Nonsmooth simulation of dense granular flows with pressure-dependent yield stress

Journal of Non-Newtonian Fluid Mechanics

Volumn 234, Issue , 2016, Pages 15-35

  Daviet, Gilles ^a,b   Bertails Descoubes, Florence ^a,b  

^a INRIA RHÔNE ALPES   (France)

^b UNIV GRENOBLE ALPES   (France)

Author keywords

Convex optimization; Coulomb friction; Drucker Prager yield criterion; Granular materials; Viscoplastic fluids

Indexed keywords

CEMENT INDUSTRY; CONTINUUM MECHANICS; CONVEX OPTIMIZATION; ELASTICITY; FRICTION; GRAIN (AGRICULTURAL PRODUCT); MATERIALS HANDLING; PELLETIZING; RISK ASSESSMENT; YIELD STRESS;

CONTINUOUS SIMULATION; COULOMB FRICTIONS; DISCRETE ELEMENT MODELING (DEM); DRUCKER PRAGER YIELD CRITERION; FINITE-ELEMENT DISCRETIZATION; FRICTIONAL CONTACT PROBLEMS; NONSMOOTH OPTIMIZATION; VISCOPLASTIC FLUID;

GRANULAR MATERIALS;

EID: 84964345853     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2016.04.006     Document Type: Article

References (42)

1. Alart P., Curnier A. A mixed formulation for frictional contact problems prone to Newton like solution methods. Comp. Methods Appl. Mech. Eng. 1991, 92(3):353-375. 10.1016/0045-7825(91)90022-x.
2. Jourdan F., Alart P., Jean M. A Gauss-Seidel like algorithm to solve frictional contact problems. Comput. Methods Appl. Mech. Eng. 1998, 155:31-47. 10.1016/S0045-7825(97)00137-0.
3. Jean M. The non-smooth contact dynamics method. Comput Methods Appl Mech Eng 1999, 177(3-4):235-257. 10.1016/s0045-7825(98)00383-1.
4. De Saxcé G., Feng Z.-Q. The bipotential method: a constructive approach to design the complete contact law with friction and improved numerical algorithms. Math Comput Model 1998, 28(4-8):225-245. 10.1016/s0895-7177(98)00119-8.
5. Cadoux F. Optimization and convex analysis for nonsmooth dynamics 2009, Université Joseph-Fourier - Grenoble I, Theses.
6. Alart P., Iceta D., Dureisseix D. A nonlinear domain decomposition formulation with application to granular dynamics. Comp Methods Appl Mech Eng 2012, 205-208:59-67. 10.1016/j.cma.2011.04.024.
7. Kleinert J., Simeon B., Obermayr M. An inexact interior point method for the large-scale simulation of granular material. Comput Methods Appl Mech Eng 2014, 278:567-598. 10.1016/j.cma.2014.06.009.
8. Lim K.-W., Krabbenhoft K., Andrade J.E. A contact dynamics approach to the granular element method. Comput Methods Appl Mech Eng 2014, 268:557-573. 10.1016/j.cma.2013.10.004.
9. Bardenhagen S., Brackbill J., Sulsky D. The material-point method for granular materials. Comput Methods Appl Mech Eng 2000, 187(3-4):529-541. 10.1016/s0045-7825(99)00338-2.
10. Wellmann C., Wriggers P. A two-scale model of granular materials. Comput Methods Appl Mech Eng 2012, 205-208:46-58. 10.1016/j.cma.2010.12.023.
11. Jop P., Forterre Y., Pouliquen O. A constitutive law for dense granular flows. Nature 2006, 441(7094):727-730. 10.1038/nature04801.
12. MiDi G.D.R. On dense granular flows. Eur Phys J E 2004, 14(4):341-365. 10.1140/epje/i2003-10153-0.
13. Lagrée P.-Y., Staron L., Popinet S. The granular column collapse as a continuum: validity of a two-dimensional navier-stokes model with a μ(i)-rheology. J Fluid Mech 2011, 686:378-408. 10.1017/jfm.2011.335.
14. Kamrin K. Nonlinear elasto-plastic model for dense granular flow. Int J Plast 2010, 26(2):167-188. 10.1016/j.ijplas.2009.06.007.
15. Staron L., Lagrée P.Y., Popinet S. Continuum simulation of the discharge of the granular silo. Eur Phys J E 2014, 37(1). 10.1140/epje/i2014-14005-6.
16. Ionescu I.R., Mangeney A., Bouchut F., Roche O. Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J Non-Newton Fluid Mech 2015, 10.1016/j.jnnfm.2015.02.006.
17. Chambon G., Bouvarel R., Laigle D., Naaim M. Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics. J Non-Newton Fluid Mech 2011, 166(12-13):698-712. 10.1016/j.jnnfm.2011.03.007.
18. Chauchat J., Médale M. A three-dimensional numerical model for dense granular flows based on the mu(i) rheology. J Comput Phys 2014, 256:696-712. 10.1016/j.jcp.2013.09.004.
19. Dunatunga S., Kamrin K. Continuum modelling and simulation of granular flows through their many phases. J Fluid Mech 2015, 779:483-513. 10.1017/jfm.2015.383.
20. Frigaard I., Nouar C. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J Non-Newton Fluid Mech 2005, 127(1):1-26. 10.1016/j.jnnfm.2005.01.003.
21. Saramito P., Roquet N. An adaptive finite element method for viscoplastic fluid flows in pipes. Comput Methods Appl Mech Eng 2001, 190(40-41):5391-5412. 10.1016/s0045-7825(01)00175-x.
22. Fortin M., Glowinski R. Méthodes de lagrangien augmenté. application à la résolution numérique de problèmes aux limites. Collection méthodes mathématiques de l'informatique 1982, Dunod.
23. Bleyer J., Maillard M., de Buhan P., Coussot P. Efficient numerical computations of yield stress fluid flows using second-order cone programming. Comput Methods Appl Mech Eng 2015, 283:599-614. 10.1016/j.cma.2014.10.008.
24. Hiriart-Urruty J.-B., Lemaréchal C. Fundamentals of convex analysis. Grundlehren text editions 2001, Springer, Berlin, New York.
25. P. Saramito, Efficient C++ finite element computing with Rheolef, 2015. Lecture.
26. Renouf M., Alart P. Conjugate gradient type algorithms for frictional multi-contact problems: applications to granular materials. Comput Methods Appl Mech Eng 2005, 194(18-20):2019-2041. 10.1016/j.cma.2004.07.009.
27. Haslinger J., Tvrdỳ M. Approximation and numerical solution of contact problems with friction. Aplikace matematiky 1983, 28(1):55-71.
28. Acary V., Cadoux F., Lemaréchal C., Malick J. A formulation of the linear discrete coulomb friction problem via convex optimization. ZAMM - J Appl Math Mech 2011, 91(2):155-175. 10.1002/zamm.201000073.
29. Nesterov Y. A method of solving a convex programming problem with convergence rate o (1/k2). Soviet Mathematics Doklady 1983, 27(2):372-376.
30. Heyn T.D. On the modeling, simulation, and visualization of many-body dynamics problems with friction and contact 2013, THE UNIVERSITY OF WISCONSIN-MADISON, Ph.D. thesis.
31. Barzilai J., Borwein J.M. Two-point step size gradient methods. IMA J Num Ana 1988, 8(1):141-148. 10.1093/imanum/8.1.141.
32. Tasora A. Efficient simulation of contacts, friction and constraints using a modified spectral projected gradient method. Poster Proceedings of WSCG 2013 2013, 69-72.
33. Moreau J. Numerical aspects of the sweeping process. Comput Methods Appl Mech Eng 1999, 177(3-4):329-349. http://dx.doi.org/10.1016/S0045-7825(98)00387-9.
34. P. Saramito, Efficient C++ finite element computing with Rheolef, 2012.
35. Andersen E., Roos C., Terlaky T. On implementing a primal-dual interior-point method for conic quadratic optimization. Math Prog 2003, 95(2):249-277. 10.1007/s10107-002-0349-3.
36. Beverloo W., Leniger H., van de Velde J. The flow of granular solids through orifices. Chem Eng Sci 1961, 15(3-4):260-269. 10.1016/0009-2509(61)85030-6.
37. Staron L., Lagrée P.-Y., Popinet S. The granular silo as a continuum plastic flow: the hour-glass vs the clepsydra. Phys Fluids 2012, 24(10):103301. 10.1063/1.4757390.
38. Mankoc C., Janda A., Arévalo R., Pastor J.M., Zuriguel I., GarcimartÃn A., Maza D. The flow rate of granular materials through an orifice. Granul Matt 2007, 9(6):407-414. 10.1007/s10035-007-0062-2.
39. Chehata D., Zenit R., Wassgren C.R. Dense granular flow around an immersed cylinder. Phys Fluids 2003, 15(6):1622. 10.1063/1.1571826.
40. Daviet G., Bertails-Descoubes F., Boissieux L. A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics. ACM Trans Graph 2011, 30(6):1. 10.1145/2070781.2024173.
41. Domnik B., Pudasaini S.P. Full two-dimensional rapid chute flows of simple viscoplastic granular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations. J. Non-Newton Fluid Mech. 2012, 173-174:72-86. 10.1016/j.jnnfm.2012.03.001.
42. Barker T., Schaeffer D., Bohorquez P., Gray J. Well-posed and ill-posed behaviour of the -rheology for granular flow. J. Fluid Mech. 2015, 779:794-818. 10.1017/jfm.2015.412.