A rigid line inclusion in a nonlocal elastic medium : mode I deformation

In this paper, the problem of a rigid line inclusion in a nonlocal elastic medium is solved. Two special inclusion orientations are considered. These are (1) inclusion is parallel to the border of the medium, and (2) inclusion is perpendicular to the border of the medium. The two-dimensional stress and strain field and the effective mechanical property of the medium with inclusion are obtained. Because of the nonlocal effect, the stresses near the tips of the inclusion are significantly smaller than those based on the classic continuum mechanics framework. Essentially, under the nonlocal theory, there is no stress singularity at the tips of the inclusion. When the nonlocal effect vanishes, the results for the classic continuum theory of elasticity are recovered. In addition to the single inclusion, results for collinear inclusions are also presented.