Abstract
A general contact theory for modelling normal contact of non-spherical particles in discrete element modelling is proposed in the current work. It is established based on two principles: (1) the energy-conservation and (2) geometrical considerations, and presented in four theorems. The theorem of Energy Conserving Contact Model states that the normal force must be the gradient of a potential field, when such a potential function is defined, a complete normal contact model will be completely determined. When the potential is a function of the contact volume, a special contact model with clear geometric meanings is developed as described by the theorem of Contact Volume Based Model. Then the contact of any axi-symmetric objects is also addressed through two theorems that reveal a fundamental relationship between the contact point and the contact normal, and offer a simple approach to determine the normal direction based on the contact point and vice versa.
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References
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)
Wriggers, P.: Computational Contact Mechanics, 2nd edn. Springer, Berlin (2006)
Kane, C., Repetto, E.A., Ortiz, M., Marsden, J.E.: Finite element analysis of nonsmooth contact. Comput. Methods Appl. Mech. Eng. 180, 1–26 (1999)
Munjiza, A.: The Combined Finite-Discrete Element Method. Wiley, England (2004)
Cundall, P.A.: Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int. J. Rock Mech. Min. Sci. Geomech. 25, 107–116 (1988)
Shi, G.-H.: Discontinuous deformation analysis—a new model for the statics and dynamics of block systems. Ph.D. thesis, University of California, Berkeley (1988)
Feng, Y.T., Owen, D.R.J.: A 2D polygon/polygon contact model: algorithmic aspects. Int. J. Eng. Comput. 21, 265–277 (2004)
Feng, Y.T., Han, K., Owen, D.R.J.: An energy based polyhedron-to-polyhedron contact model. In: Proceeding of 3rd M.I.T. Conference of Computational Fluid and Solid Mechanics, 14–17 June 2005, pp 210–214. MIT, USA (2005)
Han, K., Feng, Y.T., Owen, D.R.J.: Contact resolution for non-circular discrete objects. Int. J. Numer. Methods Eng. 66(3), 485–501 (2006)
Feng, Y.T., Han, K., Owen, D.R.J.: Energy-conserving contact interaction models for arbitrarily shaped discrete elements. Comput. Methods Appl. Mech. Eng. 205–208, 169–177 (2012)
Feng, Y.T., Han, K., Owen, D.R.J.: A generic contact detection framework for cylindrical particles in discrete element modelling. Comput. Methods Appl. Mech. Eng. (2016, to appear)
Marsden, J., Weinstein, A.: Calculus III, 2nd edn. Springer, New York (1985). ISBN 978-0-387-90985-1
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Feng, Y.T. (2017). A General Contact Theory for Non-spherical Particles. In: Li, X., Feng, Y., Mustoe, G. (eds) Proceedings of the 7th International Conference on Discrete Element Methods. DEM 2016. Springer Proceedings in Physics, vol 188. Springer, Singapore. https://doi.org/10.1007/978-981-10-1926-5_4
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DOI: https://doi.org/10.1007/978-981-10-1926-5_4
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