Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism

Renaud Toussaint (1, 2) , Steven R Pride (1, 3)

1 GR - Géosciences Rennes
2 IPGS - Institut de physique du globe de Strasbourg
3 LBNL - Lawrence Berkeley National Laboratory [Berkeley]

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.

Domaines: Autre [cond-mat.other]

Renaud Toussaint, Steven R Pride. Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2002, 66 (3), pp.036135. ⟨10.1103/physreve.66.036135⟩. ⟨hal-00110576⟩