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International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 18, 2020 Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v2.i1.50
14 pages

Exact Relations for the Effective Properties of Nonlinearly Elastic Inhomogeneous Materials

Qi-Chang He
Southwest Jiaotong University, School of Mechanical Engineering, Chengdu 610031, China; Université Paris-Est, Laboratoire de Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 Boulevard Descartes, 77454 Marne-la-Vallée, France
B. Bary
Laboratoire de Mécanique, Université de Marne-la-Vallee, 19 rue A. Nobel, F-77420 Champs sur Marne, France

Краткое описание

This study is concerned with the effective behavior of nonlinearly elastic materials, which are locally inhomogeneous in one, two, or three directions and whose prototypes are layered, fiber reinforced, matrix-inclusion composites or polycrystals. A systematic method based on the implicit function theorem is proposed to find conditions for the existence of locally uniform strain fields and to exactly determine the overall stress response of such a material to a macroscopic strain associated with a locally uniform strain field. General exact connections are established between the effective elastic tangent moduli evaluated at each macroscopic strain inducing a locally uniform strain field. These results are applied to a cubic polycrystal whose elastic constitutive relation is the most general one, and to power-law fiber-reinforced composites. In particular, it is proven that the overall nonlinear elastic stress response of a cubic polycrystal to an isotropic strain is identical to that of a cubic monocrystal. This conclusion constitutes a nonlinear extension of a well-known result of Hill (1952).