Numerical computations for shear bands in an antiplane shear model

• Published in: Journal of the mechanics and physics of solids 1994, Vol.42 (1), p.21-50
• Main Authors: Garaizar, F.Xabier, Schaeffer, David G.
• Format: Article
• Language: English
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Granular solids; Inelasticity (thermoplasticity, viscoplasticity...); Material form; Physics; Rheology; Solid mechanics; Structural and continuum mechanics; Viscoelasticity, plasticity, viscoplasticity
• ISSN: 0022-5096
• DOI: 10.1016/0022-5096(94)90049-3

We study numerically a model for shear bands that is loosely based on antiplane shearing of granular material. In the model, a shear band is idealized to a jump discontinuity in the solution to the dynamic PDE. We do not explicitly incorporate small scale effects within this shear band into the model—rather at the shear band we impose a jump condition which includes a length parameter modeling the grain diameter. At this level of approximation, we study in several cases the process by which shear bands first form and subsequently develop, including the growth of the unloading region containing the shear band(s). Our computations use a Godunov method, based on solving appropriate Riemann problems. In some cases, depending on the size of the jump, the Riemann problems under study do not admit a similarity solution because scale invariance is violated by the jump condition at the shear band. This novel feature adds mathematical interest to the present computations.