Gradient-enhanced damage-plasticity approaches for modeling failure of concrete: phase-field fracture vs. localizing gradient damage

In this contribution we discuss the differences and similarities of two extensions of damage-plasticity approaches for concrete: (localizing) gradient-enhancement and the phase-field approach to fracture. Due to the similarities of their governing equations, we first present a general framework encompassing both approaches. In a second step we elaborate on their numerical implementation, and show that the same type of finite element—characterized by one scalar field, i.e., the phase field or the nonlocal damage driving force, in addition to the displacement field—can be used for both approaches. However, the consistent tangent operators on finite element level differ slightly. The capabilities of the models are assessed by means of two numerical benchmark examples, namely the L-shaped panel test and three-point bending tests on notched specimens. In conclusion, both approaches are promising in terms of their ability to deliver mesh-insensitive solutions, localized crack patterns, and overall structural response. Hence, in the future, a more detailed investigation, including more complex failure mechanisms, is required for an in-depth assessment of the models.