Edge dislocation with surface flexural resistance in micropolar materials

Abstract

We employ a micropolar surface model, capable of incorporating bending and twisting rigidities, to analyze the fundamental problem of the deformation of a micropolar half-plane containing a single-edge dislocation. The surface model is based on a Kirchhoff–Love micropolar thin shell of separate elasticity perfectly bonded to the surrounding micropolar bulk. Combining micropolar elasticity with a higher-order surface model allows for the incorporation of size effects well known to be essential in, for example, continuum-based modeling of nanostructured materials. The corresponding boundary value problems are solved analytically using Fourier integral transforms. We illustrate our results by constructing the resulting stress distributions for the most general case of a micropolar material with surface stretching, flexural, and micropolar twisting resistance. To verify our results, we show that under appropriate simplifying assumptions, our solutions reduce to the corresponding solutions in the literature from classical elasticity and also to those which employ micropolar elasticity in the absence of surface effects. Finally, we report on the significance of the contribution of the newly incorporated surface and bulk parameters on the overall solution of the micropolar edge dislocation problem.