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
收藏
页码：1025 / 1072
页数：48
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