Statistical mechanics of damage phenomena

TL;DR

This paper develops a statistical mechanics framework for non-thermal damage phenomena, modeling damage as a phase transition with an effective temperature in fiber-bundle systems.

Contribution

It introduces a novel application of Gibbs-Boltzmann statistical mechanics to non-thermal damage, including equations of state and phase transition analysis.

Findings

Identification of a first order phase transition in damage behavior

Development of a free energy formalism for damage phenomena

Description of topological damage dynamics via an effective temperature

Abstract

This paper applies the formalism of classical, Gibbs-Boltzmann statistical mechanics to the phenomenon of non-thermal damage. As an example, a non-thermal fiber-bundle model with the global uniform (meanfield) load sharing is considered. Stochastic topological behavior in the system is described in terms of an effective temperature parameter thermalizing the system. An equation of state and a topological analog of the energy-balance equation are obtained. The formalism of the free energy potential is developed, and the nature of the first order phase transition and spinodal is demonstrated.