Strong displacement discontinuities and Lagrange multipliers in the analysis of finite displacement fracture problems

The finite displacement formulation of a quadrilateral element containing an embedded displacement discontinuity is presented. The formulation is based on the kinematically optimal technique, and some known defects of this technique are addressed. Lagrange multipliers are adopted to ensure the correct crack closure prior to initiation. Six additional degrees of freedom in each element allow the representation of the two states of the crack. A classical enhanced strain technique is employed to improve the bending performance of the element. Numerical examples illustrate both the robustness and the accuracy of the proposed solutions.