Relaxation dynamics in strained fiber bundles

Area of Science:

• Materials Science
• Statistical Mechanics
• Continuum Mechanics

Background:

• The global load-sharing fiber bundle model simulates material failure under stress.
• Individual fiber strengths are randomly distributed, leading to progressive failure.
• The model exhibits relaxation to equilibrium or complete breakdown.

Purpose of the Study:

• To determine the dependence of the number of failure steps (tf) on applied stress and initial load per fiber.
• To analyze subcritical and supercritical stress regimes.
• To characterize the critical divergence of the failure process.

Main Methods:

• Utilizing computational simulations to model the fiber bundle behavior.
• Employing theoretical estimations to derive relationships for tf.
• Analyzing the impact of varying stress levels and initial load conditions.

Main Results:

• The number of failure steps (tf) was found to depend on stress and initial load per fiber.
• A finite number of steps (tf) was observed for finite fiber bundles.
• The two-sided critical divergence was characterized by an exponent of -1/2.

Conclusions:

• The exponent -1/2 for critical divergence is independent of the fiber strength distribution.
• The study provides insights into the failure dynamics of heterogeneous materials.
• Understanding these dynamics is crucial for predicting material reliability.