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Experimental Measures of Affine and Non-affine Deformation in Granular Shear

Brian Utter·R. P. Behringer
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Abstract

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces smooth affine deformations in such a solid and also irresversible so-called non-affine particle displacements. We examine both processes. We show that the non-affine part is associated with diffusion, and also can be used to define a granular temperature. Distributions for single particle non-affine displacements, $\dri$, satisfy $P_1(\dri) \propto \exp [-|\dri/Δr|^α]$ ($α\stackrel{<}{\sim} 2$). We suggest that the shear band forms due to a radially outward diffusive flux/non-affine motion which is balanced in the steady state by inward diffusion due to density gradients.

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Brian Utter, R. P. Behringer. 2007-02-14. Experimental Measures of Affine and Non-affine Deformation in Granular Shear. https://doi.org/10.1103/physrevlett.100.208302

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