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

被引：0
|
作者：
Ana Cristina Barroso
José Matias
Marco Morandotti
David R. Owen
机构：
[1] Universidade de Lisboa,Departamento de Matemática and CMAF
[2] Instituto Superior Técnico,CIO, Faculdade de Ciências
[3] Technische Universtität München,Departamento de Matemática
[4] Carnegie Mellon University,Fakultät für Mathematik
来源：
Archive for Rational Mechanics and Analysis | 2017年 / 225卷
关键词：
D O I：
暂无
中图分类号：
学科分类号：
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：47
相关论文
共 50 条
  • [31] On second-order tensor representation of derivatives in shape optimization
    Laurain, Antoine
    Lopes, Pedro T. P.
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2024, 382 (2277):
  • [32] The manipulation of second-order nonlinear harmonic wave by structured material and structured light
    Liu, Haigang
    Chen, Xianfeng
    [J]. JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS, 2018, 27 (04)
  • [33] On a factorization of second-order elliptic operators and applications
    Kravchenko, Vladislav V.
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (40): : 12407 - 12425
  • [34] A SECOND-ORDER IDENTITY FOR THE RIEMANN TENSOR AND APPLICATIONS
    Mantica, Carlo Alberto
    Molinari, Luca Guido
    [J]. COLLOQUIUM MATHEMATICUM, 2011, 122 (01) : 69 - 82
  • [35] Second-order hyperbolic Fuchsian systems and applications
    Beyer, Florian
    LeFloch, Philippe G.
    [J]. CLASSICAL AND QUANTUM GRAVITY, 2010, 27 (24)
  • [36] Second-order distributions: construction, operations, applications
    Dobronets, Boris S.
    Popova, Olga A.
    [J]. VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-UPRAVLENIE VYCHISLITELNAJA TEHNIKA I INFORMATIKA-TOMSK STATE UNIVERSITY JOURNAL OF CONTROL AND COMPUTER SCIENCE, 2022, (61): : 61 - 68
  • [37] A transfer principle for second-order arithmetic, and applications
    Carl, Merlin
    Jamneshan, Asgar
    [J]. JOURNAL OF LOGIC AND ANALYSIS, 2018, 10 : 1 - 32
  • [38] Analytical applications of second-order calibration methods
    Gomez, Veronica
    Callao, Maria Pilar
    [J]. ANALYTICA CHIMICA ACTA, 2008, 627 (02) : 169 - 183
  • [39] A Mathematical Approach to Integral Resonant Control of Second-order Systems
    Namavar, Mohammad
    Aleyaasin, Majid
    Nakkeeran, K.
    Aphale, Sumeet S.
    [J]. PROCEEDINGS OF THE 2012 24TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2012, : 700 - 705
  • [40] Regularity of Solutions to Second-Order Integral Functionals in Variational Calculus
    Ammi, Moulay Rchid Sidi
    Torres, Delfim F. M.
    [J]. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2008, 13 (J08): : 1 - 12
12345