Computational Piezo-Grains (CPGs) for a highly-efficient micromechanical modeling of heterogeneous piezoelectric-piezomagnetic composites

Influenced by the need for composites with stronger magneto-electric coupling, we present a novel numerical method called "Computational Piezo-Grains" (CPGs) for modeling different types of piezoelectric/piezomagnetic composites in the microscale. The advantage of this method is that the matrix and the inclusion of a grain can be modeled using only one element in a finite element sense. The geometric shapes of these computational grains mimic the shapes of grains in the microscale and each grain may contain an embedded micro-void or micro-inclusion. The material of the matrix or the inclusion in any grain could be elastic with no couplings, piezoelectric, or piezomagnetic; thus allowing for modeling different configurations of piezo-composites. Lekhnitskii formulation is extended to model any of these composites and is used in the development of these computational grains to express the fields in the matrix and the inclusion of each computational grain.