| The present study consists of experimental investigation and analytical modeling of size effect in elasticity. To model the size effect, a general strain gradient theory, comprised of a modified set of second strain measures, (the dilatation gradient vector, the deviatoric stretch gradient tensor and the rotation gradient tensor), has been adopted. With this, plane strain, plane stress, and plane bending theories for elastic materials were derived. In deriving the solution for plane strain deformation, one of the displacement components is assumed to be zero. For the plane stress deformation, the displacement fields are expressed in terms of power series of the thickness h in the out-of-plane direction. The governing equations and boundary conditions for plane stress were obtained by taking the limit h → 0. Both plane strain gradient solutions can be degenerated to conventional plane solutions. A comparison of the governing equations and boundary conditions for plane deformation has been made. Contrary to the conventional plane solutions, results show that no similarity exists in the governing equations and boundary conditions between plane strain and plane stress problem. Solutions of both plane theories have been obtained for a thin film on a substrate subjected to remote shear. A discussion of the boundary layer effect and the influence of higher material scale parameters on the magnitude of layer thickness is given.; A bending theory for wide plates has been developed from the general theory of strain gradient elasticity. In classical bending theory, the deformation measures are the second derivatives of plate deflection. To account for the effect of strain gradients, the third derivatives of plate deflection and corresponding higher order moments and stresses, were included yielding the strain gradient bending theory. Solutions for cantilever bending with moment applied and line force applied at the free end were constructed. In the classical bending theory, the normalized bending rigidity (fixed loading location to thickness ratio) is independent of the length and thickness of the plate. However, the normalized higher order bending rigidity is dependent on Poisson's ratio (nu), the higher order bending parameter (bh), and the thickness of the plate. A comparison of the bending rigidities for epoxy beams with that predicted by the higher order solution shows that they are in good agreement. Both experiment and theory shows that strain gradient effects are significant in micron-scaled and nanometer-scaled structures. (Abstract shortened by UMI.)... |
