Mechanical response of an inclined frictional granular layer approaching unjamming

¹ Departamento de Física e Matemática and National Institute of Science and Technology for Complex Systems, Centro Federal de Educação Tecnológica de Minas Gerais, CEFET - MG - Av. Amazonas 7675, 30510-000, Belo Horizonte-MG, Brazil
² Laboratoire de Physique et Mécanique des Milieux Hétérogènes, (PMMH UMR 7636 CNRS - ESPCI - Univ. P. et M. Curie - Univ. Paris Diderot) - 10 rue Vauquelin, 75231 Paris Cedex 05, France, EU
³ UJF-Grenoble 1, Grenoble-INP, CNRS UMR 5521, 3SR Lab. - B.P. 53, 38041 Grenoble Cedex 09, France, EU

Received: 2 November 2012
Accepted: 4 February 2013

Abstract

We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle α with respect to the critical angle α_c. We find that the shear modulus of the system decreases with α, but reaches a finite value as α → α_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.