This paper presents an application of the extended finite element method (X‐FEM) to the analysis of fracture in piezoelectric materials. These materials are increasingly used in actuators and sensors. New applications can be found as constituents of smart composites for adaptive electromechanical structures. Under in service loading, phenomena of crack initiation and propagation may occur due to high electromechanical field concentrations. In the past few years, the X‐FEM has been applied mostly to model cracks in structural materials. The present paper focuses at first on the definition of new enrichment functions suitable for cracks in piezoelectric structures. At second, generalized domain integrals are used for the determination of crack tip parameters. The approach is based on specific asymptotic crack tip solutions, derived for piezoelectric materials. We present convergence results in the energy norm and for the stress intensity factors, in various settings. Copyright © 2008 John Wiley & Sons, Ltd.

SUMMARYThis paper delivers an e cient solution technique for the numerical simulation of crack propagation of 2D linear elastic formulations based on ÿnite elements together with the conjugate gradient method in order to solve the corresponding linear equation systems. The developed iterative numerical approach using hierarchical preconditioners has the interesting feature that the hierarchical data structure will not be destroyed during crack propagation. Thus, it is possible to simulate crack advance in a very e ective numerical manner, including adaptive mesh reÿnement and mesh coarsening. Test examples are presented to illustrate the e ciency of the given approach. Numerical simulations of crack propagation are compared with experimental data.

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Finite element (I%)-simulations represent a useful tool to evaluate the thermo-mechanical behaviour of electronic packages. However, the use of the FE-method generates special difficulties, in particular concerning the proper constitutive modelling of materials used in the assembly. One more general problem in the numerical investigations of encapsulated silicon chips is the occurrence of interfaces between the dissimilar materials. Due to the assumption of sharp interface edges and interface crack tips stress singularities arise which might be accounted for only approximately in the FEcalculation. The paper intends to show solutions of these simulation difficulties, also by means of materials testing. The complex material behaviour is discussed for different filled epoxy materials, especially with regard to the influence of filler content. A new solution method of the interfacial edge problem is shortly introduced. As an example, the pull strength test is used and the asymptotic solution of an interface edge is presented.

The development and application of smart structures and smart composite materials require efficient numerical tools to analyze the thermo-piezoelectric behavior and stress state. In this paper, finite element (FE) techniques are suggested for three-dimensional coupled thermo-electro-mechanical analyses. The actual thermo-piezoelectric responses of smart structures subjected to thermal loadings can be determined by adopting a procedure TPESAP. The detailed implementation is presented with emphasis on the integration with software ABAQUS. A benchmark problem is discussed afterwards.