Sensitivity of the macroscopic elasticity tensor to topological microstructural changes

被引：30

作者：

Giusti, S. M. ^{[1
]}

Novotny, A. A. ^{[1
]}

de Souza Neto, E. A. ^{[2
]}

Feijoo, R. A. ^{[1
]}

机构：

[1] LNCC MCT, BR-25651075 Petropolis, RJ, Brazil

[2] Swansea Univ, Civil & Computat Engn Ctr, Sch Engn, Swansea SA2 8PP, W Glam, Wales

来源：

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS | 2009年 / 57卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Homogenized; Elasticity tensor; Topological derivative; Sensitivity analysis; Multi-scale modelling; Synthesis of microstructures; ASYMPTOTIC-EXPANSION; INVERSE SCATTERING; SHAPE; OPTIMIZATION; GRADIENT; DESIGN;

D O I：

10.1016/j.jmps.2008.11.008

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A remarkably simple analytical expression for the sensitivity of the two-dimensional macroscopic elasticity tensor to topological microstructural changes of the underlying material is proposed. The derivation of the proposed formula relies on the concept of topological derivative, applied within a variational multi-scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. The derived sensitivity-a symmetric fourth order tensor field over the RVE domain-measures how the estimated two-dimensional macroscopic elasticity tensor changes when a small circular hole is introduced at the microscale level. This information has potential use in the design and optimisation of microstructures. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：555 / 570

页数：16

共 51 条

[1]

ALMGREN RF, 1985, J ELASTICITY, V15, P427, DOI 10.1007/BF00042531

[2]

Ammari H., 2007, Applied Mathematical Sciences

[3]

Amstutz S, 2005, CONTROL CYBERN, V34, P81

[4] The topological asymptotic for the Navier-Stokes equations [J].