A viscoplastic approach to model the flow of granular solids

The flow of granular solids within rigid walls is modeled using continuum mechanics. The problem is represented as a viscoplastic flow in which the discontinuity function is taken as in previous works by Gray and Stiles, while the flow rule is modeled by the von-Mises criterion. The resulting model is incompressible and based on non-associated viscoplasticity. The apparent viscosity results in a non-linear function of the second invariant of the symmetric rate of deformation tensor and of the pressure. Friction, cohesion and fluidity of the granular model are taken into account. The constitutive model has been implemented assuming steady-state, in which the granular material flows under a critical state (incompressible behavior). Discretization of the problem has been carried out by finite elements, with direct iteration techniques to solve the non-linear system of equations. The model has been applied to the massive flow of granular material stored in vertical silos and hoppers with axisymmetric or planar shape. Comparisons with experimental tests performed by other authors are presented, together with parametric investigations to identify the main variables affecting the response.

[1]  E. Bruce Pitman,et al.  Stability of time dependent compressible granular flow in two dimensions , 1987 .

[2]  J. Z. Zhu,et al.  The finite element method , 1977 .

[3]  Poul V. Lade,et al.  Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces , 1977 .

[4]  J. Eibl,et al.  Numerical investigations on discharging silos , 1984 .

[5]  Christopher E. Brennen,et al.  Gravity Flow of Granular Materials in Conical Hoppers , 1979 .

[6]  R. Jackson,et al.  Frictional–collisional constitutive relations for granular materials, with application to plane shearing , 1987, Journal of Fluid Mechanics.

[7]  S. Elaskar,et al.  Constitutive relations for compressible granular materials using non-Newtonian fluid mechanics , 1998 .

[8]  D. Jeffrey,et al.  Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield , 1984, Journal of Fluid Mechanics.

[9]  Ismail Celik,et al.  Theoretical and numerical studies of constitutive relations for frictional granular flow , 1991 .

[10]  Wing Kam Liu,et al.  Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation , 1979 .

[11]  M. A. Diez,et al.  Viscoplastic incompressible flow of frictional-cohesive solids , 1992 .

[12]  R. M. Nedderman,et al.  Principles of Powder Mechanics. : Pergamon Press, 1970. 221 pp.,£3. , 1971 .

[13]  D. D. Gray,et al.  On the constitutive relation for frictional flow of granular materials: Topical report , 1988 .

[14]  P. Perzyna.  Fundamental Problems in Viscoplasticity , 1966 .

[15]  Raffaella Ocone,et al.  Compression and rarefaction waves in granular flow , 1995 .

[16]  David G. Schaeffer,et al.  Instability in the evolution equations describing incompressible granular flow , 1987 .

[17]  S. Savage.  Streaming motions in a bed of vibrationally fluidized dry granular material , 1988, Journal of Fluid Mechanics.

[18]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[19]  R. Aris.  Vectors, Tensors and the Basic Equations of Fluid Mechanics , 1962 .

[20]  E. N. Bromhead,et al.  Computer methods and advances in geomechanics: G. Beer, J.R. Booker and J.P. Carter (eds) Balkema, Rotterdam, 1991, £122, (3 volumes) ISBN (Set) 90-6191-189-3 , 1993 .

[21]  D. M. Walker,et al.  Pressures in experimental coal hoppers , 1967 .