Second-Order Structured Deformations: Relaxation, Integral Representation and Applications

被引：15

作者：

Barroso, Ana Cristina ^{[1
,2
]}

Matias, Jose ^{[3
]}

Morandotti, Marco ^{[4
]}

Owen, David R. ^{[5
]}

机构：

[1] Univ Lisbon, Fac Ciencias, Dept Matemat, Edificio C6 Piso 1, P-1749016 Lisbon, Portugal

[2] Univ Lisbon, Fac Ciencias, CMAF CIO, Edificio C6 Piso 1, P-1749016 Lisbon, Portugal

[3] Inst Super Tecn, Dept Matemat, Ave Rovisco Pais 1, P-1049001 Lisbon, Portugal

[4] Tech Univ Munich, Fak Math, Boltzmannstr 3, D-85748 Garching, Germany

[5] Carnegie Mellon Univ, Dept Math Sci, 5000 Forbes Ave, Pittsburgh, PA 15213 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2017年 / 225卷 / 03期

基金：

欧洲研究理事会;

关键词：

STABLE DISARRANGEMENT PHASES; ENERGY; MODEL; TRANSFORMATIONS; INTERFACES; THEOREM; BULK;

D O I：

10.1007/s00205-017-1120-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications.

引用

页码：1025 / 1072

页数：48

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