Mechanics Framework for Micron-Scale Planar Structures

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