17th European Conference on Fracture 2 -5 September,2008, Brno, Czech Republic Crack Analysis in Magneto-Electro-Elastic Solids Jan Sladek 1, a , Vladimir Sladek 1,b and Peter Solek 2,c 1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia 2 Department of Mechanics, Slovak Technical University, Bratislava, Slovakia a sladek@savba.sk, b vladimir.sladek@savba.sk, c peter.solek@stuba.sk Keywords: Meshless local Petrov-Galerkin method (MLPG), Moving least-squares (MLS) interpolation, cracks, intensity factors, 2-D dynamic problems Abstract. A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic problems are considered in this paper. The local weak formulation is employed on circular subdomains where surrounding nodes randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. Introduction Modern smart structures made of piezoelectric and piezomagnetic materials offer certain potential performance advantages over conventional ones due to their capability of converting the energy from one type to other (among magnetic, electric, and mechanical) [1]. Former activities were focused on modeling of magneto-electric-elastic fields to determine the field variables [2,3]. Recently, increasing interest is devoted to fracture mechanics of magneto-electric-elastic materials [4-8]. All above mentioned works are made under a static deformation assumption. However, dynamic fracture analyses are occurring in literature very seldom. Some works on relatively simple anti-plane problems have been published [9,10]. Magnetoelectric coupling plays an important role in the dynamic behaviour of certain materials, especially compounds which possess simultaneously ferroelectric and ferromagnetic phases. Remarkably large magnetoelectric effects are observed in composites rather than in either single phase/constituent [11]. If the volume fraction of constituents is varying in a predominant direction we are talking about functionally graded materials (FGMs). A review on various aspects of FGMs can be found in the monograph of Suresh and Mortensen [12]. According the best of authors’ knowledge there is available only one paper [13] with applications to continuously nonhomogeneous magneto-electric materials. The solution of general boundary value problems for continuously nonhomogeneous magneto- electric-elastic solids requires advanced numerical methods due to the high mathematical complexity. Besides this complication, the magnetic, electric and mechanical fields are coupled with each other in the constitutive equations. In spite of the great success of the finite element method (FEM) and boundary element method (BEM) as effective numerical tools for the solution of boundary value problems in magneto-electric-elastic solids, there is still a growing interest in the development of new advanced numerical methods. In recent years, meshless formulations are becoming popular due to their high adaptability and low costs to prepare input and output data in numerical analysis. A variety of meshless methods has been proposed so far with some of them applied only to piezoelectric problems [14,15]. The meshless local Petrov-Galerkin (MLPG) method is a fundamental base for the derivation of many meshless formulations, since trial and test 1693