Determination of the closure of the set of elasticity functionals

被引：84

作者：

Camar-Eddine, M ^{[1
]}

Seppecher, P ^{[1
]}

机构：

[1] Univ Toulon & Var, Lab Anal Non Lineaire Appl & Modelisat, F-83957 La Garde, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2003年 / 170卷 / 03期

关键词：

OPTIMAL BOUNDS; HOMOGENIZATION; COMPOSITES;

D O I：

10.1007/s00205-003-0272-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine the closure for Mosco-convergence in L-2(Omega,R-3) of the set of elasticity functionals. We prove that this closure coincides with the set of all non-negative lower-semicontinuous quadratic functionals which are objective, i.e., which vanish for rigid motions. The result is still valid if we consider only the set of isotropic elasticity functionals which have a prescribed Poisson coefficient. This shows that a very large family of materials can be reached when homogenizing a composite material with highly contrasted rigidity coefficients.

引用

页码：211 / 245

页数：35

共 29 条

[1] Truss modular beams with deformation energy depending on higher displacement gradients [J].

Alibert, JJ ;

Seppecher, P ;

Dell'Isola, F .

MATHEMATICS AND MECHANICS OF SOLIDS, 2003, 8 (01) :51-73

[2]

[Anonymous], 1967, Ann.Scuola Normale Sup. Pisa

[3]

[Anonymous], 2002, APPL MATH SCI

[4]

Attouch H., 1984, VARIATIONAL CONVERGE

[5] OPTIMAL BOUNDS AND MICROGEOMETRIES FOR ELASTIC 2-PHASE COMPOSITES [J].

AVELLANEDA, M .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1987, 47 (06) :1216-1228

[6]

Bellazzi Monza G, 1998, CRITICA LETT, V26, P407

[7]

Bellieud M, 1996, CR ACAD SCI I-MATH, V323, P1135

[8] DIRICHLET SPACES [J].

BEURLING, A ;

DENY, J .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1959, 45 (02) :208-215

[9] Closure of the set of diffusion functionals with respect to the mosco-convergence [J].

Camar-Eddine, M ;

Seppecher, P .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (08) :1153-1176

[10] Non-local interactions resulting from the homogenization of a linear diffusive medium [J].

Camar-Eddine, M ;

Seppecher, P .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 332 (05) :485-490

← 1 2 3 →