Homogenization of discrete diffusion models by asymptotic expansion

Diffusion behaviors of heterogeneous materials are paramount importance in many engineering problems. Numerical models that take into account the internal structure such robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then practical application is limited to relatively small material volumes. paper formulates a homogenization scheme for diffusion models. Asymptotic expansion applied distinguish between (i) continuous macroscale description approximated standard finite element method and (ii) fully resolved mesoscale local representative volume (RVE) material. Both transient steady-state variants with nonlinear constitutive relations discussed. In all cases, resulting RVE problem becomes simple linear easily pre-computed. The scale separation provides significant reduction computational time allowing solution problems negligible error introduced mainly discretization at macroscale.