Statistical mechanics of damage phenomena

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.

Critical point appeared to be a spinodal point

References in corpus (5)

• First-Order Transition in the Breakdown of Disordered Media
• Interacting damage models mapped onto Ising and percolation models
• Thermodynamics of fiber bundles
• Fracture of disordered solids in compression as a critical phenomenon: II. Model Hamiltonian for a population of interacting cracks
• Fracture of disordered solids in compression as a critical phenomenon: III. Analysis of the localization transition

Cited by in corpus (4)

• Applicability and non-applicability of equilibrium statistical mechanics to non-thermal damage phenomena: II. Spinodal behavior
• General formalism of non-equilibrium statistical mechanics, a path approach
• Non-equilibrium statistical mechanics of non-equilibrium damage phenomena
• Critical behavior of slider-block model