Finite element study of ceramic matrix piezocomposites with mechanical interface properties by the effective moduli method with different types of boundary Conditions

The paper deals with the problem of finding the effective moduli of a ceramic matrix composite with surface stresses on the interphase boundaries. The composite consists of a PZT ceramic matrix, elastic inclusions and interface boundaries. It is assumed that the interface stresses depend on the surface strains according to the Gurtin-Murdoch model. This model describes the size effects and contributes to the total stress-strain state only for nanodimensional inclusions. The homogenization problem was set and solved with the help of the effective moduli method for piezoelectric composites with interface boundaries and finite-element technologies used for simulating the representative volumes and solving the resulting boundary-value electroelastic problems. Here in the effective moduli method, different combinations of linear first-kind boundary conditions and constant second-kind boundary conditions for mechanical and electric fields were considered. The representative volume consisted of cubic finite elements with the material properties of the matrix or inclusions and also included the surface elements on the interfaces. Bulk elements were supplied with the material properties of the matrix or inclusions, using a simple random method. In the numerical example, the influence of the fraction of inclusions, the interface stresses and boundary conditions on the effective electroelastic modules were analysed.