[en] In a dense granular system, particles interact in networks containing many particles and interaction times are long compared with the particle binary collision time. In these systems, the streaming part of the granular stress is negligible. We only consider the collisional stress in this paper. The average behavior of particle contacts is studied. By following the statistical method developed recently by the authors [Zhang and Rauenzahn, J. Rheol. 41, 1275 (1997)], we derive an evolution equation for the collisional stress. This equation provides guidance to collateral numerical simulations, which show that the probability distribution of particle contact times is exponential for long contact times. This can be explained by network interactions in a dense granular system. In general, the relaxation of the collisional stress is a combined effect of the decay of the contact time probability and the relaxation of collisional forces among particles. In the numerical simulations, the normal force between a pair of particles is modeled as parallel connect of a spring and a dashpot. In this case, the relaxation of the force magnitude conditionally averaged given a specific contact time is negligible, and the major contribution to the stress relaxation is from the exponential decay of the contact time probability. We also note that the probability decay rate is proportional to the imposed strain rate. Consequently, in a simple shear flow with a constant particle volume fraction, as the shear rate approaches zero, the shear stress approaches a finite value. This value is the yield stress for that particle volume fraction. Hence, the evolution equation of the collisional stress predicts viscoplasticity of dense granular systems. (c) 2000 Society of Rheology

[en] I propose a model of fracture in which the curvature of the crack tip is a relevant dynamical variable and crack advance is governed solely by plastic deformation of the material near the tip. This model is based on a rate-and-state theory of plasticity introduced in earlier papers by Falk, Lobkovsky, and myself. In the approximate analysis developed here, fracture is brittle whenever the plastic yield stress is nonzero. The tip curvature finds a stable steady-state value at all loading strengths, and the tip stress remains at or near the plastic yield stress. The crack speed grows linearly with the square of the effective stress intensity factor above a threshold that depends on the surface tension. This result provides a possible answer to the fundamental question of how breaking stresses are transmitted through plastic zones near crack tips. (c) 2000 The American Physical Society

[en] We show that a simple rate-and-state theory accounts for most features of both time-independent and time-dependent plasticity in a spatially inhomogeneous situation, specifically, a circular hole in a large stressed plate. Those features include linear viscoelastic flow at small applied stresses, strain hardening at larger stresses, and a dynamic transition to viscoplasticity at a yield stress. In the static limit, this theory predicts the existence of a plastic zone near the hole for some but not all ranges of parameters. The rate-and-state theory also predicts dynamic failure modes that we believe may be relevant to fracture mechanics. (c) 1999 The American Physical Society