Micromechanics-BE solution for properties of piezoelectric materials with defects

Abstract

A micromechanics boundary element (BE) algorithm is developed to predict the overall properties of a piezoelectric material with defects such as cracks or holes. The algorithm is based on micromechanics models and boundary element formulation for piezoelectric materials with cracks or holes. In particular, the self-consistent and Mori-Tanaka methods are considered. A representative volume model for materials with defects is employed and introduced into a BE formulation to provide an effective means for estimating overall material constants of the defected materials. The micromechanics method produces formulas for overall material constants as functions of the concentration matrix A 2, and A2 is in turn related to the boundary displacement. The boundary element simulation presents numerical solutions of boundary displacement and electric potential for crack or hole problems. In the micromechanics-BE model, the volume (or area) average stress and strain is calculated by the boundary tractions and displacements of the RVE. Thus BEM is suitable for performing calculations on average stress and strain fields of such defected materials. An iterative scheme is introduced for the self-consistent-BE method. Numerical results for a piezoelectric plate with elliptic holes are presented to illustrate the application of the proposed micromechanics BE formulation. Show more