Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture

TL;DR

This paper introduces a probabilistic method for modeling time-dependent load transfer in fracture mechanics, accommodating various load redistribution rules and distinguishing between annealed and quenched randomness approaches.

Contribution

The paper develops a unified probabilistic framework for load-transfer models in fracture, applicable to different redistribution rules and clarifies the equivalence of annealed and quenched randomness methods.

Findings

The probabilistic method effectively models fracture dynamics.

Annealed and quenched approaches are shown to be equivalent.

Applicable to various load redistribution rules.

Abstract

A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during the breaking process (annealed randomness) while in the usual method, the random lifetimes are fixed at the beginning (quenched disorder). Both approaches are equivalent.