On the lack of rotational equilibrium in cohesive zone elements

Abstract

This paper unravels an intrinsic shortcoming of several cohesive zone models, whereby commonly adopted traction separation laws do not necessarily satisfy rotational equilibrium at the cohesive element level. The necessary condition to ensure rotational equilibrium is derived. To demonstrate the error that is caused by the lack of rotational equilibrium, examples for three traction separation laws are shown, for both homogeneous and inhomogeneous deformation. For a large range of values of the critical opening length the error scales almost linearly with this critical opening length. For large critical opening length the error may even become significant, requiring the use of a traction separation law that satisfies the condition for rotational equilibrium.