Two-scale modelling of strongly heterogeneous continua using the homogenization approach

Abstract eng:
The notion of strong heterogeneity is considered in the sense of material scaling: the idea is to study mathematical models where the coefficients of the partial differential equations associated with one of the material phases depend on the characteristic size ε of the microstructure. This modeling ansatz is justified to represent high contrasts in material properties of different components; it was applied to study wave propagation in two-phase elastic composites with “weak” inclusions, where elasticity is scaled by ε2 , or to describe poroelastic behaviour in double-porous media, where permeability of the second porosity is proportional ε2 . Perforated structures can be handled using similar mathematical tools. For homogenization of thin structures the scaling is related to the thickness, which leads to reduced spatial dimension of the problem. This paper summarizes some models developed using the homogenization approach; namely applications in modelling elastic waves, acoustic transmission and fluid flow in porous media are discussed.

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