The technique of distributed dislocations has proved to be an effective approach to studying crack problems within classical elasticity. The present work was intended to extend this technique to studying crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. This extension was not an obvious one since rotations and couple-stresses were involved in the theory employed to analyze the crack problems. Here, the technique was introduced to study the case of a mode I crack. Due to the nature of the boundary conditions that arise in couple-stress elasticity, the crack was modelled by a continuous distribution of climb dislocations and constrained wedge disclinations (the concept of ‘constrained wedge disclination’ was first introduced in the present work). These distributions create both standard stresses and couple stresses in the body. In particular, it was shown that the mode-I case was governed by a system of coupled singular integral equations with both Cauchy-type and logarithmic kernels. The numerical solution of this system shows that a cracked solid governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a solid governed by classical elasticity. Also, the stress level at the crack-tip region was appreciably higher than the one predicted by classical elasticity.

An Approach Based on Distributed Dislocations and Disclinations for Crack Problems in Couple-Stress Elasticity. P.A.Gourgiotis, H.G.Georgiadis: International Journal of Solids and Structures, 2008, 45[21], 5521-39