Modified non-local damage model: resolving spurious damage evolution

TL;DR

This paper introduces a modified non-local gradient damage model that prevents unrealistic damage band widening, ensuring more accurate and reliable damage evolution predictions in engineering structures.

Contribution

The paper proposes a novel modification to the stress degradation function and forcing term in the Helmholtz free energy to maintain constant damage band width during evolution.

Findings

Model reliably produces fixed-width damage bands

Numerical validation on 1D and 2D benchmarks

Can be integrated into existing finite element frameworks

Abstract

Accurate prediction of damage and fracture evolution is critical for the safety design and preventive maintenance of engineering structures, however existing computational methods face significant limitations. On one hand, discrete damage and phase-field models are often computationally prohibitive for real world applications and they are less generalizable across different material classes. On the other hand, conventional gradient damage models which are based on phenomenological laws, though more computationally efficient, they suffer from unrealistic widening of the damage-band as damage progresses. This paper presents a modified non-local gradient damage model (MNLD) that overcomes these shortcomings by introducing modifications to the stress degradation function and forcing term in the Helmholtz free energy expression. These two modifications ensure that as damage approaches its maximum value, both the thermodynamic damage driving force for damage vanishes and the evolution of the forcing term decays. Consequently, the damage band retains a non-growing constant width throughout its evolution. The proposed approach builds on insights gained from two intermediate models, which addressed the necessary conditions separately before integrating them into a unified formulation. Numerical validation is performed on several 1D and 2D benchmark problems, demonstrating that the proposed model can reliably produce fixed-width damage bands. The proposed approach can be implemented within existing gradient damage-based finite element frameworks with minimal implementation changes. The results highlight the potential of this approach to resolve the decades-long challenge of spurious widening in gradient damage models, offering an effective and practical solution for engineering applications.