TL;DR
This paper investigates shear dilatancy in marginal solids, revealing a divergence near rigidity loss and contrasting behaviors between packings expanding and networks contracting under shear.
Contribution
It provides the first calculation of elastic dilatancy coefficients in soft sphere packings and spring networks, highlighting their contrasting responses near the rigidity transition.
Findings
Dilatancy diverges near the rigidity transition.
Packings expand under shear, networks contract.
Contrasting behaviors explained by contact formation and destabilization.
Abstract
Shearing stresses can change the volume of a material via a nonlinear effect known as shear dilatancy. We calculate the elastic dilatancy coefficient of soft sphere packings and random spring networks, two canonical models of marginal solids close to their rigidity transition. We predict a dramatic enhancement of dilatancy near rigidity loss in both materials, with a surprising distinction: while packings expand under shear, networks contract. We show that contraction in networks is due to the destabilizing influence of increasing hydrostatic or uniaxial loads, which is counteracted in packings by the formation of new contacts.
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