The Contact Dynamics method: A nonsmooth story

被引:93
作者
Dubois, Frederic [1 ,2 ]
Acary, Vincent [4 ]
Jean, Michel [3 ]
机构
[1] Univ Montpellier, CNRS, LMGC, Montpellier, France
[2] Univ Montpellier, MIST, CNRS, IRSN, Montpellier, France
[3] Aix Marseille Univ, CNRS, Cent Marseille, Marseille, France
[4] Univ Grenoble Alpes, LJK, INRIA, Grenoble, France
来源
COMPTES RENDUS MECANIQUE | 2018年 / 346卷 / 03期
关键词
Nonsmooth dynamics; Shock; Coulomb law; Contact Dynamics; Discrete element method; DISCRETE ELEMENT METHOD; TIME-STEPPING SCHEMES; DEFORMATION ANALYSIS; GRANULAR-MATERIALS; FLOATING FRAME; HILBERT-SPACE; SYSTEMS; EQUIVALENCE; CONSTRAINTS; FORMULATION;
D O I
10.1016/j.crme.2017.12.009
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
When velocity jumps are occurring, the dynamics is said to be nonsmooth. For instance, in collections of contacting rigid bodies, jumps are caused by shocks and dry friction. Without compliance at the interface, contact laws are not only non-differentiable in the usual sense but also multi-valued. Modeling contacting bodies is of interest in order to understand the behavior of numerous mechanical systems such as flexible multi-body systems, granular materials or masonry. These granular materials behave puzzlingly either like a solid or a fluid and a description in the frame of classical continuous mechanics would be welcome though far to be satisfactory nowadays. Jean-Jacques Moreau greatly contributed to convex analysis, functions of bounded variations, differential measure theory, sweeping process theory, definitive mathematical tools to deal with nonsmooth dynamics. He converted all these underlying theoretical ideas into an original nonsmooth implicit numerical method called Contact Dynamics (CD); a robust and efficient method to simulate large collections of bodies with frictional contacts and impacts. The CD method offers a very interesting complementary alternative to the family of smoothed explicit numerical methods, often called Distinct Elements Method (DEM). In this paper developments and improvements of the CD method are presented together with a critical comparative review of advantages and drawbacks of both approaches. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS.
引用
收藏
页码:247 / 262
页数:16
相关论文
共 81 条
[1]  
Acary V, 2001, THESIS
[2]   Energy conservation and dissipation properties of time-integration methods for nonsmooth elastodynamics with contact [J].
Acary, Vincent .
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2016, 96 (05) :585-603
[3]   Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb's friction [J].
Acary, Vincent .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2013, 256 :224-250
[4]   Higher order event capturing time-stepping schemes for nonsmooth multibody systems with unilateral constraints and impacts [J].
Acary, Vincent .
APPLIED NUMERICAL MATHEMATICS, 2012, 62 (10) :1259-1275
[5]  
Alart P., 2017, COMPUT PART MECH, P1
[6]   How to overcome indetermination and interpenetration in granular systems via nonsmooth contact dynamics. An exploratory investigation [J].
Alart, Pierre .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2014, 270 :37-56
[7]  
Allen M. P., 1987, COMPUTER SIMULATION
[8]  
[Anonymous], NUMERICAL METHODS NO
[9]  
[Anonymous], 2014, LECT NOTES APPL COMP
[10]   Packings of irregular polyhedral particles: Strength, structure, and effects of angularity [J].
Azema, Emilien ;
Radjai, Farhang ;
Dubois, Frederic .
PHYSICAL REVIEW E, 2013, 87 (06)