Crack-tip Fields in Gradient Enhanced Elasticity

Nonlocal and gradient theories are capable of describing deformation of heterogeneous elastic materials better than classical elasticity theory. Crack-tip stress and strain fields in a gradient enhanced elastic material are derived on closed form. Physical requirements of finite stresses and strains at infinity and at the tip are applied to remove singularities. A fracture criterion is derived that links applied remote macroscopic stress via microscopic cohesive stress in the vicinity of the crack-tip to the Griffith's energy. A comparison to a classical nonlocal theory by Eringen is made. It is believed that the solutions will help engineers to deal with fracture analyses in elastic brittle heterogeneous materials. (C) 2012 Elsevier Ltd. All rights reserved.