Fracture with nonlocal elasticity: analytical and meshless approaches

Abstract

In this paper, two-dimensional fracture mechanics problem using the theory of nonlocal elasticity is investigated. According to the Eringen’s model, the nonlocal stresses at the crack tip are regular. Based on the nonlocal theory, the stresses at the crack tip are approximated using the singular stress fields of the classical elasticity theory. A closed form approximate estimation of stresses at the crack tip is proposed using the stress intensity factors of the classical theory. The mesh reduction formulation of Local Integral Equation Method (LIEM) is also developed for the nonlocal theory to allow for numerical solution of 2D fracture problems. A central crack in a rectangular plate subjected to tensile load is solved using the proposed approach.

Keywords:

• Nonlocal elasticity
• fracture mechanics
• Eringen’s model
• meshless method of weak form