Comparison of conventional and localizing gradient enhancements for concrete damage-plasticity models

Cracking in quasi-brittle materials, like concrete, is known to be a nonlocal process associated with an intrinsic material length scale.To take into account these nonlocal effects in continuum damage models for concrete, many approaches have been proposed in the past decades.The latter comprise integral nonlocal formulations, implicit or explicit gradient-enhanced models, as well as the phase field approach to cohesive fracture.Among them, implicit gradient-enhanced models have proved to represent a powerful approach, when applied in Finite Element simulations.However, it is well-known that conventional gradient-enhanced models yield a nonphysical broadening of the damaged zone.To overcome this issue, the so-called localizing gradient damage model with decreasing interaction has been proposed by Poh and Sun.However, to the authors' best knowledge, this formulation has only rarely been applied to damage-plasticity models, and a comprehensive discussion of its impact on the structural behavior is missing in the literature.In this study, we investigate the localizing gradient formulation proposed by Poh and Sun for the widely recognized concrete damage-plasticity (CDP) model by Grassl and Jirsek.Specifically, we discuss the advantages and disadvantages compared to the conventional gradient enhancement through a simple 1D tensile test and a numerical benchmark example.