Finite element techniques for dynamic crack analysis in piezoelectrics

This paper deals with numerical methods, developed to analyze plane stationary cracks in piezoelectric structures under dynamic electromechanical loading conditions. In the first part an explicit finite element scheme is presented, which has been developed to solve the transient coupled electromechanical boundary value problem. A special technique is implemented in the algorithm, accounting for the limited electrical permeability of the crack. In contrast to well known algorithms for static calculations it does not require any iteration. In order to calculate dynamic stress and electric displacement intensity factors for arbitrary crack configurations, the interaction integral is generalized for electromechanical problems. The efficient applicability and the high accuracy of the implementations are demonstrated by numerical examples, giving insight into several effects occuring with dynamically loaded cracks in piezoelectrics