Functionals Defined on Piecewise Rigid Functions: Integral Representation and Γ -Convergence

Friedrich M, Solombrino F (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Archive for Rational Mechanics and Analysis Springer Verlag (Germany)

Book Volume: 236

Pages Range: 1325-1387

Journal Issue: 3

DOI: 10.1007/s00205-020-01493-8

Abstract

We analyse integral representation and Γ-convergence properties of functionals defined on piecewise rigid functions, that is, functions which are piecewise affine on a Caccioppoli partition where the derivative in each component is constant and lies in a set without rank-one connections. Such functionals account for interfacial energies in the variational modeling of materials which locally show a rigid behavior. Our results are based on localization techniques for Γ-convergence and a careful adaption of the global method for relaxation (Bouchitté et al. in Arch Ration Mech Anal 165:187–242, 2002; Bouchitté et al. in Arch Ration Mech Anal 145:51–98, 1998), to this new setting, under rather general assumptions. They constitute a first step towards the investigation of lower semicontinuity, relaxation, and homogenization for free-discontinuity problems in spaces of (generalized) functions of bounded deformation.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Friedrich, M., & Solombrino, F. (2020). Functionals Defined on Piecewise Rigid Functions: Integral Representation and Γ -Convergence. Archive for Rational Mechanics and Analysis, 236(3), 1325-1387. https://doi.org/10.1007/s00205-020-01493-8

MLA:

Friedrich, Manuel, and Francesco Solombrino. "Functionals Defined on Piecewise Rigid Functions: Integral Representation and Γ -Convergence." Archive for Rational Mechanics and Analysis 236.3 (2020): 1325-1387.

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