The Variational Modeling of Hierarchical Structured Deformations

被引：2

作者：

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

Matias, Jose ^{[3
]}

Morandotti, Marco ^{[4
]}

Owen, David R. ^{[5
]}

Zappale, Elvira ^{[6
]}

机构：

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

[2] Univ Lisbon, CMAFcIO, Fac Ciencias, Ediffcio C6,Piso 1, P-1749016 Lisbon, Portugal

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

[4] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

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

[6] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via Antonio Scarpa 16, I-00161 Rome, Italy

来源：

JOURNAL OF ELASTICITY | 2024年 / 155卷 / 1-5期

关键词：

Structured deformations; Hierarchies; Relaxation; Energy minimization; Integral representation; RELAXATION; DENSITIES; THEOREM; BULK;

D O I：

10.1007/s10659-022-09961-w

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to minimize mechanically relevant energies defined on hierarchical structured deformations. Two results are obtained here: (i) an approximation theorem and (ii) the assignment of an energy to a hierarchical structured deformation by means of an iterative procedure. This has the effect of validating the proposal made in Deseri and Owen (J. Elast. 135:149-182, 2019) to study deformations admitting slips and separations at multiple submacroscopic levels. An explicit example is provided to illustrate the behavior of the proposed iterative procedure and relevant directions for future research are highlighted.

引用

页码：371 / 392

页数：22

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