Effective Properties of Periodic and Random Media

We are interested in the general problem of transport phenomena in multiscale ordered or disordered media. Many engineering materials such as composites, porous media, granular media, biomaterials encountered in many fields of application display multiscale, heterogeneous microstructures. We are seeking to better understand and predict the macroscopic transport properties of these materials, such as their electric permittivity, thermal conductivity or permeability, through a modeling approach which combines probabilistic concepts, asymptotic analysis and efficient numerical formulations. Although our initial work is based on linear, elliptic equations characterized by second-order random tensors, we are also interested in linear and nonlinear problems which characterize the elastic behavior of composite materials.

Stochastic homogenization of randomly perturbed, multiscale periodic heat conduction problems, K. Ogbuanu & R.V. Roy, 2018 ASME’s ICME, November 9-14, Pittsburgh.