OPTIMAL LOWER BOUNDS ON LOCAL STRESS INSIDE RANDOM MEDIA

被引：6

作者：

Alali, Bacim ^{[1
]}

Lipton, Robert ^{[2
]}

机构：

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2009年 / 70卷 / 04期

基金：

美国国家科学基金会;

关键词：

random heterogeneous materials; failure criteria; stress concentrations; elastic-perfectly plastic; 2-PHASE ELASTIC COMPOSITE; 2 SPACE DIMENSIONS; MICROSTRUCTURES; STRAIN; CONJECTURE; ENERGY;

D O I：

10.1137/080744967

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A methodology is presented for bounding the higher L-p norms, 2 <= p <= infinity, of the local stress inside random media. We present optimal lower bounds that are given in terms of the applied loading and volume fractions for random two phase composites. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. These results deliver tight upper bounds on the macroscopic strength domains for statistically defined heterogeneous media.

引用

页码：1260 / 1282

页数：23

共 48 条

[1]

ALALI B, 2008, NEW BOUNDS LOC UNPUB

[2]

[Anonymous], 2001, 19 AIAA APPL AER C S

[3]

Bazant Z.P., 1998, NEW D CIV E

[4] ON THE HOMOGENIZED YIELD STRENGTH OF 2-PHASE COMPOSITES [J].

CASTANEDA, PP ;

DEBOTTON, G .

PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1992, 438 (1903) :419-431

[5] Yield functions failure criteria for isotropic materials [J].

Christensen, RM .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 453 (1962) :1473-1491

[6] In quest of virtual tests for structural composites [J].

Cox, Brian ;

Yang, Qingda .

SCIENCE, 2006, 314 (5802) :1102-1107

[7] Milton's conjecture on the regularity of solutions to isotropic equations [J].

Faraco, D .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2003, 20 (05) :889-909

[8]

Garnett JCM., 1904, Trans. Roy Soc, V203, P359, DOI [DOI 10.1098/RSTA.1904.0024, 10.1098/rsta.1904.0024]

[9] Dielectric breakdown: optimal bounds [J].

Garroni, A ;

Nesi, V ;

Ponsiglione, M .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2014) :2317-2335

[10] BOUNDS FOR EFFECTIVE PARAMETERS OF HETEROGENEOUS MEDIA BY ANALYTIC CONTINUATION [J].

GOLDEN, K ;

PAPANICOLAOU, G .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 90 (04) :473-491

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