Eur. Phys. J. B 68, 89-101 (2009)
https://doi.org/10.1140/epjb/e2009-00063-1

Nonlinear elasticity of composite materials

Landau coefficients in dispersions of spherical and cylindrical inclusions

¹ Sardinian Laboratory for Computational Materials Science (SLACS, INFM-CNR), Sardinia, Italy
² Department of Physics, University of Cagliari, Cittadella Universitaria, 09042 Monserrato (Ca), Italy

Corresponding author: ^a stefano.giordano@dsf.unica.it

Received: 11 December 2008
Published online: 21 February 2009

Abstract

We investigate the elastic properties of model composites, consisting in a dispersion of nonlinear (spherical or cylindrical) inhomogeneities into a linear solid matrix. Both phases are considered isotropic. Under the simplifying hypotheses of small deformation for the material body and of small volume fraction of the embedded phase, we develop a homogenization procedure based on the Eshelby theory, aimed at describing nonlinear features. We obtain the bulk and shear moduli and Landau coefficients of the overall material in terms of the elastic behavior of the constituents and of their volume fractions. The mixing laws for the nonlinear properties describe a complex scenario where possible strong amplifications of the nonlinearities may arise in some given conditions.