Stochastic modeling of heterogeneous materials - A process for the analysis and evaluation of alternative formulations

The paper addresses the problem of understanding and modeling the constitutive behavior of complex, heterogeneous solid materials. Several issues in the area of stochastic material modeling remain open, thus a process for the analysis of different formulations is proposed and examined in detail. Using the proposed process, it is shown that a number of basic models are stochastically similar to each other. Furthermore, often, small apparently unimportant changes in a formulation may result in significant changes in the predicted response. For some formulations, inequalities are established that when satisfied it is guaranteed that the entropy of a structure/system cannot decrease. Attention is given to stochastic formulations within the context of non-local theories because such formulations provide new information to the subject of localization of deformation and fracture toughness.