Thermoelastic effective properties and stress concentrator factors of composites reinforced by heterogeneities of noncanonical shape

摘要

We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of heterogeneities of arbitrary shape. The general integral equations connecting the stress and strain fields in the point being considered with the stress and strain fields in the surrounding points are obtained for the random fields of heterogeneities. The method is based on a recently developed centering procedure (Buryachenko, 2010a) where the notion of perturbator is introduced and statistical averages are obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. Effective properties (such as compliance and thermal expansion) as well as the first statistical moments of stresses in the phases are estimated for statistically homogeneous composites with the general case of both the shape and inhomogeneity of the thermoelastic heterogeneities properties. The explicit new representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for one heterogeneity inside the infinite medium subjected to the homogeneous remote loading. Numerical results are obtained for some model statistically homogeneous composites reinforced by aligned identical homogeneous heterogeneities of noncanonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.