Numerical predictions for the effective size-dependent properties of piezoelectric composites with spherical inclusions

Abstract

In the present paper, the effective properties of particulate piezoelectric composites are evaluated numerically in the framework of second gradient electroelasticity theory. Simplified strain gradient and distortion gradient elasticity theories generalized for accounting the piezoelectric effects are studied. Electric field gradients are used as additional independent constitutive variables in considered models. Numerical finite element simulations are realized for the three-dimensional representative volume elements (RVE) of the isotropic matrix filled with spherical piezoelectric inclusions. Non-classical type of the elastic and electric fields inside the inclusions of various sizes are studied. Difference between strain gradient and distortion gradient models solutions are shown. Effective properties of the composites are estimated based on obtained numerical results. It is shown that the strong positive size effects are predicted for the composites with smaller inclusions in the considered theories. Effective elastic, dielectric and piezoelectric moduli increase when the particles size get smaller and compare with material length scale parameters that present in the high order statement of gradient theory. Additionally, it is shown that the inclusions clustering effects can be also captured considering RVE’s that contain several inclusions. Decreasing of all effective electroelastic moduli is predicted for the composites with agglomerated filler particles. However, the significant effect of clustering is realized for very small inclusions and the greatest sensitivity to clustering is exhibited by effective piezoelectric constants.