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A Unified Model for Stress-Driven Rearrangement Instabilities
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is characterized by an energy displaying both elastic and surface...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7343841/ https://www.ncbi.nlm.nih.gov/pubmed/32669730 http://dx.doi.org/10.1007/s00205-020-01546-y |
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author | Kholmatov, Shokhrukh Yu. Piovano, Paolo |
author_facet | Kholmatov, Shokhrukh Yu. Piovano, Paolo |
author_sort | Kholmatov, Shokhrukh Yu. |
collection | PubMed |
description | A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is characterized by an energy displaying both elastic and surface terms, and allows for a unified treatment of a wide range of settings, from epitaxially-strained thin films to crystalline cavities, and from capillarity problems to fracture models. The existence of minimizing configurations is established by adopting the direct method of the Calculus of Variations. The compactness of energy-equibounded sequences and energy lower semicontinuity are shown with respect to a proper selected topology in a class of admissible configurations that extends the classes previously considered in the literature. In particular, graph-like constraints previously considered for the setting of thin films and crystalline cavities are substituted by the more general assumption that the free crystalline interface is the boundary, consisting of an at most fixed finite number m of connected components, of sets of finite perimeter. Finally, it is shown that, as [Formula: see text] , the energy of minimal admissible configurations tends to the minimum energy in the general class of configurations without the bound on the number of connected components for the free interface. |
format | Online Article Text |
id | pubmed-7343841 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-73438412020-07-13 A Unified Model for Stress-Driven Rearrangement Instabilities Kholmatov, Shokhrukh Yu. Piovano, Paolo Arch Ration Mech Anal Article A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is characterized by an energy displaying both elastic and surface terms, and allows for a unified treatment of a wide range of settings, from epitaxially-strained thin films to crystalline cavities, and from capillarity problems to fracture models. The existence of minimizing configurations is established by adopting the direct method of the Calculus of Variations. The compactness of energy-equibounded sequences and energy lower semicontinuity are shown with respect to a proper selected topology in a class of admissible configurations that extends the classes previously considered in the literature. In particular, graph-like constraints previously considered for the setting of thin films and crystalline cavities are substituted by the more general assumption that the free crystalline interface is the boundary, consisting of an at most fixed finite number m of connected components, of sets of finite perimeter. Finally, it is shown that, as [Formula: see text] , the energy of minimal admissible configurations tends to the minimum energy in the general class of configurations without the bound on the number of connected components for the free interface. Springer Berlin Heidelberg 2020-06-20 2020 /pmc/articles/PMC7343841/ /pubmed/32669730 http://dx.doi.org/10.1007/s00205-020-01546-y Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Kholmatov, Shokhrukh Yu. Piovano, Paolo A Unified Model for Stress-Driven Rearrangement Instabilities |
title | A Unified Model for Stress-Driven Rearrangement Instabilities |
title_full | A Unified Model for Stress-Driven Rearrangement Instabilities |
title_fullStr | A Unified Model for Stress-Driven Rearrangement Instabilities |
title_full_unstemmed | A Unified Model for Stress-Driven Rearrangement Instabilities |
title_short | A Unified Model for Stress-Driven Rearrangement Instabilities |
title_sort | unified model for stress-driven rearrangement instabilities |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7343841/ https://www.ncbi.nlm.nih.gov/pubmed/32669730 http://dx.doi.org/10.1007/s00205-020-01546-y |
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