On the continuous contact force models for soft materials in multibody dynamics.

*(English)*Zbl 1263.70007Summary: A general and comprehensive analysis on the continuous contact force models for soft materials in multibody dynamics is presented throughout this work. The force models are developed based on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process. In a simple way, these contact force models are based on the analysis and development of three main issues: (i) the dissipated energy associated with the coefficient of restitution that includes the balance of kinetic energy and the conservation of the linear momentum between the initial and final instant of contact; (ii) the stored elastic energy, representing part of initial kinetic energy, which is evaluated as the work done by the contact force developed during the contact process; (iii) the dissipated energy due to internal damping, which is evaluated by modeling the contact process as a single degree-of- freedom system to obtain a hysteresis damping factor. This factor takes into account the geometrical and material properties, as well as the kinematic characteristics of the contacting bodies. This approach has the great merit that can be used for contact problems involving materials with low or moderate values of coefficient of restitution and, therefore, accommodate high amount of energy dissipation. In addition, the resulting contact force model is suitable to be included into the equations of motion of a multibody system and contributes to their stable numerical resolution. A demonstrative example of application is used to provide the results that support the analysis and discussion of procedures and methodologies described in this work.

##### Keywords:

contact force; continuous analysis; soft materials; coefficient of restitution; elastic energy; internal damping; multibody dynamics##### Software:

MUBODYNA
PDF
BibTeX
XML
Cite

\textit{P. Flores} et al., Multibody Syst. Dyn. 25, No. 3, 357--375 (2011; Zbl 1263.70007)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Stolarsky, T.A.: Tribology in Machine Design. Butterworth-Heinemann, Stoneham-London (1990) |

[2] | Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies. Lecture Notes in Applied and Computational Mechanics, vol. 34. Springer, Berlin (2008) · Zbl 1142.70001 |

[3] | Johnson, K.L.: One hundred years of Hertz contact. Proc. Inst. Mech. Eng. 196, 363–378 (1982) |

[4] | Goldsmith, W.: Impact, The Theory and Physical Behaviour of Colliding Solids. Edward Arnold, Sevenoaks (1960) · Zbl 0122.42501 |

[5] | Brach, R.M.: Mechanical Impact Dynamics, Rigid Body Collisions. Wiley, New York (1991) |

[6] | Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley, New York (1996) · Zbl 0922.70001 |

[7] | Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1999) · Zbl 0599.73108 |

[8] | Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2000) · Zbl 0961.74002 |

[9] | Wriggers, P.: Computational Contact Mechanics, 2nd edn. Springer, Berlin (2006) · Zbl 1104.74002 |

[10] | Hippmann, G.: An algorithm for compliant contact between complexly shaped bodies. Multibody Syst. Dyn. 12, 345–362 (2004) · Zbl 1174.70309 |

[11] | Gonthier, Y., McPhee, J., Lange, C., Piedboeuf, J.-C.: A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody Syst. Dyn. 11, 209–233 (2004) · Zbl 1143.74344 |

[12] | Flores, P., Ambrósio, J., Claro, J.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12, 47–74 (2004) · Zbl 1174.70307 |

[13] | Sharf, I., Zhang, Y.: A contact force solution for non-colliding contact dynamics simulation. Multibody Syst. Dyn. 16, 263–290 (2006) · Zbl 1207.70006 |

[14] | Sousa, L., Veríssimo, P., Ambrósio, J.: Development of generic multibody road vehicle models for crashworthiness. Multibody Syst. Dyn. 19, 133–158 (2008) · Zbl 1210.70017 |

[15] | Djerassi, S.: Collision with friction; Part A: Newton’s hypothesis. Multibody Syst. Dyn. 21, 37–54 (2009) · Zbl 1163.70007 |

[16] | Djerassi, S.: Collision with friction; Part B: Poisson’s and Stronge’s hypotheses. Multibody Syst. Dyn. 21, 55–70 (2009) · Zbl 1163.70008 |

[17] | Bowling, A., Flickinger, D.M., Harmeyer, S.: Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction. Multibody Syst. Dyn. 22, 27–45 (2009) · Zbl 1189.70006 |

[18] | Dopico, D., Luaces, A., Gonzalez, M., Cuadrado, J.: Dealing with multiple contacts in a human-in-the-loop application. Multibody Syst. Dyn. doi: 10.1007/s11044-010-9230-y (2011) |

[19] | Ambrósio, J., Veríssimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. 22, 341–365 (2009) · Zbl 1272.70034 |

[20] | Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L., Sawyer, W.G.: Analysis of planar multibody systems with revolute joint wear. Wear 268(5–6), 643–652 (2010) |

[21] | Choi, J., Ryu, H.S., Kim, C.H., Choi, J.H.: An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry. Multibody Syst. Dyn. 23, 99–120 (2010) · Zbl 1192.70005 |

[22] | Flores, P., Leine, R., Glocker, C.: Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Syst. Dyn. 23, 165–190 (2010) · Zbl 1219.70014 |

[23] | Gilardi, G., Sharf, I.: Literature survey of contact dynamics modeling. Mech. Mach. Theory 37, 1213–1239 (2002) · Zbl 1062.70553 |

[24] | Shabana, A.A.: Dynamics of Multibody Systems. Wiley, New York (1989) · Zbl 0698.70002 |

[25] | Ryan, R.R.: ADAMS-Multibody System Analysis Software, Multibody Systems Handbook. Springer, Berlin (1990) |

[26] | Smith, R.C., Haug, E.J.: DADS-Dynamic Analysis and Design System, Multibody Systems Handbook. Springer, Berlin (1990) |

[27] | Visual NASTRAN 4D, MSC Software (2002) |

[28] | Lee, T.W., Wang, A.C.: On the dynamics of intermittent-motion mechanisms, part 1: dynamic model and response. J. Mech. Transm. Autom. Des. 105, 534–540 (1983) |

[29] | Jackson, R.L., Green, I., Marghitu, D.B.: Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres. Nonlinear Dyn. 60(3), 217–229 (2010) · Zbl 1189.74091 |

[30] | Barkan, P.: Impact design. In: Mechanical Design and Systems Handbook, McGraw-Hill, New York (1974). Section 31 |

[31] | Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 7, 440–445 (1975) |

[32] | Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994) |

[33] | Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112, 369–376 (1990) |

[34] | Shivaswamy, S.: Modeling contact forces and energy dissipation during impact in multibody mechanical systems. Ph.D. Dissertation, Wichita State University, Wichita, Kansas (1997) |

[35] | Machado, M., Flores, P., Claro, J.C.P., Ambrósio, J., Silva, M., Completo, A., Lankarani, H.M.: Development of a planar multibody model of the human knee joint. Nonlinear Dyn. 60(3), 459–478 (2010) · Zbl 1189.92008 |

[36] | Meireles, S., Completo, A., Simões, J.A., Flores, P.: Strain shielding in distal femur after patellofemoral arthroplasty under different activity conditions. J. Biomech. 43(3), 477–484 (2010) |

[37] | Bei, Y., Fregly, B.J.: Multibody dynamic simulation of knee contact mechanics. Med. Eng. Phys. 26, 777–789 (2004) |

[38] | Lin, Y.-C., Walter, J.P., Banks, S.A., Pandy, M.G., Fregly, B.J.: Simultaneous prediction of muscle and contact forces in the knee during gait. J. Biomech. 43, 945–952 (2010) |

[39] | Burgin, L.V., Aspen, R.M.: Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone. J. Mater. Sci., Mater. Med. 19, 703–711 (2008) |

[40] | Piazza, S.J., Delp, S.L.: Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. J. Biomech. Eng. 123, 599–606 (2001) |

[41] | Silva, P.C., Silva, M.T., Martins, J.M.: Evaluation of the contact forces developed in the lower limb/orthosis interface for comfort design. Multibody Syst. Dyn. 24, 367–388 (2010) · Zbl 1376.70018 |

[42] | Lankarani, H.M.: Canonical equations of motion and estimation of parameters in the analysis of impact problems. Ph.D. Dissertation, University of Arizona, Tucson, Arizona (1988) |

[43] | Ye, K., Li, L., Zhu, H.: A note on the Hertz contact model with nonlinear damping for pounding simulation. Earthquake Eng. Struct. Dyn. 38, 1135–1142 (2009) |

[44] | Hertz, H.: On the contact of solids–on the contact of rigid elastic solids and on hardness. In: Miscellaneous Papers, pp. 146–183. Macmillan and Co., London (1896) (Translated by D.E. Jones and G.A. Schott) |

[45] | Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw Hill, New York (1970) · Zbl 0266.73008 |

[46] | Khulief, Y.A., Shabana, A.A.: A continuous force model for the impact analysis of flexible multibody systems. Mech. Mach. Theory 22, 213–224 (1987) |

[47] | Marhefka, D.W., Orin, D.E.: A compliant contact model with nonlinear damping for simulation of robotic systems. IEEE Trans. Syst. Man Cybern., Part A, Syst. Humans 29(6), 566–572 (1999) |

[48] | Bibalan, P.T., Featherstone, R.: A study of soft contact models in simulink. In: Proceedings of the Australasian Conference on Robotics and Automation (ACRA), 2–4 December 2009, Sydney, Australia (2009). 8 p. |

[49] | Flores, P.: Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44(6), 1211–1222 (2009) · Zbl 1178.70022 |

[50] | Tian, Q., Zhang, Y., Chen, L., Flores, P.: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87(13–14), 913–929 (2009) |

[51] | Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contact-impact force model on the dynamic response of multibody systems. Proc. Inst. Mech. Eng., Proc. Part K, J. Multi-Body Dyn. 220(1), 21–34 (2006) |

[52] | Tian, Q., Zhang, Y., Chen, L., Yang, J.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60(4), 489–511 (2010) · Zbl 1194.70013 |

[53] | Ambrósio, J., Veríssimo, P.: Sensitivity of a vehicle ride to the suspension bushing characteristics. J. Mech. Sci. Technol. 23, 1075–1082 (2009) |

[54] | Beer, F.B., Johnston, E.R.: Vector mechanics for engineers. Statics and Dynamics (1997) |

[55] | Greenwood, D.T.: Principles of Dynamics. Englewood Cliffs, Prentice Hall (1965) |

[56] | Maw, N., Barber, J.R., Fawcett, J.N.: The oblique impact of elastic spheres. Wear, 101–114 (1975) |

[57] | Zukas, J.A., Nicholas, T., Greszczuk, L.B., Curran, D.R.: Impact Dynamics. Wiley, New York (1982) |

[58] | Hartog, J.P.: Mechanical Vibrations. Dover, New York (1985) · JFM 66.1361.03 |

[59] | Steidel, R.F.: An Introduction to Mechanical Vibrations, 3rd edn. Wiley, New York (1989) · Zbl 0747.73003 |

[60] | Flores, P.: Contact-impact analysis in multibody systems based on the nonsmooth dynamics approach. Post Doctoral Report, ETH-Zurich, Switzerland (2009) |

[61] | Flores, P., Ambrósio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24(1), 103–122 (2010) · Zbl 1375.70021 |

[62] | Flores, P.: MUBODYNA–A FORTRAN program for dynamic analysis of planar multibody systems. University of Minho, Guimarães, Portugal (2010) |

[63] | Piskounov, N.: Cálculo Diferencial e Integral. Edições Lopes da Silva, Porto, Portugal (1990) |

[64] | Atkinson, K.A.: An Introduction to Numerical Analysis, 2nd edn. Wiley, New York (1989) · Zbl 0718.65001 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.