A Cellular Automaton Model of Damage

TL;DR

This paper explores how the range of stress transfer influences damage progression and failure mechanisms in a cellular automaton model, revealing that equilibrium methods are limited and failure nature varies with transfer range.

Contribution

It demonstrates that equilibrium approaches are inadequate for short-range stress transfer damage modeling and characterizes how failure mechanisms differ between short and long-range systems.

Findings

Equilibrium methods fail for short-range stress transfer damage.

Long-range transfer systems exhibit nucleation-like failure.

Short-range systems show continuous, critical-point-like failure.

Abstract

We investigate the role of equilibrium methods and stress transfer range in describing the process of damage. We find that equilibrium approaches are not applicable to the description of damage and the catastrophic failure mechanism if the stress transfer is short ranged. In the long range limit, equilibrium methods apply only if the healing mechanism associated with ruptured elements is instantaneous. Furthermore we find that the nature of the catastrophic failure depends strongly on the stress transfer range. Long range transfer systems have a failure mechanism that resembles nucleation. In short range stress transfer systems, the catastrophic failure is a continuous process that, in some respects, resembles a critical point.