Mechanism of delayed elastic state absorption versus fatigue failure in cyclic shear of amorphous materials
Abstract
We study cyclic shear in a lattice elastoplastic model of amorphous materials. The model displays a threshold shear amplitude γc, which increases with sample annealing. For imposed amplitudes γ0≲γc, it shows slow progression to an absorbing elastic state. For γ0≳ γc, it shows slow fatigue and delayed material failure. Our key contribution is to elucidate a mechanistic understanding of this behaviour. We show that progression to an absorbing state maps to single element diffusion on a finite interval with two absorbing boundaries. We derive expressions for the decay rate of the fraction of active elements, and the survival distribution. The diffusing variable is the local elemental strain, which takes two jumps stroboscopically per cycle. Once the value at any site diffuses below its yielding threshold, the element behaves elastically. This leads to a gradual accumulation of strains just below threshold. For γ0≲ γc this diffusive behaviour is preceded by many cycles in which cooperativity between elements via stress propagation is also important. For γ0 > γc, stress propagation dominates and precipitates failure. For γ0≳ γc, the same accumulation of elements just below local threshold that led to an elastic state for γ0≲γc accounts for the fatigue that brings the system to the brink of failure. We evidence this via simulations in which the strain amplitude artificially exceeds $γ_0 $ in each half cycle, before reverting to the system's actual state at ±γ0 and resuming the next half cycle. During fatigue, the stress-strain slope dσ/dγ evolves towards unity at |γ|=γ0-, signifying perfect elasticity within cycle, yet towards zero at |γ|=γ0+, precipitating failure.
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BibTeX
@misc{walker2026mechanism,
title = {{Mechanism of delayed elastic state absorption versus fatigue failure in cyclic shear of amorphous materials}},
author = {Samuel B. Walker and Suzanne M. Fielding},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29615},
eprint = {2610.29615},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29615},
}
RIS
TY - UNPB
TI - Mechanism of delayed elastic state absorption versus fatigue failure in cyclic shear of amorphous materials
AU - Samuel B. Walker
AU - Suzanne M. Fielding
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29615
UR - https://arxiv.org/abs/2610.29615
AB - We study cyclic shear in a lattice elastoplastic model of amorphous materials. The model displays a threshold shear amplitude γ_c, which increases with sample annealing. For imposed amplitudes γ_0≲γ_c, it shows slow progression to an absorbing elastic state. For γ_0≳ γ_c, it shows slow fatigue and delayed material failure. Our key contribution is to elucidate a mechanistic understanding of this behaviour. We show that progression to an absorbing state maps to single element diffusion on a finite interval with two absorbing boundaries. We derive expressions for the decay rate of the fraction of active elements, and the survival distribution. The diffusing variable is the local elemental strain, which takes two jumps stroboscopically per cycle. Once the value at any site diffuses below its yielding threshold, the element behaves elastically. This leads to a gradual accumulation of strains just below threshold. For γ_0≲ γ_c this diffusive behaviour is preceded by many cycles in which cooperativity between elements via stress propagation is also important. For γ_0 > γ_c, stress propagation dominates and precipitates failure. For γ_0≳ γ_c, the same accumulation of elements just below local threshold that led to an elastic state for γ_0≲γ_c accounts for the fatigue that brings the system to the brink of failure. We evidence this via simulations in which the strain amplitude artificially exceeds $γ_0 $ in each half cycle, before reverting to the system's actual state at ±γ_0 and resuming the next half cycle. During fatigue, the stress-strain slope dσ/dγ evolves towards unity at |γ|=γ_0^-, signifying perfect elasticity within cycle, yet towards zero at |γ|=γ_0^+, precipitating failure.
ER -