Convergence of a gradient damage model toward a cohesive zone model

The study starts from a specific gradient damage model which admits a closed-form solution in the case of uniaxial tension. It enables to separate the parameters of the model between a length scale, characteristic of nonlocal effects, and macroscopic parameters which retain their meaning in a cohesive crack setting. A convergence analysis is performed: the response of a cohesive zone model is retrieved when the length scale goes to zero while keeping the macroscopic parameters constant.