On the tangential restitution problem: independent friction–restitution modeling

A single modeling of impact in terms of independent contributions of tangential restitution and friction is presented and tested with available literature data. Using this formulation, a description of oblique rebound of a homogenous sphere on a infinitely massive wall is obtained for both stick and gross slip regimes of impact using the same set of coefficients of restitution (normal and tangential) and friction based on the consideration of tangential forces at impact without viscose nor adhesive effects. This formulation which avoids sharp (apparent) variations in the coefficient of tangential restitution on the incident angle, provides a justification of several experimental results considered as anomalous in literature.

[1]  J. N. Fawcett,et al.  The oblique impact of elastic spheres , 1976 .

[2]  J. N. Fawcett,et al.  THE REBOUND OF ELASTIC BODIES IN OBLIQUE IMPACT , 1977 .

[3]  J. N. Fawcett,et al.  The Role of Elastic Tangential Compliance in Oblique Impact , 1981 .

[4]  Raymond M. Brach,et al.  Friction, Restitution, and Energy Loss in Planar Collisions , 1984 .

[5]  R. L. Braun,et al.  Viscosity, granular‐temperature, and stress calculations for shearing assemblies of inelastic, frictional disks , 1986 .

[6]  T. Kane,et al.  An explicit solution of the general two-body collision problem , 1987 .

[7]  M. Louge,et al.  Inelastic microstructure in rapid granular flows of smooth disks , 1991 .

[8]  Mihail C. Roco,et al.  Particulate two-phase flow , 1993 .

[9]  Michel Y. Louge,et al.  Measurements of the collision properties of small spheres , 1994 .

[10]  M. Louge,et al.  Measurements of impact properties of small, nearly spherical particles , 1997 .

[11]  C. Thornton,et al.  A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres , 1998 .

[12]  L. Vu-Quoc,et al.  An elastoplastic contact force–displacement model in the normal direction: displacement–driven version , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Dynamics of inelastically colliding spheres with Coulomb friction: Relaxation of translational and rotational energy , 1999, cond-mat/9911306.

[14]  A. Ruina,et al.  Anomalous Frictional Behavior in Collisions of Thin Disks , 1999 .

[15]  Ahmad H. Kharaz,et al.  The measurement of particle rebound characteristics , 2000 .

[16]  Agba D. Salman,et al.  An experimental study of the elastic rebound of spheres , 2001 .

[17]  L. Vu-Quoc,et al.  Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions , 2002 .

[18]  M. Louge,et al.  Anomalous behavior of normal kinematic restitution in the oblique impacts of a hard sphere on an elastoplastic plate. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  B. Bhushan,et al.  Introduction to Tribology , 2002 .

[20]  Sung Joon Moon,et al.  Role of friction in pattern formation in oscillated granular layers. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Melany L. Hunt,et al.  Oblique particle–wall collisions in a liquid , 2004, Journal of Fluid Mechanics.

[22]  G. Weir,et al.  The coefficient of restitution for normal incident, low velocity particle impacts , 2005 .

[23]  Michael H. Moys,et al.  Experimental study of oblique impacts with initial spin , 2006 .

[24]  Loc Vu-Quoc,et al.  An accurate elasto-plastic frictional tangential force-displacement model for granular-flow simulations: Displacement-driven formulation , 2007, J. Comput. Phys..

[25]  S. Luding.  Cohesive, frictional powders: contact models for tension , 2008 .

[26]  H. Briesen,et al.  Tangential-force model for interactions between bonded colloidal particles. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Colin Thornton,et al.  A semi-analytical model for oblique impacts of elastoplastic spheres , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[28]  T Pöschel,et al.  Coefficient of tangential restitution for viscoelastic spheres , 2008, The European physical journal. E, Soft matter.

[29]  A. Doménech.  Non-smooth modelling of billiard-and superbilliard-ball collisions , 2008 .

[30]  A. Chatterjee,et al.  Anomalous Frictional Behavior in Collisions of Thin Disks Revisited , 2008 .

[31]  François Rioual,et al.  Experimental study of the bouncing trajectory of a particle along a rotating wall , 2009 .

[32]  H. Shen,et al.  Comparisons of physical experiment and discrete element simulations of sheared granular materials in an annular shear cell , 2009 .

[33]  Stefan Heinrich,et al.  Energy absorption during compression and impact of dry elastic-plastic spherical granules , 2010 .

[34]  Andrés D. Orlando,et al.  Effect of rolling friction on binary collisions of spheres , 2010 .

[35]  Thorsten Pöschel,et al.  Oblique impact of frictionless spheres: on the limitations of hard sphere models for granular dynamics , 2011, 1108.3930.

[36]  S. Heinrich,et al.  The normal and oblique impact of three types of wet granules , 2011 .

[37]  Antonio Doménech-Carbó,et al.  Analysis of oblique rebound using a redefinition of the coefficient of tangential restitution coefficient , 2013 .

[38]  William James Stronge,et al.  Smooth dynamics of oblique impact with friction , 2013 .