  The topologies of existing interface elements used to discretize cohesive
cracks are such that they can be used to compute the relative displacements
(displacement discontinuities) of two opposing segments (in 2D) or of two
opposing facets (in 3D) belonging to the opposite crack faces and enforce the
cohesive traction-separation relation. In the present work we propose a novel
type of interface element for fracture mechanics sharing some analogies with
the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact
elements. The displacement gap of a node belonging to the finite element
discretization of one crack face with respect to its projected point on the
opposite face is used to determine the cohesive tractions, the residual vector
and its consistent linearization for an implicit solution scheme. The following
advantages with respect to classical interface finite elements are
demonstrated: (i) non-matching finite element discretizations of the opposite
crack faces is possible; (ii) easy modelling of cohesive cracks with
non-propagating crack tips; (iii) the internal rotational equilibrium of the
interface element is assured. Detailed examples are provided to show the
usefulness of the proposed approach in nonlinear fracture mechanics problems.
