Finite Element Techniques for Dynamic Crack Analysis in Piezoelectrics

Abstract

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.

Analysis of dynamic stress intensity factor of finite piezoelectric composite plate under a dynamic load

“…an anisotropic piezoelectric material (BaTiO 3 ) with a pre-crack. This case study is available in the previous study and it is possible to compare our results with the previously obtained results [13].…”

“…2. The results obtained from simulation of the piezoelectric (BaTiO 3 ) plate and a previous study by M. Enderlein [13], are indicated in fig. 3.…”

“…Finite element modelling is utilized to find dynamic stress intensity factor near the crack tip. The simulation method is checked and calibrated with a simple case study [13]. Later the numerical results for the dynamic stress intensity factor are obtained for several piezoelectric layered composite plates and are reported in the following sections.…”

Analysis of Thermo-Piezoelectricity Problems by Meshless Method

“…Thus, the SIF is vanishing in such a case since the stresses are zero ahead the crack-tip on the crack line because of the immediate electromechanical interaction. In the dynamic case the stress field is coupled not only to the immediate electric field, but also to inertia forces [9]. Numerical results for the normalized stress intensity factor fI=KI/ ra a11c11i0 are presented in Fig.…”

“…In order to solve the boundary or the initial-boundary value problems for piezoelectric solids, efficient computational methods are required. Mostly, the finite element method (FEM) as shown in [9], [11], [13] and the boundary element method (BEM) [7], [10], [14] and [25] are applied to solve general piezoelectric problems. Meshless methods have been also successfully applied to piezoelectric problems in [16] and [20].…”