International Journal of Fracture 114: 359–378, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. Finite element-computation of the electromechanical J-Integral for 2-D and 3-D crack analysis M. ABENDROTH ∗ , U. GROH, M. KUNA and A. RICOEUR Freiberg University of Mining and Technology, Institute of Mechanics and Fluid Dynamics, Lampadiusstraße 4, D-09596 Freiberg, Germany ( ∗ Author for correspondence: E-mail: Martin.Abendroth@imfd.tu-freiberg.de) Received 27 February 2001; accepted in revised form 29 January 2002 Abstract. Piezoelectric ceramics find an application in many fields of technology. They may serve as sensors or actuators, mostly beeing exposed to high electric and mechanical loads. Therefore, fracture mechanics of piezoelectrics is an important field preserving strength and reliability under different conditions of application. This paper deals with the calculation of electromechanical energy release rates for arbitrary cracks in spatial piezoelectric structures applying a generalized J -integral. The crack problem is solved using a commercial FEM- code obtaining electric and mechanical field variables in nodes and integration points. These results serve as input data for the numerical computation of the electromechanical J -integral. The results are compared to findings from analytical and alternative numerical methods. Key words: Ceramics, brittle fracture, finite element method, fracture mechanics, J -integral, piezoelectricity. 1. Introduction Multi functional materials such as piezoelectric ceramics are gaining growing interest for the development of electromechanical systems, recently applied in electronics, micro system technology, mechatronics or adaptive structures. The integration of these smart materials into structural components supplies the essential sensing and actuating functionality. As a conse- quence, these smart materials may be exposed to extraordinary high mechanical and electric static, dynamic or cyclic loading. Thus, besides their functional features improved mechanical properties are required as well. Therefore, problems of strength, fracture and fatigue of the involved smart electroceramics arise. They play an important role for the optimum design and the reliable performance of electromechanical systems and devices. The macroscopic failure of piezoelectric ceramics is mainly determined by the growth of microscopic cracks. Here, mechanical and electric intensity factors and energy release rates play an important role as fracture quantities. This paper presents an efficient method for the numerical implementation of the J -integral yielding electromechanical energy release rates. In contrast with recent papers (Kemmer and Balke, 1997; Kuna, 1995b), our work is focussed on cracks in 3-dimensional (3-D) piezo- electric structures with arbitrary shaped crack fronts. J -integral calculations of spatial crack configurations have been restricted to mechanical (Hellen, 1975; Moran and Shih, 1987; Shih et al., 1988) or thermo-mechanical problems, yet (Eisentraut, 1990; Shih et al., 1982). Starting from the well known classical J -integral by Rice (1968) and Cherepanov (1967), the theory of the J -integral in coupled electromechanical fields goes back to Pak (1990, 1992) and has been further generalized by Kuna (1995a,b, 1998), accounting for volume forces and charges, as well as tractions and charges at the crack faces and heterogenous structures.