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.

► Closed form crack-tip stress and strain fields in gradient enhanced elasticity. ► The strain field resembles experimental results. ► A fracture criterion links remote macroscopic stress to microscopic cohesive stress.