A new constant displacement discontinuity (CDD) element is presented for the numerical solution of Mode I, II and III crack problems, based on the straingradient 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.
a b s t r a c tIn the previous Part I, the G2 constant displacement discontinuity element was presented that is dedicated for the fast (only one collocation point per element), stable and accurate numerical solution of modes I, II and III cracks of arbitrary shape in an infinite plane isotropic elastic body. Herein, another G2 constant displacement discontinuity element is constructed for the case of cracks in the half-plane. It is successfully validated against existing semi-analytical and numerical solutions of crack problems in the half-plane.
a b s t r a c tA 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 straingradient 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.
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