Shear band dynamics from a mesoscopic modeling of plasticity

E. A. JAGLA

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Lugar: Londres; Año: 2010 vol. 2010 p. 1 - 23

1742-5468

The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model allows us to include relaxational (ageing) effects. In the absence of relaxational effects the model displays a monotonically increasing dependence of stress on strain rate, and stationary shear bands do not occur. However in start-up experiments transient (although long lived) shear bands occur, that widen without bound in time. I investigate this transient effect in detail, reproducing and explaining a t1/2 law for the thickness increase of the shear band that has been obtained in atomistic numerical simulations. Relaxation produces a negatively sloped region in the stress versus strain-rate curve that stabilizes the formation of shear bands of a well-defined width, which is a function of strain rate. Simulations at very low strain rates reveal a non-trivial stick–slip dynamics of very thin shear bands that has relevance in the study of seismic phenomena. In addition, other non-stationary processes, such as stop-and-go, or strain-rate inversion situations display a phenomenology that matches very well the results of recent experimental studies.