The present paper aims to develop an efficient fracture model allowing the prediction of the quasi-brittle material phase field damage coupled to cohesion. The adopted method is based on finite element simulations using COMSOL Multiphysics when considering the penalization approach as an irreversibility constraint. A comparative study is conducted applying linear and quadratic Ambrosio–Tortorelli’s models and the phase field cohesive zone model (PF-CZM), in order to evaluate their performance and assess the ability of the PF-CZM to generate a realistic crack path. Particularly, its effectiveness coupled with the penalized approach is applied to predict the French Pantheon crack. The originality of this work lies on different aspects. First, the study presents the penalization technique within the phase field framework as an alternative to Miehe history field, providing a robust enhancement to the irreversibility condition. Second, the implementation adopts a staggered algorithmic scheme which refines the stability and the robustness of computations. Third, this study gives a more in-depth numerical analysis for the optimal penalty parameter so that the optimal range is provided for solver stability and computational efficiency of the cohesive zone model. Also, the effectiveness of PF-CZM coupled with the penalization approach is investigated in predicting complex crack phenomena. The test of the French Pantheon structure response is validated with literature, and an extended solution is provided based on the developed cohesive penalized approach.
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