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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 49J45
Secondary: 74A60, 74G65, 15A99
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Milestones
Received: 8 July 2016
Accepted: 31 October 2016
Published: 13 May 2017
Communicated by Miroslav Šilhavý
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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 |
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| José Matias | |
| Departamento de Matemática Instituto Superior Técnico Avenida Rovisco Pais 1 1049-001 Lisboa Portugal |
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| Marco Morandotti | |
| Fakultät für Mathematik Technische Universität München Boltzmannstraße 3 85748 Garching bei München Germany |
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| David R. Owen | |
| Department of Mathematical
Sciences Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 United States |
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