Micromechanically based stochastic finite elements

A stochastic finite element method for analysis of effects of spatial variability of material properties is developed with the help of a micromechanics approach. The method is illustrated by evaluating the first and second moments of the global response of a membrane with microstructure of a spatially random inclusion-matrix composite under a deterministic uniformly distributed load. It is shown that two mesoscale random continuum fields have to be introduced to bound the material properties and, in turn, the global response from above and from below. The intrinsic scale dependence of these two random fields is dictated by the choice of the finite element mesh.