Onsager-symmetric constitutive laws for 3D granular flow in the inertial regime

Hu, Y., Schaeffer, D. G. and Barker, Thomas 2024. Onsager-symmetric constitutive laws for 3D granular flow in the inertial regime. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences 480 (2304) 10.1098/rspa.2023.0955

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Abstract

This paper introduces a new mathematical technique for deriving continuum rheological models of granular matter. Specifically, it is shown that, under the hypothesis of Onsager symmetry, 3D dynamic constitutive laws for general strain rates can be derived from a 3D yield condition plus steady-state empirical data of quasi-2D flow. To illustrate the technique, a new rate-dependent 3D yield condition,suitable for dry granular materials in the inertial regime, is proposed and combined with DEM particle simulation data of simple-shear flow. In combination with Onsager symmetry, this generates a complete 3D viscoplastic model for such materials. Despite the simplicity of the inputs, the resulting constitutive laws agree very well with the pioneering non-planar DEM simulations of Clemmer et al. Phys. rev. lett. 127 (2021). Unlike several previous theories, the novel Onsager-symmetric constitutive relations incorporate a nonzero second normal stress difference in simple shear and are able to distinguish between general triaxial deformations via dependence on the Lode angle.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Publisher:	The Royal Society
ISSN:	0080-4630
Date of First Compliant Deposit:	24 September 2024
Date of Acceptance:	2 October 2024
Last Modified:	13 Dec 2024 12:15
URI:	https://orca.cardiff.ac.uk/id/eprint/172352

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