Closed-form phase-field cohesive fracture models are derived for linear, bilinear, exponential, hyperbolic, and Dugdale softening laws, with several distinct models sharing the same overall response.
Wu, A unified phase-field theory for the mechanics of damage and quasi- brittle failure, Journal of the Mechanics and Physics of Solids 103 (2017) 72–
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Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application
Closed-form phase-field cohesive fracture models are derived for linear, bilinear, exponential, hyperbolic, and Dugdale softening laws, with several distinct models sharing the same overall response.