Multi-physics computational grains (MPCGs) for direct numerical simulation (DNS) of piezoelectric composite/porous materials and structures

Conceptually simple and computationally most efficient polygonal computational grains with voids/inclusions are proposed for the direct numerical simulation of the micromechanics of piezoelectric composite/porous materials with non-symmetrical arrangement of voids/inclusions. These are named "Multi-Physics Computational Grains" (MPCGs) because each "mathematical grain" is geometrically similar to the irregular shapes of the physical grains of the material in the micro-scale. So each MPCG element represents a grain of the matrix of the composite and can include a pore or an inclusion. MPCG is based on assuming independent displacements and electric-potentials in each cell. The trial solutions in each MPCG do not need to satisfy the governing differential equations, however, they are still complete, and can efficiently model concentration of electric and mechanical fields. MPCG can be used to model any generally anisotropic material as well as nonlinear problems. The essential idea can also be easily applied to accurately solve other multi-physical problems, such as complex thermal-electro-magnetic-mechanical materials modeling. Several examples are presented to show the capabilities of the proposed MPCGs and their accuracy.