Numerical estimation of strain intensity factors at the tip of a rigid line inclusion embedded in a finite matrix

In this paper, the strain intensity factor at the tip of a rigid line inclusion, embedded in an isotropic matrix, is studied using analytical and numerical techniques. We first revisit the elasticity solution of a rigid inclusion embedded in an infinite elastic matrix using Stroh formulation as a basic framework. This study reveals that the strain intensity factor is appropriate for quantifying the magnitude of singularities at the inclusion tip. Next, we propose a numerical methodology, based on the reciprocal theorem, to calculate the strain intensity factor of the inclusion problem embedded in a matrix of finite geometry. The input to this method is the actual elasticity solution, which is obtained using finite element analysis (FEA). The FEA model is qualitatively validated by comparing FEA results with that of photoelasticity experiments. Finally, strain intensity factor in the case of finite geometry specimen is also estimated.