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

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.

[1]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[2]  W. Goldsmith,et al.  Impact: the theory and physical behaviour of colliding solids. , 1960 .

[3]  H. A. Rothbart,et al.  Mechanical Design and Systems Handbook , 1964 .

[4]  D. T. Greenwood.  Principles of dynamics , 1965 .

[5]  J. L. Meriam.  Statics and dynamics , 1966 .

[6]  Robert F. Steidel,et al.  An introduction to mechanical vibrations , 1971 .

[7]  R. D. Galletly.  Literature Review : Books: AN INTRODUCTION TO MECHANICAL VIBRATIONS Robert F. Steidel, Jr. John Wiley and Sons, Inc. New York, N. Y. (1971) , 1972 .

[8]  K. H. Hunt,et al.  Coefficient of Restitution Interpreted as Damping in Vibroimpact , 1975 .

[9]  J. N. Fawcett,et al.  The oblique impact of elastic spheres , 1976 .

[10]  Kendall E. Atkinson.  An introduction to numerical analysis , 1978 .

[11]  K. Johnson.  One Hundred Years of Hertz Contact , 1982 .

[12]  T. W. Lee,et al.  On The Dynamics of Intermittent-Motion Mechanisms. Part 1: Dynamic Model and Response , 1983 .

[13]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[14]  Ahmed A. Shabana,et al.  A continuous force model for the impact analysis of flexible multibody systems , 1987 .

[15]  H. Movahedi-Lankarani.  Canonical equations of motion and estimation of parameters in the analysis of impact problems. , 1988 .

[16]  Hamid M. Lankarani,et al.  A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems , 1989 .

[17]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[18]  E. J. Haug,et al.  DADS — Dynamic Analysis and Design System , 1990 .

[19]  R. R. Ryan,et al.  ADAMS — Multibody System Analysis Software , 1990 .

[20]  T. Stolarski.  Tribology in Machine Design , 1990 .

[21]  R. Brach,et al.  Mechanical Impact Dynamics: Rigid Body Collisions , 1991 .

[22]  Hamid M. Lankarani,et al.  Continuous contact force models for impact analysis in multibody systems , 1994, Nonlinear Dynamics.

[23]  Friedrich Pfeiffer,et al.  Multibody Dynamics with Unilateral Contacts , 1996 .

[24]  G. Stavroulakis.  Multibody Dynamics with Unilateral Contacts by Friedrich Pfeiffer and Christoph Glocker, Wiley, New York, 1996 , 1998 .

[25]  David E. Orin,et al.  A compliant contact model with nonlinear damping for simulation of robotic systems , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[26]  S J Piazza,et al.  Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. , 2001, Journal of biomechanical engineering.

[27]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

[28]  Inna Sharf,et al.  Literature survey of contact dynamics modelling , 2002 .

[29]  F. Beer.  Vector Mechanics for Engineers: Statics and Dynamics , 2003 .

[30]  J. Ambrósio,et al.  Dynamic Analysis for Planar Multibody Mechanical Systems with Lubricated Joints , 2004 .

[31]  Benjamin J Fregly,et al.  Multibody dynamic simulation of knee contact mechanics. , 2004, Medical engineering & physics.

[32]  John McPhee,et al.  A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction , 2004 .

[33]  Gerhard Hippmann,et al.  An Algorithm for Compliant Contact Between Complexly Shaped Bodies , 2004 .

[34]  I. Sharf,et al.  A contact force solution for non-colliding contact dynamics simulation , 2006 .

[35]  R. Aspden,et al.  Impact testing to determine the mechanical properties of articular cartilage in isolation and on bone , 2008, Journal of materials science. Materials in medicine.

[36]  P. Flores.  Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies , 2008 .

[37]  Shlomo Djerassi.  Collision with friction; Part B: Poisson’s and Stornge’s hypotheses , 2008 .

[38]  S. Djerassi.  Collision with friction; Part A: Newton’s hypothesis , 2009 .

[39]  Paulo Veríssimo,et al.  Development of generic multibody road vehicle models for crashworthiness , 2008 .

[40]  Yunqing Zhang,et al.  Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints , 2009 .

[41]  Jorge Ambrósio,et al.  Improved bushing models for general multibody systems and vehicle dynamics , 2009 .

[42]  Hongping Zhu,et al.  A note on the Hertz contact model with nonlinear damping for pounding simulation , 2009 .

[43]  Chang-Wan Kim,et al.  An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry , 2009 .

[44]  Roy Featherstone,et al.  A Study of Soft Contact Models in Simulink , 2009 .

[45]  Alan Bowling,et al.  Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction , 2009 .

[46]  Jorge Ambrósio,et al.  Sensitivity of a vehicle ride to the suspension bushing characteristics , 2009 .

[47]  Paulo Flores,et al.  Modeling and simulation of wear in revolute clearance joints in multibody systems , 2009 .

[48]  Jorge Ambrósio,et al.  Development of a planar multibody model of the human knee joint , 2010 .

[49]  Paulo Flores.  Mubodyna - dynamic analysis of multibody systems: a fortran program for dynamic analysis of planar multibody systems: user’s manual version 1.0 , 2010 .

[50]  Yunqing Zhang,et al.  Simulation of planar flexible multibody systems with clearance and lubricated revolute joints , 2010 .

[51]  Christoph Glocker,et al.  Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach , 2010 .

[52]  Dan B. Marghitu,et al.  Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres , 2010 .

[53]  P. Flores,et al.  Strain shielding in distal femur after patellofemoral arthroplasty under different activity conditions. , 2010, Journal of biomechanics.

[54]  Jorge Ambrósio,et al.  On the contact detection for contact-impact analysis in multibody systems , 2010 .

[55]  Jorge Martins,et al.  Evaluation of the contact forces developed in the lower limb/orthosis interface for comfort design , 2010 .

[56]  Marcus G Pandy,et al.  Simultaneous prediction of muscle and contact forces in the knee during gait. , 2010, Journal of biomechanics.

[57]  W. Sawyer,et al.  Analysis of planar multibody systems with revolute joint wear , 2010 .

[58]  Daniel Dopico,et al.  Dealing with multiple contacts in a human-in-the-loop application , 2011 .