Papers by Author: Pin Tong

Abstract: Structures are assemblies of planar and three-dimensional objects. Planar components and parts are commonly because the deformation behaviors of plates and beams can be analyzed within the plane problem framework. For micron-scale structures, patterning processes in microfabrications are intrinsically planar and the resulting fabricated structures are also planar. These planar micron-scale structures have been designed and analyzed using conventional mechanics, but increasingly as the sizes of these structures become smaller, higher order effects become significant. In nanometer-scale, surfaces were recognized to play significant roles in affecting the physical behavior. Size dependent elastic and plastic deformation behaviors in micron-scale structures were also observed. Size dependence is an intrinsic part of higher order theory of mechanics and has been used successfully to explain scale dependent behavior in threedimensional structures. In this paper, two-dimensional higher order elastic relations in plane stress and plane strain for compressible solids are developed. The difference between the higher order and conventional elasticity theories is compared

Abstract: This paper studies the effect of the Columbic force on piezoelectric fracture. Bound charges emerge on the upper and lower surfaces of a permeable crack when a piezoelectric solid with the crack is subjected to far-field mechanical/electric loading. Taking into account the Columbic force between the bound charges, we obtain a non-linear equation governing the normal component of electric displacement D₂(x₁)on the crack faces. The results show that D₂(x₁)is, in general, not a constant along the crack faces and depends on the mechanical/electric loading conditions, the crack profile and the material properties outside and inside the crack. Furthermore, we examine the Columbic force under low mechanical/electric loads and then discuss the effect of the Columbic force on the fracture behaviour of piezoelectric materials.

Abstract: Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include the strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scaled structure [1]. This paper focus on the structural size effects on torsion of cylinders. The torsional stiffness of cylinders can be higher than conventional expectation when the cylinder size is in the nanometer - or micron-scale. Following the Saint-Venant theory of torsion, we established the equation of torsion in terms of the warping function on the basis of the nano-mechanical theory of elasticity. The torsional equations contain two higher order material length scale parameters and two conventional Lame constants. The equilibrium equation is a fourth order partial differential equation which can be reduced to two second order equations. Two formulations in terms of pseudo warping function and stress function are presented. Closed-form solutions for circular and thin wall section and series solutions for rectangular microbars have been obtained. The total torque depends only on the stresses conjugated to the strain and is only implicitly dependent on the higher order stress metrics. The solution reveals that the torsional rigidity is dependent on the higher order length scale parameters and strain gradients and increases asymptotically upward when the cylinder size is reduced to the size of the higher order length scale material parameters. The increase is most marked for thin walled cylinders, stiffening to more then 10 times the conventional value when the cylinder size is near that of the higher order length scaled parameters.