Analysis of cracked piezoelectric solids by a mixed three-dimensional BE approach

This paper has two main objectives in relation to the analysis of three-dimensional crack problems in piezoelectric solids. The first one is to present the formulation, effective implementation and numerical treatment of a mixed boundary element technique for the study of this type of problems. The numerical procedure is based on the use of extended displacement and extended traction integral equations for external and crack boundaries, respectively. The boundary element formulation is presented with particular emphasis on numerical aspects related to singular kernels regularization and evaluation of boundary integrals. Quadratic boundary elements and quarter-point boundary elements are implemented in a computer code. By using these elements, electric and stress intensity factors are directly computed from nodal values at quarter-point elements. The second purpose is to study several realistic piezoelectric crack problems for the first time. Unbounded and bounded cracked piezoelectric three-dimensional (3D) solids with different geometries are studied. Results presented in this paper can be used as a reference for future research. Prior to the analysis of problems whose solution was previously unknown, the technique is validated by solving some simple problems with known analytical or numerical solution. Then, more realistic crack problems of engineering interest have been analysed for the first time. In all cases, results for the solid deformed shape, the crack opening displacements and the extended stress intensity factor components, are shown.