Geometrically nonlinear extended isogeometric analysis for cohesive fracture with applications to delamination in composites

We propose a geometrically nonlinear extended isogeometric analysis approach for cohesive fracture. A shifting technique is used to enforce compatibility in the direction perpendicular to the crack path, while a blending technique has been adopted to remove the effect of the discontinuity in the extension of the cohesive crack. Bézier extraction is employed to cast the formulation in a finite element datastructure. The use of a sign function instead of a Heaviside step function removes the need to make an assumption for the normal to the crack at its centreline. Examples are given to illustrate the methodology, including buckling of a delaminated structure and an assessment of the interface contribution to the tangent stiffness matrix.