2002/09/05 by Renaud Toussaint, Steven R. Pride · 3 citations
Engineering · Physics and Astronomy · #Geotechnical and Geomechanical Engineering #Granular flow and fluidized beds #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.036135
published as Phys. Rev. E 66, art. 036135 (2002) · 11 pages, 2 figures
arxiv created 2002/09/05 · openalex publication_date 2002/09/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.