Modeling Fatigue-Induced Anisotropic Quasi-Brittle Damage Based on the Endurance Surface Concept
2026-07-06 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors present a new way to model how materials get damaged from repeated use, focusing on the energy released during damage and using an endurance surface to capture when damage starts. Their method allows damage to build up gradually over many cycles, even if the load stays the same, and works well for complex loads like twisting and multi-directional stresses. They improve accuracy with a special mathematical technique called micromorphic gradient enhancement and consider effects like cracks opening and closing. Their model matches real tests on concrete and steel, showing it can simulate both simple and complicated fatigue scenarios reliably.
continuum damage mechanicsfatigueendurance surfaceenergy-release ratemicromorphic gradient enhancementanisotropic damagemicrocrack closuremultiaxial loadinghigh-cycle fatiguestress-life behavior
Authors
Klas Feike, Patrick Kurzeja, Kai Langenfeld, Jörn Mosler
Abstract
This work proposes a novel continuum damage framework for fatigue based on the endurance-surface concept and uses the energy-release rate as the driving force. Damage evolution is governed by the distance of the thermodynamic driving force from the endurance surface. In contrast to classic failure surfaces, this allows damage to accumulate over many cycles even under constant-amplitude loading. The endurance surface therefore directly dictates the physical endurance limit of the material. To obtain mesh-objective results, the formulation is regularized by a micromorphic gradient enhancement. The incorporation of anisotropic damage evolution and the microcrack-closure-reopening effect extends the framework to multiaxial fatigue and loading-path-dependent degradation. The chosen prototype damage evolution fulfills three requirements: reasonable physics, computational robustness, and calibration flexibility. The model is successfully calibrated to both the monotonic response of plain concrete and to the high-cycle fatigue behavior of low-alloy steel. The numerical examples cover monotonic failure of an L-shaped concrete specimen, stress-life behavior under cyclic loading, and combined axial-torsional fatigue. These cases demonstrate how the proposed formulation applies to practical scenarios ranging from standard quasi-brittle fracture benchmarks to classical fatigue characterization and complex multiaxial damage evolution. The examples demonstrate that the formulation captures progressive degradation over many cycles and reproduces characteristic stress-life behavior. The influence of anisotropic degradation becomes especially relevant under multiaxial loading conditions during the near-failure phase. Overall, the approach provides a thermodynamically consistent, gradient-enhanced, and computationally robust framework for simulating fatigue-driven damage in the high-cycle regime.