This paper is concerned with the propagation of a crack along the interface of a piezoelectric bimaterial, which can travel at subsonic or intersonic speed. The inertial effects are taken into account while the static approximation is applied to the electric fields. The effect of piezoelectricity on the asymptotic crack-tip field is discussed for an interface crack propagating subsonically and intersonically. An alternative method is used to avoid solving for the eigenvectors. This paper provides a unified method to analyze the crack-tip field of a crack propagating along a piezoelectric bimaterial interface.

This paper provides a unified method to solve the problem of an interfacial crack propagating subsonically and intersonically along a general anisotropic bimaterial interface. The asymptotic structure of the interfacial crack-tip field propagating subsonically and intersonically in a general anisotropic bimaterial system is investigated. Using the extended version of the Eshelby–Stroh formulation and the method of analytic continuation, the problem is recast into a Riemann–Hilbert problem of vector form. Upon solving the Riemann-Hilbert equation, the near-tip asymptotic fields are obtained, which reveals characteristics of the intersonic crack growth in an anisotropic bimaterial system. Some important cases are listed. The procedure presented in this paper will provide a theoretical tool for studying intersonic crack growth in a broader range of materials systems. The range of the powers of the crack-tip singularity is reported for four different material combinations.

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, 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.

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.