A generalization of the Hashin-Shtrikman variational formulation is employed to derive a micromechanics-based, explicit nonlocal constitutive equation relating the ensemble averages of stress and strain for random linear elastic composite materials. 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 the case of an isotropic matrix reinforced/weakened by a random distribution of isotropic, non-overlapping identical spheres. Here we describe two new sets of results. The first is an improvement to the previous results for higher volume fractions of inclusions by use of an improved statistical model. The second is an analysis showing how to derive an explicit nonlocal constitutive equation for a matrix reinforced/weakened by a random distribution of non-spherical voids, cracks or inclusions.
Micromechanics - based nonlocal constitutive equations for elastic composites containing non-spherical inclusions
MONETTO, ILARIA;
2001-01-01
Abstract
A generalization of the Hashin-Shtrikman variational formulation is employed to derive a micromechanics-based, explicit nonlocal constitutive equation relating the ensemble averages of stress and strain for random linear elastic composite materials. 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 the case of an isotropic matrix reinforced/weakened by a random distribution of isotropic, non-overlapping identical spheres. Here we describe two new sets of results. The first is an improvement to the previous results for higher volume fractions of inclusions by use of an improved statistical model. The second is an analysis showing how to derive an explicit nonlocal constitutive equation for a matrix reinforced/weakened by a random distribution of non-spherical voids, cracks or inclusions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.