  We present a simple set of data structures, and a collection of methods for
constructing and updating the structures, designed to support the use of
cohesive elements in simulations of fracture and fragmentation. Initially all
interior faces in the triangulation are perfectly coherent, i.e., conforming in
the usual finite element sense. Cohesive elements are inserted adaptively at
interior faces when the effective traction acting on those face reaches the
cohesive strength of the material. The insertion of cohesive elements changes
the geometry of the boundary and, frequently, the topology of the model as
well. The data structures and methods presented here are straightforward to
implement and enable the efficient tracking of complex fracture and
fragmentation processes. The efficiency and versatility of the approach is
demonstrated with the aid of two examples of application to dynamic fracture.
