Time-dependent statistical failure of fiber networks

Area of Science:

• Materials Science
• Statistical Physics
• Network Theory

Background:

• Fiber bundle models are well-studied for material failure.
• Fiber networks represent a higher structural hierarchy with complex load sharing.
• Understanding network-level failure is crucial for predicting material behavior.

Purpose of the Study:

• To investigate time-dependent stochastic failure in 2D fiber networks.
• To analyze how fiber-level probabilistic failure laws transform at the network level.
• To determine the influence of network mechanics and fiber disorders on failure response.

Main Methods:

• Numerical simulations using a central-force, triangular lattice model.
• Application of Coleman's probabilistic failure law with Weibull shape parameter β=1.
• Analysis of weakest-link scaling (WLS) and lifetime distributions with increasing network size (N).

Main Results:

• Weakest-link scaling observed, with lifetime distributions approximating Weibull.
• Network failure distributions exhibit a double exponential form, deviating from predicted Weibull scaling.
• Network structure increases load sensitivity (ρ) and Weibull shape parameter (β), reducing lifetime uncertainty.

Conclusions:

• Coleman's probabilistic failure law holds approximately for 2D network systems.
• Network mechanics introduce unique failure characteristics distinct from individual fiber behavior.
• Fiber-level disorders decrease network brittleness and lifetime uncertainty.