A new method to solve crack problems based on gradient elasticity

A new constant displacement discontinuity method is presented for the numerical solution of cracks of the three fundamental deformation modes I, II and III lying either in the plane or in the half-plane. This method is based on the strain-gradient elasticity theory in its simplest possible Grade-2 (G2) variant for the solution of classical crack problems. The assumption of the G2 expression for the stresses results to a more accurate average stress value at the mid-point of the straight displacement discontinuity since it takes into account the stress-gradient effect and gives considerably better predictions of the stress intensity factors compared to the compared to the classical elasticity solution. Moreover, the proposed method preserves the simplicity and hence the high speed of computations. For brevity of this paper we present here the specific case of mode-II cracks perpendicular to the free-surface of the half-plane. Validation of the method is made against analytical solution. © 2010 Taylor & Francis Group, LLC.