A generalization of the Hashin-Shtrikman variational formulation is employed to derive a micromechanics-based nonlocal constitutive equation relating the ensemble averages of stress and strain for random linear elastic composites. The analysis builds on that of Drugan and Willis (1996, J Mech Phys Solids 44, 497-524) and Drugan (2000, J Mech Phys Solids 48, 1359-1387), who derived completely explicit results for isotropic matrices containing random distributions of isotropic, non-overlapping identical spheres. Here, it is shown how to generalise this nonlocal constitutive equation to the case of non-spherical inclusions and how to separate the effects of inclusion shape and spatial distribution. The new constitutive model is then used to improve previous results for higher volume fractions of inclusions.
A micromechanics - based nonlocal constitutive equation for composites containing non-spherical voids and inclusions
MONETTO, ILARIA;
2002-01-01
Abstract
A generalization of the Hashin-Shtrikman variational formulation is employed to derive a micromechanics-based nonlocal constitutive equation relating the ensemble averages of stress and strain for random linear elastic composites. The analysis builds on that of Drugan and Willis (1996, J Mech Phys Solids 44, 497-524) and Drugan (2000, J Mech Phys Solids 48, 1359-1387), who derived completely explicit results for isotropic matrices containing random distributions of isotropic, non-overlapping identical spheres. Here, it is shown how to generalise this nonlocal constitutive equation to the case of non-spherical inclusions and how to separate the effects of inclusion shape and spatial distribution. The new constitutive model is then used to improve previous results for higher volume fractions of inclusions.
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