A BOUNDARY ELEMENT FORMULATION FOR MICROMECHANICAL HOMOGENIZATION OF POLYCRYSTALLINE MATERIALS WITH PIEZOELECTRIC COUPLING

Abstract

A novel boundary element formulation for the evaluation of the effective properties of threedimensional polycrystalline aggregates with piezoelectric coupling is presented. The aggregates are modelled at the scale of their constituent crystals and are artificially generated through Voronoi-Laguerre tessellations. The electro-mechanical behaviour of each crystal is represented upon introducing an ad-hoc mesh of its boundary and a generalised integral representation of the governing equations of the piezoelectric problem. The behaviour of the whole aggregate is then retrieved upon introducing a suitable set of electro-mechanical interface conditions at the grain boundaries. With respect to classic FE formulations, the present approach has the advantages of: i) expressing the problems in term of boundary values only, thus allowing a natural expression of the interface conditions; ii) requiring the grain boundary mesh only, thus reducing the meshing effort; iii) reducing the number of degrees of freedom of the problem, which is highly desirable in three-dimensional problems. Numerical analyses are performed to study the effect of the statistical distribution of the grains’ orientation on the effective properties of BaTiO3 aggregates. The obtained results are consistent with theoretical estimates and the results available in the literature, showing the potential and accuracy of the proposed formulation.