Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-09-05
Phys. Rev. E 66, art. 036135 (2002)
Physics
Condensed Matter
Statistical Mechanics
11 pages, 2 figures
Scientific paper
10.1103/PhysRevE.66.036135
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.
Pride Steven R.
Toussaint Renaud
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