Finite element analysis of the effective properties of corundum-containing piezoceramics with multiscale pores

The homogenization problems for determining the effective material modules of ceramicmatrix piezocomposites with respect to multiscale porosity are considered. The piezocomposite consists of a piezoceramic matrix, more rigid elastic corundum inclusions and pores. Two porosity models for micropores and for mesopores are used. Here the pores, distributed in piezoceramics with sizes much smaller than the sizes of inclusions, are called micropores, and the pores, comparable in size to inclusions, are called mesopores. Mesopores are considered as a separate phase of a piezocomposite. In the presence of microporosity, the homogenization problem is solved at two scale levels. First, we calculate the effective modules for microporous piezoceramics, where micropores are considered as a separate phase of a two-phase piezocomposite without inclusions, and then we solve the homogenization problem in the general case, i.e. for a three-phase composite consisting of microporous piezoceramics, inclusions and, possibly, mesopores...