Skip to main content

A robust asymmetrical contact algorithm for explicit solid dynamics

Computational Mechanics volume 64, pages 15–32 (2019)Cite this article

Abstract

We describe a novel algorithm for the robust approximation of elastic, inelastic, and frictional contact problems in explicit computations. The method is based on a master-slave concept and a predictor/corrector split of the dynamic update. In the predictor step, the bodies move ignoring all contact interactions; in the correction, the nodes that have penetrated a body are pushed back while correcting their velocities to preserve linear momentum and balance the kinetic energy. In contrast with existing predictor/corrector contact algorithms, no iterations nor global computations are required in the correction step. Moreover, thanks to the geometrical basis of the method, the choice of an artificial penalty parameter is avoided. The contact algorithm does not require the computation of the normal vectors at the contacting surfaces, making it especially useful for simulations that employ finite element and certain meshfree discretizations, and for the simulation of contact among bodies with non-smooth boundaries.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

References

  1. Zhong Z-H, Mackerle J (1992) Static contact problems—a review. Eng Comput 9(1):3–37

    Article  MathSciNet  Google Scholar 

  2. Zhong Z-H, Mackerle J (1994) Contact-impact problems: a review with bibliography. Appl Mech Rev 47(2):55

    Article  Google Scholar 

  3. Bourago NG, Kukudzhanov VN (2005) A review of contact algorithms. Mech Solids 40(1):35–71

    Google Scholar 

  4. Laursen TA (2002) Computational contact and impact mechanics. Springer, Berlin

    MATH  Google Scholar 

  5. Wriggers P (2002) Computational contact mechanics. Wiley, New York

    MATH  Google Scholar 

  6. Goudreau GL, Hallquist JO (1982) Recent developments in large-scale finite element Lagrangian hydrocode technology. Comput Methods Appl Mech Eng 33:725–757

    Article  MathSciNet  MATH  Google Scholar 

  7. Hallquist JO, Goudreau GL, Benson DJ (1985) Sliding interfaces with contact-impact in large-scale Lagrangian computations. Comput Methods Appl Mech Eng 51(1–3):107–137

    Article  MathSciNet  MATH  Google Scholar 

  8. Wriggers P, Van Vu T, Stein E (1990) Finite element formulation of large deformation impact-contact problems with friction. Comput Struct 37:319–331

    Article  MATH  Google Scholar 

  9. Carpenter NJ, Taylor RL, Katona MG (1991) Lagrange constraints for transient finite element surface contact. Int J Numer Methods Eng 32(1):103–128

    Article  MATH  Google Scholar 

  10. Belytschko T, Neal MO (1991) Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int J Numer Methods Eng 31:547–572

    Article  MATH  Google Scholar 

  11. Heinstein MW, Attaway SW, Swegle JW, Mello FJ (1992) A general purpose contact detection algorithm for nonlinear structural analysis codes. Technical Report SAND92-2141, Sandia National Lab

  12. Malone JG, Johnson NL (1994) A parallel finite element contact/impact algorithm for non-linear explicit transient analysis: part I—the search algorithm and contact mechanics. Int J Numer Methods Eng 37(4):559–590

    Article  MATH  Google Scholar 

  13. Heinstein MW, Mello FJ, Attaway SW, Laursen TA (2000) Contact-impact modeling in explicit transient dynamics. Comput Methods Appl Mech Eng 187:621–640

    Article  MATH  Google Scholar 

  14. Malone JG, Johnson NL (1994) A parallel finite element contact/impact algorithm for non-linear explicit transient analysis: part II—parallel implementation. Int J Numer Methods Eng 37(4):591–603

    Article  Google Scholar 

  15. Attaway SW, Hendrickson BA, Plimpton SJ, Gardner DR, Vaughan CT, Brown KH, Heinstein MW (1998) A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D. Comput Mech 22:143–159

    Article  MATH  Google Scholar 

  16. Brown K, Attaway S, Plimpton S, Hendrickson B (2000) Parallel strategies for crash and impact simulations. Comput Methods Appl Mech Eng 184:375–390

    Article  MATH  Google Scholar 

  17. Taylor LM, Flanagan DP (1989) Pronto 3d: a three-dimensional transient solid dynamics program. Technical report, Sandia National Labs., Albuquerque

  18. Zywicz E, Puso MA (1999) A general conjugate-gradient-based predictor–corrector solver for explicit finite-element contact. Int J Numer Methods Eng 44(4):439–459

    Article  MATH  Google Scholar 

  19. Johnson GR, Stryk RA (2001) Symmetric contact and sliding interface algorithms for intense impulsive loading computations. Comput Methods Appl Mech Eng 190(35):4531–4549

    Article  MATH  Google Scholar 

  20. Cirak F, West M (2005) Decomposition contact response (DCR) for explicit finite element dynamics. Int J Numer Methods Eng 64(8):1078–1110

    Article  MathSciNet  MATH  Google Scholar 

  21. Attaway SW, Heinstein MW, Swegle JW (1994) Coupling of smooth particle hydrodynamics with the finite element method. Nucl Eng Des 150(2):199–205

    Article  Google Scholar 

  22. De Vuyst T, Vignjevic R, Campbell JC (2005) Coupling between meshless and finite element methods. Int J Impact Eng 31(8):1054–1064

    Article  Google Scholar 

  23. Zhang Z, Qiang H, Gao W (2011) Coupling of smoothed particle hydrodynamics and finite element method for impact dynamics simulation. Eng Struct 33(1):255–264

    Article  Google Scholar 

  24. Long T, Hu D, Yang G, Wan D (2016) A particle-element contact algorithm incorporated into the coupling methods of FEM-ISPH and FEM-WCSPH for FSI problems. Ocean Eng 123(C):154–163

    Article  Google Scholar 

  25. Li S, Liu WK (2004) Meshfree particle methods. Springer, Berlin Heidelberg

    MATH  Google Scholar 

  26. Cueto E, Doblaré M, Gracia L (2000) Imposing essential boundary conditions in the natural element method by means of density-scaled. Int J Numer Methods Eng 49:519–546

    Article  MathSciNet  MATH  Google Scholar 

  27. Arroyo M, Ortiz M (2006) Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. Int J Numer Methods Eng 65:2167–2202

    Article  MathSciNet  MATH  Google Scholar 

  28. Huerta A, Fernández-Méndez S (2000) Enrichment and coupling of the finite element and meshless methods. Int J Numer Methods Eng 48(11):1615–1636

    Article  MATH  Google Scholar 

  29. Taylor G (1948) The use of flat-ended projectiles for determining dynamic yield stress. I. Theoretical considerations. Proc Math Phys Eng Sci 194(1038):289–299

    Article  Google Scholar 

  30. Whiffin AC (1948) The use of flat-ended projectiles for determining dynamic yield stress. II. Tests on various metallic materials. Proc Math Phys Eng Sci 194(1038):300–322

    Article  Google Scholar 

  31. Brünig M, Driemeier L (2007) Numerical simulation of Taylor impact tests. Int J Plast 23(12):1979–2003

    Article  MATH  Google Scholar 

  32. Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: 7th International conference on Ballistics, pp 541–547

  33. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21(1):31–48

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad Politécnica de Madrid, Madrid, Spain

    D. del Pozo & I. Romero

  2. IMDEA Materials Institute, Eric Kandel, 2, Tecnogetafe, 28906, Madrid, Spain

    D. del Pozo & I. Romero

  3. California Institute of Technology, Pasadena, USA

    I. Lopez-Gomez

Authors
  1. D. del Pozo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Lopez-Gomez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Romero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Romero.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix: Flowchart

Appendix: Flowchart

See Fig. 17.

Fig. 17
figure 17

Flowchart of the dynamic update in one time step, including the contact algorithm

Full size image

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

del Pozo, D., Lopez-Gomez, I. & Romero, I. A robust asymmetrical contact algorithm for explicit solid dynamics. Comput Mech 64, 15–32 (2019). https://doi.org/10.1007/s00466-018-1654-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-018-1654-x

Keywords

  • Explicit integration
  • Contact
  • Predictor/corrector scheme
  • Finite elements
  • Meshfree methods