A G2 constant displacement discontinuity element for analysis of crack problems

A new constant displacement discontinuity (CDD) element is presented for the numerical solution of Mode I, II and III crack problems, based on the strain-gradient elasticity theory in its simplest possible Grade-2 (second gradient of strain or G2 theory) variant. The accuracy of the proposed new element is demonstrated herein in a first attempt only for isolated straight cracks or for co-linear straight cracks for which closed form solutions exist. It is shown that the results based on this new element are in good agreement with the exact solutions. Moreover, the new method preserves the simplicity and hence the high speed of the CDD method originally proposed by Crouch with only one collocation point per element for plane crack problems, but it is far more efficient compared to it, especially close to the crack tips where the displacement and stress gradients are highest.