Zheng Zhong

Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate

An exact three-dimensional analysis is presented for a functionally gradient piezoelectric material rectangular plate that is simply supported and grounded along its four edges. The state equations of the functionally gradient piezoelectric material are developed based on the state space approach. Assuming that the mechanical and electric properties of the material have the same exponent-law dependence on the thickness-coordinate, we obtain an exact three-dimensional solution of the coupling electroelastic fields in the plate under mechanical, and electric loading on the upper and lower surfaces of the plate. The influences of the different functionally gradient material properties on the structural response of the plate to the mechanical and electric stimuli are then studied through examples.

Three-dimensional solution of smart laminated anisotropic circular cylindrical shells with imperfect bonding

This paper presents an exact solution for a simply-supported and laminated anisotropic cylindrical shell strip with imperfect bonding at the off-axis elastic layer interfaces and with attached anisotropic piezoelectric actuator and sensor subjected to transverse loading. In this research, the imperfect interface conditions are described in terms of linear relations between the interface tractions in the normal and tangential directions, and the respective discontinuities in displacements. The solution for an elastic (or piezoelectric) layer of the smart laminated cylindrical shell strip is obtained in terms of the six-dimensional (or eight-dimensional) pseudo-Stroh formalism, solution for multilayered system is then derived based on the transfer matrix method. Finally, a numerical example is presented to demonstrate the effect of imperfect interface on the static response of the smart laminated cylindrical shell. The derived solutions can serve as benchmark results to assess various approximate shell theories and numerical methods.

An inclusion theory for the propagation of martensite band in NiTi shape memory alloy wires under tension

Abstract In this paper, we present analytical modelling for the pure mechanical response of uniaxial tensioned NiTi wire that experiences stress-induced martensitic transformation via a propagating martensite band at the superelastic temperature regime. The model aims to predict the overall behavior of the SMA wire as a structural response containing propagating instabilities. Based on the systematic experimental investigation of Shaw and Kyriakides (Shaw, J.A., Kyriakides, S., 1995. Thermomechemical aspects of NiTi. J. Mech. Phys. Solids 43, T243–1281 and Shaw, J.A., Kyriakides, S., 1997. On the nucleation and propogation of phase transformation fronts in a NiTi alloy. Acta Mater. 45(2), 638–700), the wire is modeled as an elastic rod containing a single cylindrical transformation inclusion with a uniform axisymmetric eigenstrain. The analytical expression of the free energy of this special matrix-inclusion system is formulated and the length of the martensite band is identified as the key variable describing the transformation process of the system. Theoretical predictions on the peak stress and the subsequent steady-state propagation stress of the wire during forward and reverse transformations are provided and compared with the available experimental data. Specimen size effect on the nominal stress-strain curves and general deformation features of the wire are discussed.

A moving conducting crack at the interface of two dissimilar piezoelectric materials

Abstract The problem of a Yoffe-type conducting crack moving with a constant velocity at the interface of two dissimilar piezoelectric half planes is investigated by employing complex variable method. Solutions for the complex potentials are derived. Explicit expressions for the field components on the interface are presented based on the obtained complex potentials. It is observed that the nature of the field singularities near the crack tip is intimately dependent on the crack moving velocity. In the extremely low speed regime, the singularities are δ=−1/2±ie1; in the low speed regime, the singularities are δ=−1±ie2; in the intermediate speed regime, the singularities are δ=−1/2±k; in the high speed regime, the singularities are δ=−1±ie3; in the extremely high speed regime, the singularities are δ=−1/2±ie4. e i (i=1–4) and k are also explicitly given. A Yoffe-type moving conducting crack in a homogeneous piezoelectric material is treated as a special case. The numerical results demonstrate that the moving velocity V will exert a significant influence on the value of the singularities, and on the field component distributions along the interface.

Analysis of a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains

This paper studies a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains. The analytical elastic solution is obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructural parameters and its evolution on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated through examples.

A conducting arc crack between a circular piezoelectric inclusion and an unbounded matrix

Abstract The present paper investigates the problem of a conducting arc crack between a circular piezoelectric inclusion and an unbounded piezoelectric matrix. The original boundary value problem is reduced to a standard Riemann–Hilbert problem of vector form by means of analytical continuation. Explicit solutions for the stress singularities δ =−(1/2)±i e are obtained, closed form solutions for the field potentials are then derived through adopting a decoupling procedure. In addition, explicit expressions for the field component distributions in the whole field and along the circular interface are also obtained. Different from the interface insulating crack, stresses, strains, electric displacements and electric fields at the crack tips all exhibit oscillatory singularities. We also define a complex electro-elastic field concentration vector to characterize the singular fields near the crack tips and derive a simple expression for the energy release rate, which is always positive, in terms of the field concentration vector. The condition for the disappearance of the index e is also discussed. When the index e is zero, we obtain conventionally defined electro-elastic intensity factors. The examples demonstrate the physical behavior and the correctness of the obtained solution.

On the elastic axisymmetric deformation of a rod containing a single cylindrical inclusion

This paper studies the axisymmetric deformation of a rod containing a single cylindrical transformation inclusion with uniform axisymmetric eigenstrain. Elastic solutions of the problem are obtained by means of the principle of superposition. The original problem is divided into two sub-problems to derive the analytical expressions for the displacements, the stresses and the elastic strain energy of the whole rod. Quantitative pictures on the stress and strain jumps across the inclusion–matrix interface and on the evolution of the strain energy of the whole rod are illustrated. The results show that the normalized elastic strain energy depends on the relative length of the cylindrical inclusion for the length–radius ratio l/a<2. This strain energy increases very quickly at the initial growth and soon reaches the peak value, then decreases with the further increase of l/a and finally reaches its steady state value. Several deformation features of this non-classical inclusion–matrix system are discussed. The work of this paper also provides a quantitative solution in the investigation of the propagation of strain discontinuity observed during thermoelastic phase transformation in solids such as TiNi shape memory alloy wires.

A circular inclusion with a nonuniform interphase layer in anti-plane shear

Abstract An analytical solution is derived for the problem of a nonuniformly coated circular inclusion in an unbounded matrix under anti-plane deformations. The inclusion/interphase/matrix system is subject to (1) remote uniform shear and uniform eigenstrain imposed on the circular inclusion, and (2) a screw dislocation or a point force in the matrix. It is found that the varying interphase thickness will exert a significant influence on the nonuniform stress field within the circular inclusion, and on the direction and magnitude of the image force acting on a screw dislocation. In the course of development, it is found that the presence of certain coated inclusions, which are termed stealth , will not cause change of elastic energy in the body. The derived analytical solution for a screw dislocation is then employed as Green’s function to investigate a radial matrix crack interacting with the nonuniformly coated inclusion. The numerical results show that the varying interphase thickness will also affect the stress intensity factors.

Numerical Simulation for Stress-Induced Phase Transformation of SMAs Tube under Tension

Recent uniaxial tension tests have shown that stress-induced phase transformation in NiTi SMAs tubes can lead to helical-type localized deformation and propagation phenomena. Based on detailed experimental observation and possible deformation mechanism, a trilinear stress-strain relationship with intrinsic strain softening is employed to represent the material constitutive behavior in this paper, and a 3-D finite deformation simulation is performed to model the tube under tension by using nonlinear FEM. The simulations successfully reproduce the nucleation and evolution of the helical-type martensite band during stress-induced transformation observed in the experiments.

The Elasto-Plastic and Geometrically Nonlinear Finite Element Model of Space Beam Considering Restraint Torsion

A new elasto-plastic and geometrically nonlinear finite element model of space beam considering restraint torsion and the coupling effect of deformations is presented in this paper. The warping restraint torsion and the coupling effect of deformation are considered in the displacement formulation of arbitrary point on the space beam. The geometrical relationship of arbitrary point is derived according to the definition of Green strain. The elasto-plastic and geometrically nonlinear finite element model of space beam is derived using Updated Lagrange description. The effect of axial force, shearing force, biaxial bending moment, moment of torsion and bimoment is involved in the geometrical stiffness matrix of element. The yielding developments both across the section and along the axis of the member are taken into consideration by selecting Gauss points. The full historical nonlinear analysis is achieved using the method of load increment and modified Newton-Raphson method. The validity of the new model derived in this paper is proved by numerical example. This new model can be used in the elasto-plastic and geometrically nonlinear analysis of space beam structures constructed by the members of arbitrary cross section.