Numerical determination of crack stress and deformation fields in gradient elastic solids

摘要

A boundary element method is developed for fracture analysis of gradient elastic 2-D solids under static loading. A simple version of Mindlin's general theory of gradient elastic materials is employed and the two required boundary integral equations, one for displacements and the other for its normal derivative are presented. Use is made of the fundamental solution of the problem and this leads to a formulation that requires only a boundary discretization. Two representative numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The first deals with a mode I crack, while the second with a mixed mode (I & II) crack. For the second case the proposed method is used in conjunction with the method of subregions. The method is employed with regular and regular plus special (near the crack tip) boundary elements. The gradient effect consists of modifying both the displacement and the stress field around the crack tip and resulting in a response which is more physically acceptable than the one coming from the classical theory of elasticity.