Generalized Stochastic Approach for Constitutive Equation in Linear Elasticity: A Random Matrix Model∗

This work is concerned with the construction of stochastic models for random elasticity matrices, allowing either for the generation of elasticity tensors exhibiting some material symmetry properties almost surely (integrating the statistical dependence between the random stiffness components), or for the modeling of random media that requires the mean of a stochastic anisotropy measure to be controlled apart from the level of statistical fluctuations. To this aim, we first introduce a decomposition of the stochastic elasticity tensor on a deterministic tensor basis and consider the probabilistic modeling of the random components, having recourse to the MaxEnt principle. Strategies for random generation and estimation are further reviewed and the approach is exemplified in the case of a material that is transversely isotropic almost surely. In a second stage, we make use of such derivations to propose a generalized model for random elasticity matrices that takes into account, almost separately, constraints on both the level of stochastic anisotropy and the level of statistical fluctuations. An example is finally provided and shows the efficiency of the approach.