Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism
Abstract
This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in defining the ensemble. Ensembles are obtained by dividing a huge rock sample into many mesoscopic volumes. Because rocks are a disordered collection of grains in cohesive contact, we expect that once shear strain is applied and cracks begin to arrive in the system, the mesoscopic volumes will have a wide distribution of different crack states. These mesoscopic volumes are the members of our ensembles. We determine the probability of observing a mesoscopic volume to be in a given crack state by maximizing Shannon's measure of the emergent crack disorder subject to constraints coming from the energy-balance of brittle fracture. The laws of thermodynamics, the partition function, and the quantification of temperature are obtained for such cracking systems.
Keywords
Cite
@article{arxiv.cond-mat/0209124,
title = {Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism},
author = {Renaud Toussaint and Steven R. Pride},
journal= {arXiv preprint arXiv:cond-mat/0209124},
year = {2009}
}
Comments
11 pages, 2 figures