Microstructural Evaluation of Effective Elasticity Coefficients in Materials with Micro-voids

The paper deals with homogenization of linear elastic continuum involving empty voids. The concept of homogenization is meaningful provided that the size of voids is much smaller than the characteristic length in structural design. Assuming a uniform distribution of voids, one can utilize the concept of the representative volume element (RVE) which is a finite part of the macrostructure with involving one or more voids. In general, a numerical approach is necessary for solution of micro-structural boundary value problems in case of arbitrary shape and/or distribution of voids. Several approaches are discussed and mathematical models developed for numerical calculation of effective material coefficients for linear elastic continuum involving arbitrary empty voids. Appropriate micro-structural boundary value problems in the RVE are proposed for numerical analyses which are utilized for a posterior evaluation of effective material coefficients. Comparisons of results by various numerical approaches are discussed for the circular and elliptical pores.