Sub-critical model of damage evolution as a phase transition

Abstract

Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the strength elements onto the spins of a lattice. This allows applying the formalism extensively developed for spin systems to damage phenomena. To improve the model the interactions of spins at the crack tips are introduced. Further, statistical mechanics of the model is developed for different external boundary constraints.

References in corpus (5)

• 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
• A thermodynamical fiber bundle model for the fracture of disordered materials