Skip to main content
SpringerLink
Log in

A constraint-based collision model for Cosserat rods

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The present paper provides a collision model for Cosserat rods, able to represent a very general collision response, including frictional effects as well as multiple simultaneous collisions of a large number of rods. The proposed collision model falls into the category of constraint-based collision models. This concept is extended to a general class of objects sharing properties of rigid and deformable bodies, here undertaken for viscoelastic Cosserat rods. The collision constraints are imposed by collision impulses added to the external loads of the equations of motion of the colliding objects. No iterations between the equations of motion and the collision model are required. Both parts are executed in a staggered manner, so that the collision model is well separated from the equations of motion. Hence, existing solvers for Cosserat rods or similar objects can easily be extended, so that the range of application is significantly enlarged to the collisional regime. Extensive validations are presented using various test cases, ranging from a collision of a single rod with a wall to more realistic configurations with multiple simultaneous collisions of numerous rods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Gere, J., Timoshenko, S. (eds.): Mechanics of Materials, vol. 6. PWS Publishing Company, Boston (1997)

    Google Scholar 

  2. Antman, S., Marsden, J., Sirovich, L. (eds.): Nonlinear Problems of Elasticity, vol. 107. Springer, Berlin (2004)

    Google Scholar 

  3. Simo, J.: A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49, 55–70 (1985)

    Article  MATH  Google Scholar 

  4. Auricchio, F., Carotenuto, P., Reali, A.: On the geometrically exact beam model: a consistent, effective and simple derivation from three-dimensional finite-elasticity. Int. J. Solids Struct. 45, 4766–4781 (2008)

    Article  MATH  Google Scholar 

  5. Lang, H., Linn, J., Arnold, M.: Multi-body dynamics simulation of geometrically exact cosserat rods. Multibody Syst. Dyn. 25(3), 285–312 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Duriez, C., Dubois, F., Kheddar, A., Andriot, C.: Realistic haptic rendering of interacting deformable objects in virtual environments. IEEE Trans. Vis. Comput. Graph. 12, 36–47 (2006)

    Article  Google Scholar 

  7. Spillmann, J.: Corde: Cosserat rod elements for the animation of interacting elastic rods. Ph.D. thesis, Albert-Ludwigs-Universität Freiburg (2008)

  8. Guendelman, E., Bridson, R., Fedkiw, R.: Nonconvex rigid bodies with stacking. ACM Trans. Graph. 22(3), 871–878 (2003)

    Article  Google Scholar 

  9. Mirtich, B., Canny, J.: Impulse-based simulation of rigid bodies. In: Symposium on Interactive 3D Graphics, I3D ’95, p. 181 (1995)

  10. Kempe, T., Fröhlich, J.: Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids. J. Fluid Mech. 709, 445–489 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lenoir, J., Meseure, P., Grisoni, L., Chaillou, C.: Surgical thread simulation. Model. Simul. Comput.-Aided Med. Surg. 12, 102–107 (2002)

    MATH  Google Scholar 

  12. Phillips, J., Ladd, A., Kavraki, L.: Surgical thread simulation. In: International Conference on Robotics and Automation, pp. 841–846 (2002)

  13. Bridson, R., Fedkiw, R., Anderson, J.: Robust treatment of collisions, contact and friction for cloth animation. In: 29th Annual Conference on Computer Graphics and Interactive Techniques, pp. 594–603 (2002)

  14. Thomaszewski, B., Wacker, M., Straer, W.: A consistent bending model for cloth simulation with corotational subdivision finite elements. In: ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 107–116 (2006)

  15. Stumpp, T., Spillmann, J., Becker, M., Teschner, M.: A geometric deformation model for stable cloth simulation. In: Workshop on Virtual Reality Interaction and Physical Simulation, pp. 39–46 (2008)

  16. Choe, B., Choi, M., Ko, H.-S.: Simulating complex hair with robust collision handling. In: ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 153–160 (2005)

  17. Bertails, F.: Linear time super-helices. Comput. Graph. Forum 28, 417–426 (2009)

    Article  Google Scholar 

  18. Vetter, R., Wittel, F., Stoop, N., Herrmann, H.: Finite element simulation of dense wire packings. Eur. J. Mech. A/Solids 37, 160–171 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Bertails, F., Audoly, B., Cani, M.-P., Querleux, B., Leroy, F., Lévêque, J.-L.: Super-helices for predicting the dynamics of natural hair. ACM Trans. Graph. 25, 1180–1187 (2006)

    Article  Google Scholar 

  20. Spillmann, J., Teschner, M.: Corde: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects. In: ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 63–72 (2007)

  21. Spillmann, J., Becker, M., Teschner, M.: Non-iterative computation of contact forces for deformable objects. J. WSCG 15(1–3), 33–40 (2007)

    Google Scholar 

  22. Bergou, M., Wardetzky, M., Robinson, S., Audoly, B., Grinspun, E.: Discrete elastic rods. ACM Trans. Graph. 27, 63:1–63:12 (2008)

    Article  Google Scholar 

  23. Dorai, F., Teixeira, C., Rolland, M., Climent, E., Marcoux, M., Wachs, A.: Fully resolved simulations of the flow through a packed bed of cylinders: effect of size distribution. Chem. Eng. Sci. 129, 180–192 (2015)

    Article  Google Scholar 

  24. Bender, J., Schmitt, A.: Constraint-based collision and contact handling using impulses. In: 19th International Conference on Computer Animation and Social Agents, pp. 3–11 (2006)

  25. Tonge, R., Benevolenski, F., Voroshilov, A.: Mass splitting for jitter-free parallel rigid body simulation. ACM Trans. Graph. 31(4), 105:1–105:8 (2012)

    Article  Google Scholar 

  26. Heidelberger, B., Teschner, M., Keiser, R., Müller, M., Gross, M.: Consistent penetration depth estimation for deformable collision response. In: Vision, Modeling and Visualization, pp. 339–346 (2004)

  27. Drumwright, E.: A fast and stable penalty method for rigid body simulation. IEEE Trans. Vis. Comput. Graph. 14, 231–240 (2008)

    Article  Google Scholar 

  28. Tang, M., Manocha, D., Otaduy, M., Tong, R.: Continuous penalty forces. ACM Trans. Graph. 31, 107:1–107:9 (2012)

    Article  Google Scholar 

  29. Bîrsan, M., Altenbach, H.: Theory of thin thermoelastic rods made of porous materials. Arch. Appl. Mech. 81(10), 1365–1391 (2011)

    Article  MATH  Google Scholar 

  30. Dörlich, V., Linn, J., Scheffer, T., Diebels, S.: Towards viscoplastic constitutive models for cosserat rods. Arch. Mech. Eng. 63(2), 215–230 (2016)

    Article  Google Scholar 

  31. Mirtich, B.: Impulse-based dynamic simulation of rigid body systems. Ph.D. thesis, University of California at Berkeley (1996)

  32. Ray, S., Kempe, T., Fröhlich, J.: Efficient modelling of particle collisions using a non-linear viscoelastic contact force. Int. J. Multiph. Flow 76, 101–110 (2015)

    Article  MathSciNet  Google Scholar 

  33. Baraff, D.: Non-penetrating rigid body simulation. In: Eurographics 93 State of the Art Reports, pp. 1–23 (1993)

  34. Baraff, D.: Fast contact force computation for nonpenetrating rigid bodies. In: 21st Annual Conference on Computer Graphics and Interactive Techniques, pp. 23–34 (1994)

  35. Baraff, D.: Coping with friction for non-penetrating rigid body simulation. In: 18th Annual Conference on Computer Graphics and Interactive Techniques, pp. 31–41 (1991)

  36. Brenan, K., Campbell, S., Petzold, L. (eds.): Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, vol. 2. Society for Industrial and Applied Mathematics, Philadelphia (1996)

    MATH  Google Scholar 

  37. Kaufman, D., Tamstorf, R., Smith, B., Aubry, J.-M., Grinspun, E.: Adaptive nonlinearity for collisions in complex rod assemblies. ACM Trans. Graph. 33(4), 123:1–123:12 (2014)

    Article  Google Scholar 

  38. Acary, V., Brogliato, B.: Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics. Vol. 35 of Lecture Notes in Applied and Computational Mechanics. Springer, Berlin (2008)

    MATH  Google Scholar 

  39. Derouet-Jourdan, A., Bertails-Descoubes, F., Daviet, G., Thollot, J.: Inverse dynamic hair modeling with frictional contact. ACM Trans. Graph. 32(6), 159:1–159:10 (2013)

    Article  MATH  Google Scholar 

  40. Matthies, H., Niekamp, R., Steindorf, J.: Algorithms for strong coupling procedures. Comput. Methods Appl. Mech. Eng. 195(17), 2028–2049 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  41. Markert, B. (ed.): Weak or Strong: On Coupled Problems in Continuum Mechanics, vol. 1. Universitt Stuttgart Inst. f. Mechanik (Bauwesen), Stuttgart (2010)

    Google Scholar 

  42. Fadlun, E., Verzicco, R., Orlandi, P., Mohd-Yusof, J.: Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  43. Tschisgale, S., Kempe, T., Fröhlich, J.: A non-iterative immersed boundary method for spherical particles of arbitrary density ratio. J. Comput. Phys. 339, 432–452 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  44. van den Bergen, G. (ed.): Collision Detection in Interactive 3D Environments. Morgan Kaufmann Publishers, Los Altos (2004)

    Google Scholar 

  45. Sutherland, I., Hodgman, G.: Reentrant polygon clipping. Commun. ACM 17(1), 32–42 (1974)

    Article  MATH  Google Scholar 

  46. Giang, T., Bradshaw, C.O.G.: Complementarity based multiple point collision resolution. In: 20th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’93, pp. 313–320 (2003)

  47. Sankin, Y., Yuganova, N.: Longitudinal vibrations of elastic rods of stepwise-variable cross-section colliding with a rigid obstacle. J. Appl. Math. Mech. 65(3), 427–433 (2001)

    Article  MATH  Google Scholar 

  48. Nepf, H.M.: Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44, 123–142 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Part of the work was funded by the DFG-ANR project EsCaFlex. The stay of L. Thiry at ISM, TU Dresden, was financed by École Polytechnique. Computing time was provided by ZIH, TU Dresden.

Author information

Authors and Affiliations

  1. Institut für Strömungsmechanik, Technische Universität Dresden, George-Bähr Str. 3c, 01062, Dresden, Germany

    Silvio Tschisgale, Louis Thiry & Jochen Fröhlich

  2. École Polytechnique, Route de Saclay, 91128, Palaiseau, France

    Louis Thiry

Authors
  1. Silvio Tschisgale
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Louis Thiry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jochen Fröhlich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Silvio Tschisgale.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tschisgale, S., Thiry, L. & Fröhlich, J. A constraint-based collision model for Cosserat rods. Arch Appl Mech 89, 167–193 (2019). https://doi.org/10.1007/s00419-018-1458-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-018-1458-7

Keywords

Search

Navigation