An accurate tangential force-displacement model for granular-flow simulations: contacting spheres with plastic deformation, force-driven formulation

An elasto-plastic frictional tangential force-displacement (TFD) model for spheres in contact for accurate and efficient granular-flow simulations is presented in this paper: the present TFD is consistent with the elasto-plastic normal force displacement (NFD) model presented in [ASME Journal of Applied Mechanics 67 (2) (2000) 363: Proceedings of the Royal Society of London, Series A 455 (1991) (1999) 4013]. The proposed elasto-plastic frictional TFD model is accurate, and is validated against non-linear finite-element analyses involving plastic flows under both loading and unloading conditions. The novelty of the present TFD model lies in (i) the additive decomposition of the elasto-plastic contact area radius into an elastic part and a plastic part, (ii) the correction of the particles' radii at the contact point, and (iii) the correction of the particles' elastic moduli. The correction of the contact-area radius represents an effect of plastic deformation in colliding particles; the correction of the radius of curvature represents a permanent indentation after impact; the correction of the elastic moduli represents a softening of the material due to plastic flow. The construction of both the present elasto-plastic frictional TFD model and its consistent companion, the elasto-plastic NFD model, parallels the formalism of the continuum theory of elasto-plasticity. Both NFD and TFD models form a coherent set of force-displacement (FD) models not available hitherto for granular-flow simulations, and are consistent with the Hertz, Cattaneo, Mindlin, Deresiewicz contact mechanics theory. Together. these FD models will allow for efficient simulations of granular flows (or granular gases) involving a large number of particles.

[1]  Shear response of a frictional interface to a normal load modulation , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  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.

[3]  R. D. Mindlin.  Elastic Spheres in Contact Under Varying Oblique Forces , 1953 .

[4]  T C Lubensky,et al.  Granular shear flow dynamics and forces: experiment and continuum theory. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Loc Vu-Quoc,et al.  An accurate and efficient tangential force–displacement model for elastic frictional contact in particle-flow simulations , 1999 .

[6]  M. Buchanan.  Think outside the sandbox , 2003, Nature.

[7]  Loc Vu-Quoc,et al.  On computer simulation of dry particle systems using discrete element method and the development of dem contact force-displacement models , 1998 .

[8]  B. Persson.  Elastoplastic contact between randomly rough surfaces. , 2001, Physical review letters.

[9]  Leonard G. Austin,et al.  A treatment of impact breakage of particles , 2002 .

[10]  David B. Bogy,et al.  Elastic-Plastic Finite Element Analysis of Repeated Indentation of a Half-Space by a Rigid Sphere , 1993 .

[11]  H. Jaeger,et al.  Physics of the Granular State , 1992, Science.

[12]  G. M. Hyde,et al.  POTATO IMPACT DAMAGE THRESHOLDS , 1997 .

[13]  S. Savage,et al.  Analyses of slow high-concentration flows of granular materials , 1998, Journal of Fluid Mechanics.

[14]  G. B. Sinclair,et al.  Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere—II. Results , 1984 .

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

[16]  Tom Mullin.  Mixing and De-mixing , 2002, Science.

[17]  J. Jaeger.  Elastic impact with friction , 1992 .

[18]  L. Vu-Quoc,et al.  A 3-D discrete-element method for dry granular flows of ellipsoidal particles , 2000 .

[19]  S. Gan-Mor,et al.  Rheological model of fruit collision with an elastic plate , 2000 .

[20]  Spahn,et al.  Model for collisions in granular gases. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  L. Vu-Quoc,et al.  A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation , 2000 .

[22]  Raymond D. Mindlin,et al.  Compliance of elastic bodies in contact , 1949 .

[23]  Marcus I. Bursik,et al.  A smoothed-particle hydrodynamic automaton of landform degradation by overland flow , 2003 .

[24]  James C. M. Li,et al.  Photoelastic and finite element analysis of different size spheres in contact , 1992 .

[25]  D. Lin,et al.  Structure, stability and evolution of Saturn's rings , 1984, Nature.

[26]  C. Thornton,et al.  Applications of Theoretical Contact Mechanics to Solid Particle System Simulation , 1988 .

[27]  Paul W. Cleary,et al.  Modelling comminution devices using DEM , 2001 .

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

[29]  Ricardo Dobry,et al.  General model for contact law between two rough spheres , 1991 .

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

[31]  L. Vu-Quoc,et al.  Normal and tangential force-displacement relations for frictional elasto-plastic contact of spheres , 2001 .