A symmetric tangent stiffness approach to cohesive mechanical interfaces in large displacements

The present article proposes a formulation for a cohesive interface element in large displacement conditions. Theoretical and computational aspects, useful for an effective and efficient finite element implementation, are examined in details. A six-node (or higher) isoparametric interface element for two dimensional cohesive fracture propagation problems is developed. The element operators are consistently derived by a variational approach enforced in the current configuration, where a current frame is defined with axes tangential and normal to the middle line of the interface opening displacement gap. Under the constitutive assumption of small value of the modulus of the vector product between the Cauchy traction and the displacement jump vector, explicit expression of the interface nodal force vector and of the consistent tangent stiffness matrix are derived in a closed form. At difference with most of the available formulations, the proposed approach allows to naturally achieve a symmetric tangent stiffness matrix, provided that all the involved terms are maintained in the development, namely without neglecting second-order partial derivatives involved in the exact linearization procedure