Equilibrium Configurations for Epitaxially Strained Films and Material Voids in Three-Dimensional Linear Elasticity

Crismale V, Friedrich M (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Archive for Rational Mechanics and Analysis Springer Verlag (Germany)

Book Volume: 237

Pages Range: 1041-1098

Journal Issue: 2

DOI: 10.1007/s00205-020-01525-3

Abstract

We extend the results about the existence of minimizers, relaxation, and approximation proven by Bonnetier and Chambolle (SIAM J Appl Math 62:1093–1121, 2002), Chambolle and Solci (SIAM J Math Anal 39:77–102, 2007) for an energy related to epitaxially strained crystalline films, and by Braides et al. (ESAIM Control Optim Calc Var 13:717–734, 2007) for a class of energies defined on pairs of function-set. We study these models in the framework of three-dimensional linear elasticity, where a major obstacle to overcome is the lack of any a priori assumption on the integrability properties of displacements. As a key tool for the proofs, we introduce a new notion of convergence for (d- 1) -rectifiable sets that are jumps of GSBDp functions, called σsymp-convergence.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

École Polytechnique - Université Paris-Saclay FR France (FR) Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Crismale, V., & Friedrich, M. (2020). Equilibrium Configurations for Epitaxially Strained Films and Material Voids in Three-Dimensional Linear Elasticity. Archive for Rational Mechanics and Analysis, 237(2), 1041-1098. https://doi.org/10.1007/s00205-020-01525-3

MLA:

Crismale, Vito, and Manuel Friedrich. "Equilibrium Configurations for Epitaxially Strained Films and Material Voids in Three-Dimensional Linear Elasticity." Archive for Rational Mechanics and Analysis 237.2 (2020): 1041-1098.

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