EFFECTIVE STIFFNESS TENSOR OF COMPOSITE MATERIALS WITH INCLUSIONS OF RANDOM SIZE AND PERIODIC LOCATION OF THEIR CENTERS

Abstract

In this study, we investigated the possibility of determining the stiffness tensor using theoretical methods. We utilized a periodicity cell, not a representative elementary volume, to solve the problem, in which the periodicity of the inclusion center locations was considered. Three options were employed to estimate the effective deformation properties of composite materials with periodic inclusion center location arrangements and random size values. In this paper, the applicability of the proposed probabilistic approach to determining the effective stiffness tensor on a periodicity cell is shown. This approach allows one to obtain not only the mean values (i.e., the effective stiffness tensor) but also three main central moments-from the second to the fourth order-characterizing the random nature of the effective stiffness tensor. The approach developed and employed in this study to estimate the effective deformation characteristics of composite materials with periodic inclusion center location arrangements, characterized by random radii values, could be practically extended to other physical and mechanical properties.