A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

To circumvent a mesh dependency of damage models, non‐local approaches such as phase‐field and gradient‐extended damage models have shown a good capability and attracted a lot of attention for modeling fracture. These models can predict crack nucleation, kinking, and branching. The gradient‐extended formulation proposed by [1, 2], which includes a micromorphic degree of freedom for damage, is connected to a phase‐field damage model presented in [3]; by connecting fracture parameters in brittle fracture. The latter is followed by comparing the thermodynamic consistency of these models. Despite having similarities in the formulation, gradient‐extended models differ from the standard phase‐field ones by having a damage threshold. Besides that, the local iteration exists in the gradient‐extended damage models. By employing the cohesive phase‐field model or the Angiotensin type 1 (AT1), a damage threshold appears in the formulation; by having a linear term for damage in the crack density function, see [4,5,12]. A comparison between these models is made, by taking several numerical examples and comparing their responses in a quasi‐static case. Moreover, the feasibility of different responses is addressed when one uses a standard Newton‐Raphson solver or the arc‐length one for solving a boundary value problem.