Multiple solutions in cohesive zone models of fracture

The use of cohesive zone models (CZM) for studying crack initiation and propagation can lead to non-unique deformed configurations. This situation can lead to solution branches that may be non-physical, leading to difficulty in interpreting computed results. These aspects are studied in this paper using the double cantilever beam (DCB) specimen first and next in the context of a mode I center crack in a thin sheet of infinite extent subjected to remote tensile loading. Analytical solutions to the CZM that employ constant stress and linear softening laws are presented, and it is shown that when the linear softening cohesive law is used, two cohesive zone sizes are valid for the same external loads, leading to two equally possible deformed configurations, satisfying all the field equations and boundary conditions. The smaller of the two cohesive zones has a lower energy which proposed as a criterion to render a unique solution.