Stress Analysis of Nanostructures Including Nanovoids and Inclusions Based on Nonlocal Elasticity Theory with Different Kernels

The stress field of a nanostructure caused by structural defects is investigated using the nonlocal elasticity with different kernels. Nanovoids and inclusions along with their inelastic strain fields are included. Mesh study is performed to solve the mesh independent solutions and numerical verification is provided. COMSOL Multiphysics code is utilized to implement the local and nonlocal elasticity equations for plane strain problems. A phase field method is used to obtain desired distribution of nanovoids and inclusions. The stress analysis of such defects is compared for local elasticity and nonlocal elasticity with two-phase, modified and compensated two-phase kernels. The compensated nonlocal kernel shows superiority over the other kernels by improving the boundary effects, fully recovering the local state and satisfying the normalization condition. The results show that the theory of nonlocal elasticity is effective in problems related to structural defects with small inelastic strains. In addition, nonlocal elasticity shows a higher accuracy than the local elasticity at strong stress concentrations. Besides the phase and characteristic parameters, the nonlocal elastic theory performance depends on the size and defect distribution in nanoscale.