A compliant visco-plastic particle contact model based on differential variational inequalities

International Journal of Non-Linear Mechanics

Volumn 53, Issue , 2013, Pages 2-12

  Tasora, A ^a   Anitescu, M ^b   Negrini, S ^c   Negrut, D ^d  

^a UNIVERSITY OF PARMA   (Italy)

^b ARGONNE NATIONAL LABORATORY   (United States)

^c POLITECNICO DI MILANO   (Italy)

^d University of Wisconsin Madison   (United States)

Author keywords

Contacts; Friction; Plasticity; Variational inequalities

Indexed keywords

CONTACTS (FLUID MECHANICS); FRICTION; PLASTICITY; SET THEORY;

COULOMB FRICTIONS; DIFFERENTIAL VARIATIONAL INEQUALITY; FRICTIONAL CONTACT; INTEGRATION TIME; NON-SMOOTH DYNAMICS; PLASTIC PARTICLE; THREE-DIMENSIONAL SHAPE; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

EID: 84897584019     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2013.01.010     Document Type: Article

References (29)

1. P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47-65. (Pubitemid 9433658)
2. F. Pfeiffer, C. Glocker, Multibody Dynamics with Unilateral Contacts, John Wiley, New York City, 1996.
3. D.E. Stewart, J.C. Trinkle, An implicit time-stepping scheme for rigid-body dynamics with inelastic collisions and Coulomb friction, International Journal for Numerical Methods in Engineering 39 (1996) 2673-2691. (Pubitemid 126648043)
4. M. Anitescu, A. Tasora, An iterative approach for cone complementarity problems for nonsmooth dynamics, Computational Optimization and Applications 47 (2) (2010) 207-235.
5. A. Tasora, M. Anitescu, A convex complementarity approach for simulating large granular flows, Journal of Computational and Nonlinear Dynamics 5 (2010) 1-10.
6. M. Renouf, P. Alart, Conjugate gradient type algorithms for frictional multicontact problems: applications to granular materials, Computer Methods in Applied Mechanics and Engineering 194 (2005) 2019-2041. (Pubitemid 40373875)
7. K. Krabbenhoft, A. Lyamin, J. Huang, M.V. da Silva, Granular contact dynamics using mathematical programming methods, Computers and Geotechnics 43 (2012) 165-176.
8. A. Tasora, M. Anitescu, A matrix-free cone complementarity approach for solving large-scale, nonsmooth rigid body dynamics, Computer Methods in Applied Mechanics and Engineering 200 (2011) 439-453.
9. K. Krabbenhoft, J. Huang, M. da Silva, A. Lyamin, Granular contact dynamics with particle elasticity, Granular Matter 14 (2012) 607-619.
10. C. Lacoursière, M. Servin, A. Backman, Fast and stable simulation of granular matter and machines, in: Proceedings of the Fifth International Conference on Discrete Element Methods (DEM5), 2010.
11. P. Song, J.-S. Pang, V. Kumar, A semi-implicit time-stepping model for frictional compliant contact problems, International Journal of Numerical Methods in Engineering 60 (2004) 267-279.
12. R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970.
13. J. Moreau, Numerical aspects of the sweeping process, Computer Methods in Applied Mechanics and Engineering 177 (1999) 329-349. (Pubitemid 30510502)
14. J.J. Moreau, Unilateral contact and dry friction in finite freedom dynamics, in: J.J. Moreau, P.D. Panagiotopoulos (Eds.), Nonsmooth Mechanics and Applications, Springer-Verlag, Berlin, 1988, pp. 1-82.
15. M. Anitescu, F.A. Potra, D. Stewart, Time-stepping for three-dimensional rigid-body dynamics, Computer Methods in Applied Mechanics and Engineering 177 (1999) 183-197.
16. D.E. Stewart, Reformulations of measure differential inclusions and their closed graph property, Journal of Differential Equations 175 (2001) 108-129. (Pubitemid 33082639)
17. F. Jourdan, P. Alart, M. Jean, A Gauss Seidel like algorithm to solve frictional contract problems, Computer Methods in Applied Mechanics and Engineering 155 (1998) 31-47.
18. C.G. Christoph Studer, Solving normal cone inclusion problems in contact mechanics by iterative methods, Journal of System Design and Dynamics 1 (2007) 458-467.
19. D. Stewart, J.-S. Pang, Differential variational inequalities, Mathematical Programming 113 (2008) 345-424. (Pubitemid 351187739)
20. D. Kinderleher, G. Stampacchia, An Introduction to Variational Inequalities and Their Application, Academic Press, New York, 1980.
21. D. Stewart, Convergence of a time-stepping scheme for rigid body dynamics and resolution of Painlevé's problems, Archive Rational Mechanics and Analysis 145 (1998) 215-260. (Pubitemid 128374203)
22. V.I. Bogachev, Measure Theory, Springer, New York, 2007.
23. A. Tasora, D. Negrut, M. Anitescu, Large-scale parallel multi-body dynamics with frictional contact on the graphical processing unit, Journal of Multi-Body Dynamics 222 (2008) 315-326.
24. R.D. Mindlin, H. Deresiewicz, Elastic spheres in contact under varying oblique forces, Journal of Applied Mechanics 20 (1953) 327-344.
25. M. Yu, G. Ma, H. Qiang, Y. Zhang, Generalized Plasticity, Springer, 2010.
26. F. Calvetti, R. Nova, Micromechanical approach to slope stability analysis, in: Degradations and Instabilities in Geomaterials, Springer, New York, 2004.
27. L. Kong, L. Tunçel, N. Xiu, Homogeneous Cone Complementarity Problems and P Properties, ArXiv e-prints, 2009.
28. E.G. Birgin, J.M. Martínez, M. Raydan, Nonmonotone spectral projected gradient methods on convex sets, SIAM Journal on Optimization 10 (1999) 1196-1211.
29. ASTM, D3080:2011, Standard test method for direct shear test of soils under consolidated drained conditions, 2011.