Exponential Cohesive Zones - energy based

Hello everyone,

I started working on cohesive zone modelling. As a damage initiation criterion, the quadratic stress criterion applies. For the damage evolution I specify an energy based approach. To attain a smooth transition around the peak traction I apply an exponential softening behaviour.

With a first trial, results show that the maximum peak traction largely exceeds the damage initiation criterion. Assuming that the input parameters for the cohesive law are the peak traction and the fracture energy, such a result is not desirable.

Does anybody know the underlying formula for the described problem? This way I may be able to adapt the cohesive law wrt. to achieve the intented cohesive behaviour. I do not intend to follow the route of trial-and-error, since this would only give a case-specific answer.

Thank you for the help.