The G2 constant displacement discontinuity method – Part I: Solution of plane crack problems

A new constant displacement discontinuity element was presented in a previous paper applied initially for the numerical solution of either isolated straight cracks or for co-linear cracks of the three fundamental deformation modes I, II and III due to the special form of the solution. It was based on the strain-gradient elasticity theory in its simplest possible Grade-2 variant. The assumption of the G2 expression for the stresses has resulted to a better average stress value at the mid-point of the straight displacement discontinuity compared to the classical elasticity solution. This new element gave considerably better predictions of the stress intensity factors compared to the constant displacement discontinuity element and the linear displacement discontinuity element. Moreover, it preserved the simplicity and hence the high speed of computations. In this Part I, the solution for this element is extended for the analysis of cracks of arbitrary shape in an infinite plane isotropic elastic body and it is validated against three known analytical solutions.