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Elastic and Plastic Collision Comparison Using Finite Element Method

Authors: Gustavo Rodrigues, Hans Weber, Larissa Driemeier


The prevision of post-impact conditions and the behavior of the bodies during the impact have been object of several collision models. The formulation from Hertz’s theory is generally used dated from the 19th century. These models consider the repulsive force as proportional to the deformation of the bodies under contact and may consider it proportional to the rate of deformation. The objective of the present work is to analyze the behavior of the bodies during impact using the Finite Element Method (FEM) with elastic and plastic material models. The main parameters to evaluate are, the contact force, the time of contact and the deformation of the bodies. An advantage of using the FEM approach is the possibility to apply a plastic deformation to the model according to the material definition: there will be used Johnson–Cook plasticity model whose parameters are obtained through empirical tests of real materials. This model allows analyzing the permanent deformation caused by impact, phenomenon observed in real world depending on the forces applied to the body. These results are compared between them and with the model-based Hertz theory.

Keywords: Collision, finite element method, Hertz’s Theory, impact models.

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[1] H. Hertz, “On the Contact of Rigid Elastic Solids and on Hardness”. Journal fur die Reine und Angewandte Mathematik 94:156-71, 1882.
[2] A. B. Stevens and C. M. Hrenya, “Comparison of soft-sphere models to measurements of collision properties during normal impacts”. Powder Technology, v. 154, n. 2-3, p. 99-109, 2005.
[3] G. Kuwabara and K. Kono, “Restitution coefficient in a collision between two spheres”. Jpn. J. Appl. Phys., Part 1 26, 1230, 1987.
[4] K. H. Hunt and F. R. E. Crossley, “Coefficient of restitution interpreted as damping in vibroimpact”. Journal of Applied Mechanics - Transactions of the ASME, p. 440 to 445, June, 1968.
[5] K. Mehraby, H. K. Beheshti and M. Poursina, “Impact noise radiated by collision of two spheres: Comparison between numerical simulations, experiments and analytical results”. Journal of mechanical science and technology, v. 25, n. 7, p. 1675, 2011.
[6] L. Vu-Quoc, X. Zhang and L. Lesburg. “Normal and tangential force–displacement relations for frictional elasto-plastic contact of spheres”. International journal of solids and structures, v. 38, n. 36-37, p. 6455-6489, 2001.
[7] C. Wu, L. Li, and C. Thornton. “Energy dissipation during normal impact of elastic and elastic–plastic spheres”. International Journal of Impact Engineering, v. 32, n. 1-4, p. 593-604, 2005.
[8] I. Altaparmakov, "Modeling of an Elastic Sphere Colliding Against an Elastic‐plastic Plate Under a Continuing Action of an Outer Force." AIP Conference Proceedings. Vol. 1301. No. 1. AIP, 2010.
[9] L. D. Landau and E. M. Lifshitz. “Course of theoretical physics. Theory of Elasticity”. Vol 7. Institute of Physical Problems, USSR Academy of Sciences, 1975.
[10] D. R. Lovett; K. M. Moulding and S. Anketell-Jones. “Collisions between elastic bodies: Newton's cradle”. European Journal of Physics, v. 9, n. 4, p. 323, 1988.
[11] A. B. Stevens and C. M. Hrenya. “Comparison of soft-sphere models to measurements of collision properties during normal impacts”. Powder Technology, v. 154, n. 2-3, p. 99-109, 2005.
[12] H. Sadeghinia, M. R. Razfar and J. Takabi. “2D Finite Element Modeling of Face Milling with Damage Effects”. In: 3rd WSEAS international conference on applied and theoretical mechanics, Spain, 2007.
[13] P. Patricio. “The Hertz contact in chain elastic collisions”. American journal of physics, v. 72, n. 12, p. 1488-1491, 2004.