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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

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


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).