Nonlocal elastic theory for a medium with one or more rigid inclusions - Mode III deformation

Abstract

The nonlocal elasticity theory is applied to the problem of anti-plane deformation of an elastic medium with a rigid inclusion. The stress and strain field and the equivalent elastic modulus of the inclusion/medium system are given. An exact solution based on the classic elastic theory is derived for the comparison of the near-tip fields between the nonlocal model and the local model. The shear stresses near the inclusion tips are greatly weakened than those in the classic elastic theory framework due to the nonlocal effect. Essentially, there is no stress singularity at the inclusion tips if the nonlocal effect is included. If the nonlocal parameter is reduced to zero, the conventional results of the linear elastic fracture mechanics are recovered. In addition, an analytical model for the problem of collinear inclusions is also established, and analytical results for two identical collinear inclusions are provided.