Stress Fluctuations in Random Structure Composites

Although the effective behavior of the composite is traditionally the main focus of micromechanics, it is also essential to supply insight into the statistical description of the local strains and stresses, such as their statistical moments of different order in each phase and at interphase. Estimation of these local fields are extremely useful for understanding the evolution of nonlinear phenomena such as plasticity, creep, and damage. When one tries to estimate the equivalent stress in the strength theories as well as in nonlinear creep theory, or when the yield function in plasticity theory is considered, squares of the first invariant or the second invariant of the deviator of local stresses are frequently used. Several papers have already been written on the problem of estimation of values of invariants averaged over the volume of the components, which involve particular assumptions or simplifications as, for instance, the two-dimensional model [362], special correlation function [840]. A very prospective idea of a perturbation method proposed by Bergman [74] is based on the estimation of the perturbation of an energetic function due to a variation of the material properties such as e.g. conductivity and elasticity modulus. This idea was developed for estimation of stress fluctuations in the case of isotropy of materials constants [89], [90], [599] and isotropy of fluctuations [602].