Multibody System Dynamics

, Volume 25, Issue 3, pp 357–375 | Cite as

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

  • Paulo Flores
  • Margarida Machado
  • Miguel T. Silva
  • Jorge M. Martins


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.


Contact force Continuous analysis Soft materials Coefficient of restitution Elastic energy Internal damping Multibody dynamics 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Paulo Flores
    • 1
  • Margarida Machado
    • 1
  • Miguel T. Silva
    • 2
  • Jorge M. Martins
    • 2
  1. 1.Mechanical Engineering DepartmentUniversity of MinhoGuimarãesPortugal
  2. 2.IDMEC/Instituto Superior TécnicoUniversidade Técnica de LisboaLisboaPortugal

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