A damage model based on failure threshold weakening

TL;DR

This paper introduces a damage model with failure threshold weakening in a cellular automaton framework, revealing a critical point and percolation transition that influence system-wide failure probabilities and scaling behaviors.

Contribution

It presents a novel failure threshold weakening parameter in a slider-block model, linking damage accumulation to percolation theory and critical phenomena in material failure.

Findings

Identification of a critical point influenced by weakening parameter

Mapping damage transition to percolation transition with mean-field exponents

Weakening parameter affects frequency-magnitude scaling and ergodicity

Abstract

A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with long range interactions and recurrent damage that is parameterized by a process of damage and partial healing during sliding. We introduce a failure threshold weakening parameter into the cellular-automaton slider-block model which allows blocks to fail at a reduced failure threshold for all subsequent failures during an event. We show that a critical point is reached beyond which the probability of a system-wide event scales with this weakening parameter. We provide a mapping to the percolation transition, and show that the values of the scaling exponents approach the values for mean-field percolation (spinodal nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the effect of the weakening parameter on the frequency-magnitude scaling relationship and the ergodic behavior of the model.