Comparison of approaches to accounting for imperfect contacts when determining the effective permeability of material

Abstract

The paper develops a complex approach to accounting for imperfect contacts (IC) when determining effective properties of various nature. The IC are assumed to be caused by various factors (microstructure features, process’s specifity and so on). To obtain macroscopic properties, we seek a solution of the homogenization problem for the material containing isolated ellipsoidal inhomogeneities when fields are discontinuous at the interphase boundaries. The paper considers, generalizes and compares two existing approaches to accounting for the IC, namely, an approach where IC is modeled by means of a field jump specified in terms of a ratio of field values on the outer and inner sides of the inhomogeneity boundary, and approach, which introduces inhomogeneity with a surface effect. To take into account IC, we have considered an equivalent inhomogeneity with ideal contacts at the boundary. Working the problem on determining the effective diffusional permeability of material provided an example.

Keywords

• effective properties
• imperfect contact
• equivalent inhomogeneity
• effective diffusional permeability
• homogenization problem