This paper focuses on the theoretical basis for the study of wave scattering from an interface crack in multilayered piezoelectric media. The materials are taken to be anisotropic with arbitrary symmetry. Based on the Fourier transform technique together with the aid of the stiffness matrix approach, the boundary value problem of wave scattering is reduced to solving a system of Cauchy-type singular equations. The intensity factors and crack opening displacements are defined in terms of the solutions of the corresponding integral equations for any incident frequencies and incident angles. Numerical results are presented. The effects of incident frequencies and crack location on both the major and coupling intensity factors are illustrated. The influence of the piezoelectricity is also shown.

In this paper, a theory of caustics for an intersonically propagating interfacial crack is developed. Using the first invariant of stress singular field in the vicinity of the intersonically propagating tip of an interface crack, mapping equations are derived for the caustic curve on the reference plane as well as the initial curve on the specimen plane. The effect of the crack velocity on the caustic pattern is investigated. Two practically measurable characteristic dimensions are proposed. Using these characteristic dimensions, a simple procedure is also proposed for the evaluation of the stress singularity factor for the intersonically propagating interfacial crack.

A comparison study of the efficiency and accuracy of a variety of meshless trial and test functions is presented in this paper, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method. 5 types of trial functions, and 6 types of test functions are explored. Different test functions result in different MLPG methods, and six such MLPG methods are presented in this paper. In all these six MLPG methods, absolutely no meshes are needed either for the interpolation of the trial and test functions, or for the integration of the weak-form; while other meshless methods require background cells. Because complicated shape functions for the trial function are inevitable at the present stage, in order to develop a fast and robust meshless method, we explore ways to avoid the use of a domain integral in the weak-form, by choosing an appropriate test function. The MLPG5 method (wherein the local, nodal-based test function, over a local sub-domain Ωs (or Ωte) centered at a node, is the Heaviside step function) avoids the need for both a domain integral in the attendant symmetric weak-form as well as a singular integral. Convergence studies in the numerical examples show that all of the MLPG methods possess excellent rates of convergence, for both the unknown variables and their derivatives. An analysis of computational costs shows that the MLPG5 method is less expensive, both in computational costs as well as definitely in human-labor costs, than the FEM, or BEM. Thus, due to its speed, accuracy and robustness, the MLPG5 method may be expected to replace the FEM, in the near future.

In this paper, the interface crack problems of a multilayered anisotropic medium under a state of generalized plane deformation are considered within the framework of anisotropic theory. A general solution procedure is introduced such that it can be uniformly applied to media with transversely isotropic, ortho-tropic, monoclinic, etc. layers. The problem is reduced to the solution of a system of singular integral equations by means of Fourier transform method and the stiffness matrix formulation. A Jacobi polynomial technique is then used to solve the integral equations numerically. The stress intensity factors are provided. The stress intensity factors have been calculated numerically and displayed graphically.

This work is concerned with the analytical characterization of the electromechanical nonlinear effects on the fields surrounding the tip of an interface crack between ferroelectric-plastic bimaterials. A strip electric saturation and mechanical yielding model is developed for a mode III interfacial crack with electrical polarization reaching a saturation limit and shear stress reaching a yield stress along a line segment in front of the crack. The electrical saturation zone and mechanical yielding zone may have dierent length scales depending on loading conditions. This model may be considered as a generalization of the classical Dugdale model for plastic yielding near cracks in homogenous materials. The results reveal insight into the structure of stress and electric displacement fields for different load conditions. The energy release rate and COD dIII are also obtained, which indicates the possibility of fracture criterion based on the COD dIII.