Localization in gradient damage models through degradation of the damage driving force
摘要
Gradient damage models offer substantial constitutive flexibility but often suffer from non-physical damage spreading during fracture evolution. Phase-field approaches enforce localization through variational constraints, yet at the cost of reduced flexibility and increased modelling complexity. This work shows that spurious damage widening in gradient damage models primarily originates from the monotonic growth of the damage driving force rather than from the gradient regularization itself. Based on this observation, an adaptive gradient damage formulation is proposed in which the damage driving force progressively degrades with damage accumulation. The driving force is consistently normalized to define an equivalent strain measure, which is subsequently regularized through a non-local gradient enhancement and used to govern damage evolution via a standard phenomenological law. The resulting system is solved monolithically using a Newton–Raphson scheme and combined with an adaptive mesh refinement strategy to efficiently resolve evolving fracture process zones. Numerical benchmarks covering tensile, shear, mixed-mode, non-proportional loading conditions, and complex three-dimensional (3D) crack demonstrate that the proposed formulation produces well-confined damage bands, mesh-independent global responses, and physically admissible load–displacement behaviour, without introducing additional localization functions or phase-field-type constraints. The proposed framework provides a simple and physically motivated pathway to improve localization behaviour in gradient damage models while preserving their constitutive flexibility and numerical efficiency.