Zhen-Bang Kuang

Interface crack in Bi-piezothermoelastic media and the interaction with a point heat source

Abstract Using the extended version of Eshelby-Strohs formulation and the method of analytical continuation, the problems of interface cracks are reduced to a Hilbert problem of vector form. A general explicit closed form solution for piezothermoelastic interface crack problem is then obtained, the whole field solutions of temperature, heat flux, displacements, electric field, stress and electric induction are given, the explicit expressions for the crack opening displacements and electric potential are also provided. A solution is obtained for the interaction problem between the interface cracks and a point heat source.

Dislocation inside a piezoelectric media with an elliptic inhomogeneity

In this paper, Green functions for an infinite piezoelectric media with an elliptic piezoelectric inhomogeneity are given for a generalized electro-mechanical force and a generalized electro-mechanical line dislocation that may be located outside, inside or on the interface of elliptic boundary of inhomogeneity. Expressions of Green functions are identical when the generalized force and the generalized dislocation approach to the elliptic boundary from points outside or inside the inhomogeneity. The interaction electric enthalpy between the inhomogeneity and the dislocation is given, which can be used to find the interaction force on the dislocation owing to the existence of the inhomogeneity. Numerical illustrations for the interaction forces are also given and some discussions on the effects of the material mismatches on the interaction forces are made.

Three-dimensional elastic stress fields near notches in finite thickness plates

Based on detailed three-dimensional finite element (3D FE) analyses, elastic notch-root fields in plates with different thicknesses and notch configurations subjected to uniaxial tension have been investigated. By comparing with the planar notch-root fields and crack-tip fields, the following characteristics of the 3D stress–strain fields near the notch front are revealed: (1) The plate thickness and notch configuration have obvious effects on the stress concentration factor (SCF) Kt, which is higher in finite thickness plates than in plane stress and plane strain cases. (2) The variation of the opening stress normalized by its value at the notch root with a distance x from the root normalized by the root radius ρ is insensitive to the notch configuration and the plate thickness and coincides well with the two-dimensional (2D) planar solution when x/ρ<0.75. (3) Strong 3D effects exist within a radius of about three-eighth the plate thickness from the notch root. Further away from the root, the through-thickness variation of field quantities decreases and, at the radial distance of approximately 1.25 times the plate thickness, all of the through-thickness changes disappear completely. At least for notches with opening angles less than 90°, these “2D–3D” transition distances and the variations of the out-of-plane constraint normalized by its value at the notch root with a distance x from the root normalized by the plate thickness B are essentially independent of the notch configuration and plate thickness. (4) In the 3D-effect zone, the gradient of the out-of-plane strain ezz in the thickness direction is significant near the free surface in thick plates. On the free surface, ezz can be 3.5 times as high as the value on the mid-plane. It is also found that the in-plane stress ratio in an arbitrary thickness plate coincides very well with the 2D solutions within a distance of about three-tenth of the root radius from the notch root.

An active control model of laminated piezothermoelastic plate

Abstract After the Hamilton principle for thermo-mechanical–electric coupling problem is derived, the third-order shear deformation theory is extended to encompass piezothermoelastic laminated plates. Based on the velocity feedback control, a model for the active vibration control of laminated plates with piezothermoelastic sensor/actuator is established. An analytical solution is obtained for the case of general forces acting on a simply supported piezothermoelastic laminated plate. Numerical results are presented. The factors that influence the controlled responses of the plate are examined.

Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates

This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction.

Interface crack problems of a laminated piezoelectric plate

The interface crack problems of a laminated piezoelectric plate under a state of generalized plane deformation have been studied within the anisotropic theory. The method of Fourier transforms and the stiffness matrix formulation have been employed and the problem has been reduced to the solution of a system of singular integral equations. The stress and induction intensity factors have been provided, and have been calculated numerically and displayed graphically.

An integral elasto-plastic constitutive theory

Abstract This paper proposes an integral elasto-plastic constitutive equation, in which it is considered that stress is a functional of plastic strain in a plastic strain space. It is indicated that, to completely describe a strain path, the arc-length and curvature of the trajectory, the turning angles at the corner points and other characteristic points on the path must be considered. In general, the plastic strain space is a non-Euclidean geometric space, hence its measure tensor is a function of not only properties of the material but also the plastic strain history. This recommended integral elasto-plastic constitutive equation is the generalization of Ilyushin, Pipkin, Rivlin and Valanis theories and is suited to research the responses of material under the complex loading path. The predictions of the proposed theory have a good agreement with the experimental results.

Wave scattering from an interface crack in multilayered piezoelectric plate

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.

Conservation laws in non-homogeneous electro-magneto-elastic materials

Noethers theorem on invariant variational principles is applied for linear transversely isotropic non-homogeneous electro-magneto-elastic material. Invariant condition of the electromagnetic enthalpy is derived and expressed in original manner. Usually, inserting infinitesimal symmetry-transformations relating to material space of homogeneous materials into the invariant condition, one can obtain some expressions for the non-homogeneous material. These expressions indicate the relations between material inhomogeneity force and energy-momentum tensor. In order to obtain conservation laws of the non-homogeneous material, it follows from the invariant condition that the material coefficients have to satisfy a set of first-order linear partial differential equations with which there is a possible mathematical form of infinitesimal symmetry-transformation relating to material space. Satisfaction of these partial differential equations not only assures the existence of infinitesimal symmetry-transformations but also determines the number of them. Several independent and non-trivial conservation laws relating to material space with different non-homogeneous material coefficients are given. Some results of the path-independent integrals emanating from the conservation laws calculated around a crack tip are presented.

On interface crack in laminated anisotropic medium

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, orthotropic, 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.