Vol. 5, No. 2, 2017

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Explicit formulas for relaxed disarrangement densities arising from structured deformations

Ana Cristina Barroso, José Matias, Marco Morandotti and David R. Owen

Vol. 5 (2017), No. 2, 163–189
DOI: 10.2140/memocs.2017.5.163
Abstract

In this paper we derive explicit formulas for disarrangement densities of submacroscopic separations, switches, and interpenetrations in the context of first-order structured deformations. Our derivation employs relaxation within one mathematical setting for structured deformations of a specific, purely interfacial density, and the formula we obtain agrees with one obtained earlier in a different setting for structured deformations. Coincidentally, our derivation provides an alternative method for obtaining the earlier result, and we establish new explicit formulas for other measures of disarrangements that are significant in applications.

Keywords
structured deformations, relaxation, disarrangements, interfacial density, bulk density, isotropic vectors
Mathematical Subject Classification 2010
Primary: 49J45
Secondary: 74A60, 74G65, 15A99
Milestones
Received: 8 July 2016
Accepted: 31 October 2016
Published: 13 May 2017

Communicated by Miroslav Šilhavý
Authors
Ana Cristina Barroso
Departamento de Matemática and Centro de Matemática
Aplicações Fundamentais e Investigação Operacional
Faculdade de Ciências da Universidade de Lisboa
Campo Grande
Edifício C6, Piso 1
1749-016 Lisboa
Portugal
José Matias
Departamento de Matemática
Instituto Superior Técnico
Avenida Rovisco Pais 1
1049-001 Lisboa
Portugal
Marco Morandotti
Fakultät für Mathematik
Technische Universität München
Boltzmannstraße 3
85748 Garching bei München
Germany
David R. Owen
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
United States