Elastoplastic phenomena in multibody impact dynamics

Impact processes are often implemented in multibody system dynamics using the coefficient of restitution representing the energy loss during impact. In this paper a multiscale simulation approach is used in order to evaluate the coefficient of restitution numerically including the phenomena of wave propagation and, in particular, plastic deformation. For the numerical investigation four different models are presented in the following: a completely nonlinear finite element (FE) model, a modal model of the elastic parts of the body combined with a nonlinear FE model of its contact region, a modal model with quasi-static FE contact, and a modal model with an elastostatic Hertzian contact law. The modal models with FE contact are very efficient for investigating repeated impacts of the bodies including the deformation history of the contact region. Simulations and experiments of repeated frictionless impacts on aluminum bodies show, due to plastic deformation of the contact area, an increase of the coefficient of restitution with increasing numbers of impacts. Finally, plastic deformation does no longer spread out and a stationary value is reached. In the stationary phase impacts on a compact body shows no energy loss, while for impacts on a slender body the remaining energy loss during impact is purely due to wave propagation phenomena. Simulations show a strong dependency of the coefficient of restitution on the yield stress of the used material, that is also verified by experiments.

[1]  Peter Eberhard,et al.  Numerical and Experimental Investigation of Radial Impacts on a Half-Circular Plate , 2003 .

[2]  Werner Schiehlen,et al.  Three Approaches for Elastodynamic Contact in Multibody Systems , 2004 .

[3]  L. Vu-Quoc,et al.  An elastoplastic contact force–displacement model in the normal direction: displacement–driven version , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  S. Bodner,et al.  Experimental and Theoretical Investigation of the Plastic Deformation of Cantilever Beams Subjected to Impulsive Loading , 1962 .

[5]  G. Gladwell,et al.  Solid mechanics and its applications , 1990 .

[6]  Ahmet S. Yigit.  On the Use of an Elastic-Plastic Contact Law for the Impact of a Single Flexible Link , 1995 .

[7]  J. O´Rourke,et al.  Computational Geometry in C: Arrangements , 1998 .

[8]  Peter Wriggers,et al.  A note on the optimum choice for penalty parameters , 1987 .

[9]  Peter Eberhard,et al.  Numerical and experimental evaluation of the coefficient of restitution for repeated impacts , 2005 .

[10]  L. Vu-Quoc,et al.  Normal and tangential force-displacement relations for frictional elasto-plastic contact of spheres , 2001 .

[11]  S. C. Hunter.  Energy absorbed by elastic waves during impact , 1957 .

[12]  Peter Eberhard,et al.  Comparison of Analytical and Experimental Results for Longitudinal Impacts on Elastic Rods , 2003 .

[13]  Xiang Zhang,et al.  A method to extract the mechanical properties of particles in collision based on a new elasto-plastic normal force-displacement model , 2002 .

[14]  X. Zhang,et al.  Efficient and Accurate Collision Detection for Granular Flow Simulation , 1998, Graph. Model. Image Process..

[15]  W. Schiehlen,et al.  Multi-time scale simulation for impact systems: from wave propagation to rigid-body motion , 2003 .

[16]  Ch. Tsakmakis,et al.  A Finite Element Analysis of the Effect of Hardening Rules on the Indentation Test , 1998 .

[17]  Peter Eberhard,et al.  Contact Simulation for Many Particles Considering Adhesion , 2003 .

[18]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[19]  L. Vu-Quoc,et al.  Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions , 2002 .

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

[21]  C. Thornton,et al.  Rebound behaviour of spheres for plastic impacts , 2003 .

[22]  C. V. Raman,et al.  On some applications of Hertz's theory of impact , 1920 .

[23]  Peter Wriggers,et al.  Nichtlineare Finite-Element-Methoden , 2001 .

[24]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[25]  David R. Owen,et al.  Finite Elements in Plasticity , 1980 .

[26]  J. Reed.  Energy losses due to elastic wave propagation during an elastic impact , 1985 .

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

[28]  R. Taylor,et al.  A mixed formulation for the finite element solution of contact problems , 1992 .

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

[30]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .

[31]  C. Brennen,et al.  Measurements of Solid Spheres Bouncing Off Flat Plates , 1990 .

[32]  Werner Schiehlen,et al.  Unilateral Contacts in Machine Dynamics , 1999 .

[33]  Xiang Zhang,et al.  An accurate tangential force-displacement model for granular-flow simulations: contacting spheres with plastic deformation, force-driven formulation , 2004 .

[34]  C. Thornton.  Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres , 1997 .

[35]  C. Glocker.  On frictionless impact models in rigid-body systems , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[36]  K. Graff.  Wave Motion in Elastic Solids , 1975 .

[37]  K. Bathe.  Finite Element Procedures , 1995 .