A stochastic framework for the micromechanical analysis of composites

The formulation of a stochastic micromechanical framework for the history-dependent analysis of composite materials is presented. The theory introduces the statistics of the underlying material microstructure through the incorporation of probability density functions (PDFs) for the different types of concentration tensors. Thus, the theory takes a fundamentally different approach to the analysis of stochastic composites than those theories that follow the current trend of treating stochastic effects by specifying PDFs for the different microstructural arrangements. The general equations governing the behavior of the different types of localization effects within the composite are presented. Based on these governing equations it is shown that in the case of two-phase composites the entire stochastic description for the history-dependent material behavior reduces to the description only of the PDFs for the elastic localization effects in conjunction with any desired set of deterministic constitutive relations for the individual phases.