Xian-Fang Li

Size effects of the bending stiffness of nanowires

This paper studies the size effect in the transverse deformation of nanowires or nanoropes subjected to flexural bending. Based on the classic strain-gradient theory, a continuum approach is proposed, in which the strain energy was expressed in terms of the linear strains and strain gradients, and two additional phenomenological internal parameters were introduced. The governing equation for the flexural deformation of the nanowires was derived according to the principle of minimum potential energy. In particular, the deformations of the nanowires under two support conditions were determined explicitly, i.e., a cantilever nanowire and a fixed nanowire. Numerical examples were demonstrated to indicate the dependence of the effective modulus and bending stiffness upon the nanowire diameter and aspect ratio. The predictions given by the present model are consistent very well with the experimental measurements reported in the recent literature. The proposed model can be further used to explain the size effect...

Transient response of a piezoelectric ceramic strip with an eccentric crack under electromechanical impacts

Abstract The transient response of a piezoelectric strip with an eccentric crack normal to the strip boundaries under applied electromechanical impacts is considered. By using the Laplace transform, the mixed initial-boundary-value problem is reduced to triple series equations, then to a singular integral equation of the first kind by introducing an auxiliary function. The Lobatto–Chebyshev collocation technique is adopted to solve numerically the resulting singular integral equation. Dynamic field intensity factors and energy release rate are obtained for both a permeable crack and an impermeable crack. The effects of the crack position and the material properties on the dynamic stress intensity factor are examined and numerical results are presented graphically.

Transient response of a piezoelectric material with a semi-infinite mode-III crack under impact loads

The problem of a semi-infinite impermeable mode-III crack in a piezoelectric material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane impact loads and electric displacements are exerted symmetrically on the upper and lower surfaces of the crack, the asymptotic electroelastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors of electroelastic field and dynamic mechanical strain energy release rate are obtained. The obtained results can be taken as fundamental solutions, from which general results may directly be evaluated by integration. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into two simultaneous dual integral equations. One may be converted into an Abels integral equation and the other into a singular integral equation with Cauchy kernel, and the solutions of both equations can be determined in closed-form, respectively. For some particular cases, the present results reduce to the previous results.

Electroelastic analysis of an anti-plane shear crack in a piezoelectric ceramic strip

The electroelastic analysis of a piezoelectric strip with an anti-plane shear crack whose surfaces are parallel to the strip boundaries is made. Four cases of combined electromechanical loadings applied at the strip boundaries are considered. For the case of a crack lying at the center of a strip, the electroelastic field, field intensity factors, and energy release rate can be determined in explicit form via solving a resulting singular integral equation. For other cases, they can be given in terms of an auxiliary function, which is obtained as a power series of δ via solving a resulting Fredholm integral equation using the iterative method, 2δ being the ratio of the crack length over the strip width. Some numerical results are presented graphically to show the influence of crack length and crack position on the normalized energy release rate.

Closed-Form Solution for a Mode-III Interface Crack Between Two Bonded Dissimilar Elastic Layers

A mode-III crack at the interface between two bonded dissimilar elastic layers of equal thickness is considered. The closed-form solution for a crack of length 2a has been analytically derived for stress-free boundaries and clamped boundaries. Furthermore, the analytic solution for a semi-infinite interface crack in two bonded dissimilar layers has been directly determined without recourse to the Wiener-Hopf technique.

Electroelastic Analysis of a Piezoelectric Layer with Electrodes

The electroelastic analysis of a piezoelectric layer with two semi-infinite electrodes is made. The layer surfaces are clamped and a voltage is applied between the layer surfaces and the electrodes. By using the integral equation method, the electroelastic field is derived for the cases of crack-type electrodes and of rigid electrodes, respectively. It indicates that the concentration of electric field an electric displacement occurs near the electrode tips for both cases. However, the stresses are bounded for the former, and possess singularity for the latter. The field intensity factors and energy release rate are obtained in explicit form. The counterpart for a single semi-infinite electrode is given.

The asymptotic stress field for a rigid circular inclusion at the interface of two bonded dissimilar elastic half-space materials

The paper considers three-dimensional interface inclusion problems. The axisymmetric elastostatics problem of a rigid circular inclusion at the interface between two perfectly bonded dissimilar elastic half spaces is analyzed. Based on the representations of displacements and stresses in terms of Loves strain potential and the Hankel transform technique, the mixed boundary value problem associated with a rigid circular inclusion at the interface reduces to a pair of simultaneous integral equations for the stress jumps across the inclusion, which are further transformed to a single singular integral equation. For the case of uniform axial and radial tensions at infinity, the asymptotic stresses near the inclusion front are obtained and they exhibit the oscillatory singularity. Meanwhile, the magnitude of the singularity for the interface inclusion depends on the material constants of the upper and lower half spaces, the dependence of singularity coefficients on material constants for interface inclusion problems, however, is different from that for interface crack problems.

Antiplane permeable edge cracks in a piezoelectric strip of finite width

A priezoelectric strip with permeable edge cracks normal to the strip boundaries is analyzed. Under uniform antiplane mechanical shear and inplane electric loading, the distribution of the entire electroelastic field in a cracked piezoelectric strip is determined in explicit analytic form via the conformal mapping technique. It is found that the strain and the electric displacement exhibit the same singularity as the stress near the crack tips, while the electric field is always uniform. The field intensity factors and the energy release rate are independent of the applied electric load for prescribed stress, and related to the applied electric load for prescribed strain.

Effects of electric boundary conditions on electroelastic field in a cracked piezoelectric strip

Effects of electric boundary conditions on electroelastic field in a cracked piezoelectric strip are examined. Attention is focussed on an antiplane shear central crack normal to the strip surfaces. By decoupling equations and using the conformal mapping technique, expressions for electroelastic field in the piezoelectric strip are determined under the assumptions of an impermeable, permeable, or conducting crack, respectively. Comparison for the singularity near the crack tips among the obtained electroelastic fields is made.