Science China Technological Sciences

, Volume 62, Issue 8, pp 1438–1454 | Cite as

A compact 3D block cutting and contact searching algorithm

  • XingChao Lin
  • Xu LiEmail author
  • XiaoGang Wang
  • YuJie Wang


The geometry relation and the contact point-pairs detection between two three dimensional (3D) objects with arbitrary shapes are essential problems involved in discontinuous computation and computational geometry. This paper reported a geometry relation judgment and contact searching algorithm based on Contact Theory. A contact cover search algorithm is proposed to find all the possible contact cover between two blocks. Two blocks can come to contact only on these covers. Each contact cover can define a possible contact point-pair between two blocks. Data structure and flow chart are provided, as well as some examples in details. Contact problems involving concave blocks or parallel planes are considered to be very difficult in past and are solved by this algorithm. The proposed algorithm is compacted and applicable to the discontinuous computation, such as robotic control, rock mass stability, dam stability etc. A 3D cutting and block searching algorithm is also proposed in this study and used to search the outer boundary of the 3D entrance block when 3D concave blocks are encountered. The 3D cutting and block searching algorithm can be also used to form the block system for jointed rock.


contact discontinuous computation block cutting computational geometry jointed rock cover 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

11431_2018_9318_MOESM1_ESM.doc (3.1 mb)
A compact 3D block cutting and contact searching algorithm


  1. 1.
    Shi G H. Contact theory. Sci China Technol Sci, 2015, 58: 1450–1496CrossRefGoogle Scholar
  2. 2.
    Zhong Z H, Nilsson L. A contact searching algorithm for general contact problems. Comput Struct, 1989, 33: 197–209zbMATHCrossRefGoogle Scholar
  3. 3.
    Benson D J, Hallquist J O. A single surface contact algorithm for the post-buckling analysis of shell structures. Comput Methods Appl Mech Eng, 1990, 78: 141–163MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Belytschko T, Neal M O. Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int J Numer Meth Engng, 1991, 31: 547–572zbMATHCrossRefGoogle Scholar
  5. 5.
    Bonnet J, Peraire J. An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problem. Int J Numer Methods Eng, 1991, 31: 1–17zbMATHCrossRefGoogle Scholar
  6. 6.
    Williams J R, O’Connor R. A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries. Eng Computations, 1995, 12: 185–201CrossRefGoogle Scholar
  7. 7.
    Perkins E, Williams J R. A fast contact detection algorithm insensitive to object sizes. Eng Computations, 2001, 18: 48–62zbMATHCrossRefGoogle Scholar
  8. 8.
    Munjiza A, Andrews K R F. NBS contact detection algorithm for bodies of similar size. Int J Numer Meth Engng, 1998, 43: 131–149zbMATHCrossRefGoogle Scholar
  9. 9.
    Diekmann R, Hungershofer J, Lux M. Efficient contact search for finite element analysis. In: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering. Barcelona, 2000Google Scholar
  10. 10.
    Wu W, Zhu H, Zhuang X, et al. A Multi-shell cover algorithm for contact detection in the three dimensional discontinuous deformation analysis. Theor Appl Fract Mech, 2014, 72: 136–149Google Scholar
  11. 11.
    Cundall P A. Formulation of a three-dimensional distinct element model-Part I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mecha Mining Sci Geomech, 1988, 25: 107–116CrossRefGoogle Scholar
  12. 12.
    Jelenic G, Crisfield M A. Non-linear master-slave relationships for joints in 3D beams with large rotations. Comp Meth Appl Mech Eng, 1996, 135: 211–228zbMATHCrossRefGoogle Scholar
  13. 13.
    Li S, Zhao M, Wang Y, et al. A new numerical method for dem-block and particle model. Int J Rock Mech Min Sci, 2004, 41: 436CrossRefGoogle Scholar
  14. 14.
    Chen W S, Zheng H, Cheng Y M, et al. Detection of 3D rock block contacts by penetration edges. Chin J Rock Mech Eng, 2004, 23: 565–571Google Scholar
  15. 15.
    Nezami E G, Hashash Y M A, Zhao D, et al. Shortest link method for contact detection in discrete element method. Int J Numer Anal Meth Geomech, 2006, 30: 783–801zbMATHCrossRefGoogle Scholar
  16. 16.
    Wu J H. New edge-to-edge contact calculating algorithm in threedimensional discrete numerical analysis. Adv Eng Software, 2008, 39: 15–24CrossRefGoogle Scholar
  17. 17.
    Keneti A R, Jafari A, Wu J H. A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis. Comput Geotechnics, 2008, 35: 746–759CrossRefGoogle Scholar
  18. 18.
    He L. Three Dimensional Numerical Manifold Method and Rock Engineering Applications. Dissertation for Dcotoral Degree. Singapore: Nanyang Technological University, 2010Google Scholar
  19. 19.
    Ahn T Y, Song J J. New contact-definition algorithm using inscribed spheres for 3D discontinuous deformation analysis. Int J Comput Methods, 2011, 08: 171–191CrossRefGoogle Scholar
  20. 20.
    An X, Ma G, Cai Y, et al. A new way to treat material discontinuities in the numerical manifold method. Comput Methods Appl Mech Eng, 2011, 200: 3296–3308zbMATHCrossRefGoogle Scholar
  21. 21.
    Konyukhov A, Schweizerhof K. Geometrically exact theory for contact interactions of 1D manifolds. Algorithmic implementation with various finite element models. Comput Methods Appl Mech Eng, 2012, 205–208: 130–138Google Scholar
  22. 22.
    Mousakhani M, Jafari A. A new model of edge-to-edge contact for three dimensional discontinuous deformation analysis. GeoMech GeoEng, 2016, 11: 135–148CrossRefGoogle Scholar
  23. 23.
    Nejati M, Paluszny A, Zimmerman R W. A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes. Comput Methods Appl Mech Eng, 2016, 306: 123–150MathSciNetCrossRefGoogle Scholar
  24. 24.
    Jiang Q, Chen Y, Zhou C, et al. Kinetic energy dissipation and convergence criterion of discontinuous deformations analysis (DDA) for geotechnical engineering. Rock Mech Rock Eng, 2013, 46: 1443–1460CrossRefGoogle Scholar
  25. 25.
    Jiao Y Y, Zhang H Q, Tang H M, et al. Simulating the process of reservoir-impoundment-induced landslide using the extended DDA method. EngGeol, 2014, 182: 37–48Google Scholar
  26. 26.
    Fan H, He S. An angle-based method dealing with vertex-vertex contact in the two-dimensional discontinuous deformation analysis (DDA). Rock Mech Rock Eng, 2015, 48: 2031–2043CrossRefGoogle Scholar
  27. 27.
    Zheng H, Zhang P, Du X. Dual form of discontinuous deformation analysis. Comput Methods Appl Mech Eng, 2016, 305: 196–216MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Sun Y, Feng X, Xiao J, et al. Discontinuous deformation analysis coupling with discontinuous galerkin finite element methods for contact simulations. Math Problems Eng, 2016, 2016: 1–25MathSciNetzbMATHGoogle Scholar
  29. 29.
    Wang T, Zhou W, Chen J, et al. Simulation of hydraulic fracturing using particle flow method and application in a coal mine. Int J CoalGeol, 2014, 121: 1–13Google Scholar
  30. 30.
    Guo Y, Curtis J S. Discrete element method simulations for complex granular flows. Ann Rev Fluid Mech, 2015, 47: 21–46MathSciNetCrossRefGoogle Scholar
  31. 31.
    Feng Y T, Han K, Owen D R J. A generic contact detection framework for cylindrical particles in discrete element modelling. Comput Methods Appl Mech Eng, 2017, 315: 632–651MathSciNetCrossRefGoogle Scholar
  32. 32.
    Shi G H. Manifold method. In: Proceedings of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media. Bekerley, 1996. 52–204Google Scholar
  33. 33.
    Ma G, An X, He L. The numerical manifold method: A review. Int J Comput Methods, 2010, 07: 1–32MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Zheng H, Liu F, Du X. Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method. Comput Methods Appl Mech Eng, 2016, 295: 150–171MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Fan H, Zhao J, Zheng H. A high-order three-dimensional numerical manifold method enriched with derivative degrees of freedom. Eng Anal Bound Elem, 2017, 83: 229–241MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Minkowski H. Volumen and oberflache. Mathematische Annalen, 1903, 57: 447–495MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Zheng H, Li X. Mixed linear complementarity formulation of discontinuous deformation analysis. Int J Rock Mech Min Sci, 2015, 75: 23–32CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • XingChao Lin
    • 1
    • 3
  • Xu Li
    • 2
    Email author
  • XiaoGang Wang
    • 1
    • 3
  • YuJie Wang
    • 1
    • 3
  1. 1.State Key Laboratory of Simulation and Regulation of Water Cycle in River BasinBeijingChina
  2. 2.Key Laboratory of Urban Underground Engineering of Ministry of EducationBeijing Jiaotong UniversityBeijingChina
  3. 3.Department of Geotechnical EngineeringChina Institute of Water Resources and Hydropower ResearchBeijingChina

Personalised recommendations