A localizing gradient-enhanced damage-plasticity approach for quasi-brittle materials: Formulation, consistent requirements, and application to concrete

Quasi-brittle fracture in materials like concrete or rock is associated with a finite-sized fracture process zone and can thus be considered a nonlocal phenomenon. Implicit gradient-enhanced formulations pose a powerful framework for taking the finite sized fracture process zone into account. However, conventional gradient-enhanced models with constant nonlocal interaction length scale suffer from unphysical broadening of damage during the loading process. To circumvent this issue, localizing gradient damage models were developed. Since this approach has originally been developed for pure damage models, it has been rarely applied to combined damage-plasticity models, which are a popular choice for representing quasi-brittle materials like concrete or rock. In this contribution, we review the derivation of gradient-enhanced continuum models with evolving interactions and discuss some of the established models, and we discuss fundamental averaging properties. Moreover, we propose a novel damage formulation for the application in gradient-enhanced damage-plasticity models with decreasing interactions. In particular, we introduce a modified exponential softening law characterized by a damage-dependent softening modulus. This model extension is incorporated in a popular damage-plasticity model for concrete. An extensive numerical study demonstrates the superior performance compared to the conventional gradient-enhanced approach and the localizing gradient-enhanced approach without the improved novel damage formulation. • Comprehensive review of fundamental aspects of gradient-enhanced continuum theories. • Novel damage formulation for a localizing gradient-enhanced damage-plasticity model. • Discussion of implementation in finite element frameworks. • Extensive numerical study using various benchmark examples for concrete. • Improved prognostic capabilities of the model compared to classical formulations.