Localization in an anisotropic planar aggregate of spheres

¹ Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura, Politecnico di Bari
² Department of Mechanical Engineering, Milwaukee School of Engineering, 53202 Milwaukee WI, USA
³ School of Civil and Environmental Engineering, Cornell University, 14853 Ithaca, NY, USA

^* e-mail: luigi.laragione@poliba.it

Published online: 30 June 2017

Abstract

We present a micro-mechanical model that is able to predict localization in a sheared planar aggregate of spheres. We assume a non-linear contact law between interacting particles that deform differently from an affine deformation. Equilibrium determines this deviation. The aggregate is isotropically compressed and then sheared so anisotropy develops because of contacts deletion and a non-linear contact law. Because of anisotropy and fluctuations in particles deformation, the resulting macroscopic stiffness tensor, which relates increments in the average stress with increments in the average strain, is characterized by a lack of major symmetry, A_ijkl ≠ A_klij. At given shear strain and coordination number it is possible to detemine a plane over which discontinuity in strain occurs; this is identified as localization.