Application of the Θ-Method to 3D BEM Analysis of Cracks in Piezoelectric Components
A general purpose direct BEM code has been developed for three-dimensional crack problems in piezoelectric structures. Special 3D non-continuous crack tip elements and several techniques for determining crack tip parameters were implemented. To calculate the electromechanical energy release rate for a virtual crack extension, the θ-method is employed, which was originally suggested by BONNET for linear elastic materials. The paper presents the generalization and numerical realization of the θ-method to 3D piezoelectric cracks. The great advantage of the θ-method is the direct computation of energy release rate, whereas the way via K-factors and the IRWIN matrix is more complicated. The efficiency and accuracy of the technique are shown for various example problems by comparing with analytical solutions.
Z. Tonković and M.H. Aliabadi
K. Wippler and M. Kuna, "Application of the Θ-Method to 3D BEM Analysis of Cracks in Piezoelectric Components", Key Engineering Materials, Vols. 488-489, pp. 363-366, 2012