  The technique of distributed dislocations proved to be in the past an
effective approach in studying crack problems within classical elasticity. The
present work is intended to extend this technique in studying crack problems
within couple-stress elasticity, i.e. within a theory accounting for effects of
microstructure. This extension is not an obvious one since rotations and
couple-stresses are involved in the theory employed to analyze the crack
problems. Here, the technique is 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 is modeled by a continuous distribution of climb
dislocations and constrained wedge disclinations (the concept of "constrained
wedge disclination" is first introduced in the present work). These
distributions create both standard stresses and couple stresses in the body. In
particular, it is shown that the mode-I case is 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 is appreciably higher than the one
predicted by classical elasticity.
