Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session B57: Physics of Granular Media
11:15 AM–2:15 PM,
Monday, March 5, 2018
LACC Room: 518
Sponsoring Units: GSOFT DMP DFD GSNP
Chair: David Henann, Brown Univ
Abstract: B57.00001 : A Van der Waals-Cahn-Hilliard regularization of granular instability via dissipation potentials*
11:15 AM–11:51 AM
View Presentation Abstract
This talk deals with the viscoplastic Hadamard (short-wavelength) instability of the so-called μ(I) model of dense rapidly-sheared granular flow, as reported recently by Barker et al. (2015, J. Fluid Mech, 779, 794-818). As explained in a subsequent paper by Goddard & Lee (2017, J. Fluid Mech., in press), one achieves stabilizing effects from higher velocity gradients by means of an enhanced-continuum model based on the dissipative analog of the Van der Waals-Cahn-Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyper-stress, with surface viscosity arising as counterpart of elastic surface tension. This allows for a description of diffuse shear bands as the rough analog of the diffuse interfaces of equilibrium thermodynamics. The later paper also presents a more comprehensive linear stability analysis, including convective (Kelvin) wave-vector stretching by the base flow that leads to asymptotic stabilization of the non-convective instability found by Barker et al. This suggests a theoretical connection between their non-convective instability and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the otherwise difficult numerical simulation of continuum field equations involving Hadamard-unstable viscoplasticity.
*Work supported in part by a grant of HPC computer time at the San Diego Supercomper Center of the University of California, San Diego.
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