2002/09/05 by Renaud Toussaint, Steven R. Pride · 2 citations
Engineering · Materials Science · Physics and Astronomy · #Elasticity and Wave Propagation #Geotechnical and Geomechanical Engineering #Material Dynamics and Properties #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.036136
published as Phys. Rev. E 66, art. 036136 (2002) · 9 pages, 1 figure
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
To obtain the probability distribution of two-dimensional crack patterns in mesoscopic regions of a disordered solid, the formalism of Paper I requires that a functional form associating the crack patterns (or states) to their formation energy be developed. The crack states are here defined by an order parameter field representing both the presence and orientation of cracks at each site on a discrete square network. The associated Hamiltonian represents the total work required to lead an uncracked mesovolume into that state as averaged over the initial quenched disorder. The effect of cracks is to create mesovolumes having internal heterogeneity in their elastic moduli. To model the Hamiltonian, the effective elastic moduli corresponding to a given crack distribution are determined that includes crack-to-crack interactions. The interaction terms are entirely responsible for the localization transition analyzed in Paper III. The crack-opening energies are related to these effective moduli via Griffith's criterion as established in Paper I.