Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals

To effectively reduce the field concentration around a hole or crack, an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) is investigated subject to remotely mechanical and electrical loadings. The surface effect and dielectric characteristics inside the hole are considered for actuality. By utilizing the technique of conformal mapping and the complex variable method, the phonon stresses, phason stresses, and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions. Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack. Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer, the aspect ratio of the hole, and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip. The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack, which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.

Boundary Element Modeling of Pyroelectric Solids with Shell Inclusions

The paper presents general boundary element approach for analysis of thermoelectroelastic (pyroelectric) solids containing shell-like electricity conducting permittive inclusions. The latter are modeled with opened surfaces with certain boundary conditions on their faces. Rigid displacement and rotation, along with constant electric potential of inclusions are accounted for in these boundary conditions. Formulated boundary value problem is reduced to a system of singular boundary integral equations, which is solved numerically by the boundary element method. Special attention is paid to the field singularity at the front line of a shell-like inclusion. Special shape functions are introduced, which account for this square-root singularity and allow accurate determination of field intensity factors. Numerical examples are presented.

Exact Solutions for Interaction of Parallel Screw Dislocations with a Wedge Crack in One-Dimensional Hexagonal Quasicrystal with Piezoelectric Effects

The purpose of this paper is to consider the interaction between many parallel dislocations and a wedge-shaped crack and their collective response to the external applied generalized stress in one-dimensional hexagonal piezoelectric quasicrystal, employing the complex variable function theory and the conformal transformation method; the problem for the crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann–Hilbert boundary value problems. The analytical solutions of the generalized stress field are obtained. The dislocations are subjected to the phonon field line force, phason field line force, and line charge at the core. The positions of the dislocations are arbitrary, but the dislocation distribution is additive. The dislocation is not only subjected to the external stress and the internal stress generated by the crack, but also to the force exerted on it by other dislocations. The closed-form solutions are obtained for field intensity factors and the image force on a screw dislocation in the presence of a wedge-shaped crack and a collection of other dislocations. Numerical examples are provided to show the effects of wedge angle, dislocation position, dislocation distribution containing symmetric configurations and dislocation quantities on the field intensity factors, energy release rate, and image force acting on the dislocation. The principal new physical results obtained here are (1) the phonon stress, phason stress, and electric displacement singularity occur at the crack tip and dislocations cores, (2) the increasing number of dislocations always accelerates the crack propagation, (3) the effect of wedge angle on crack propagation is related to the distribution of dislocations, and (4) the results of the image force on the dislocation indicate that the dislocations can either be attracted or rejected and reach stable positions eventually.

Electric and heat conduction across an elliptic cavity in an anisotropic medium

It is well known that the anisotropy of materials will significantly affect heat conduction, and the corresponding results have been applied to the thermal analysis of materials. An elliptic cavity in a nonlinearly coupled anisotropic medium, on the other hand, is much more difficult to analyze. Based on the complex variable method, the problem of a two-dimensional elliptical cavity in an anisotropic material is analyzed in this paper, and the field distributions have been obtained in closed-form. The field intensity factors are discussed in detail. The results show that both the temperature and electric potential gradients at a crack tip are always perpendicular to the crack surface, regardless of the anisotropy and the nonlinearity in the constitutive equations and the arbitrariness of loading direction. These results provide a powerful tool to analyze the effective behavior and reliability of anisotropic materials with cavities.

Nonuniformly Loaded Stack of Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

Boundary Element Analysis of Anisotropic Thermomagnetoelectroelastic Solids with 3D Shell-Like Inclusions

The paper presents novel boundary element technique for analysis of anisotropic thermomagnetoelectroelastic solids containing cracks and thin shell-like soft inclusions. Dual boundary integral equations of heat conduction and thermomagnetoelectroelasticity are derived, which do not contain volume integrals in the absence of distributed body heat and extended body forces. Models of 3D soft thermomagnetoelectroelastic thin inclusions are adopted. The issues on the boundary element solution of obtained equations are discussed. The efficient techniques for numerical evaluation of kernels and singular and hypersingular integrals are discussed. Nonlin-ear polynomial mappings are adopted for smoothing the integrand at the inclusion’s front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the inclusion’s front. Numerical example is presented.

Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane

This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velocity has great effect on the field intensity factors.

Stress analysis of a functionally graded magneto-electro-elastic strip with multiple moving cracks

This paper investigates the linear steady state problem of several moving cracks in a functionally graded magneto-electro-elastic strip subjected to anti-plane mechanical and in-plane electric and magnetic loading. For simplicity, it is assumed that the properties of the strip vary continuously according to exponential functions along the thickness of the functionally graded piezoelectric piezomagnetic (FGPP) layer. By combining the dislocation method and integral transform technique, an exact solution in closed form to this problem is obtained. Electro-magneto-mechanical loads are applied on the crack surfaces, which are assumed to be magneto-electrically impermeable. Numerical examples are presented to show the interesting mechanical and electromagnetic coupling phenomena induced by multi-crack interactions. Finally, the effects of crack velocity, material constants, and geometric parameters upon the field intensity factors are studied. The results are useful for the design of the magneto-electro-elastic structures.

Boundary Element Analysis for Piezoelectric Cracks by an Interaction Integral

In this paper, an interaction integral is applied to evaluate the crack-tip field intensity factors for piezoelectric cracks by using BEM. Based on this, the fracture parameters for different crack configurations and loading conditions are analyzed in details for both the center crack and edge crack problem. According to the present results, the path-independent behavior of the interaction integral is verified. The comparison of the I-integral results with those by the J-integral and the displacement interpolating methods shows a good agreement.