified: | 07 May 2019 13:53 |
| URI: | https://pred.uni-regensburg.de/id/eprint/4556 |
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