An Internal Variable Update Procedure for the Treatment of Inelastic Material Behavior within an ALE-Description of Rolling Contact


Article Preview

Arbitrary Lagrangian Eulerian (ALE) methods provide a well established basis for the numerical analysis of rolling contact problems, the theoretical framework is well developed for elastic constitutive behavior. Special measures are necessary for the treatment of history dependent and explicitly time dependent material behavior within the relative–kinematic ALE– picture. In this presentation a fractional step approach is suggested for the integration of the evolution equation for internal variables. A Time–Discontinuous Galerkin (TDG) method is introduced for the numerical solution of the related advection equations. The advantage of TDG–methods in comparison with more traditional integration schemes is studied in detail. The practicability of the approach is demonstrated by the finite element analysis of rolling tires.



Edited by:

Tadeusz Uhl and Andrzej Chudzikiewicz




M. Ziefle and U. Nackenhorst, "An Internal Variable Update Procedure for the Treatment of Inelastic Material Behavior within an ALE-Description of Rolling Contact", Applied Mechanics and Materials, Vol. 9, pp. 157-171, 2008

Online since:

October 2007




[1] ABAQUS/Standard Theory Manual, Version 6. 6, (2006).

[2] R. E. Bauer: Discontinuous Galerkin Methods for ordinary differential equations, University of Northern Colorado, (1995).

[3] A. Becker and B. Seifert: Simulation of wear with a FE Tyre model using a steady state rolling formulation. In M. H. Aliabadi and A. Samartin (eds. ): Computational Methods in Contact Mechanics III, CMP, Southamption, Boston, 119-128, (1997).

[4] D. Benson: An efficient accurate simple ALE method for nonlinear finite element programs. Computer Methods in Applied Mechanics and Engineering, 72, 305-350, (1989).

DOI: 10.1016/0045-7825(89)90003-0

[5] B. Cockburn, G. Karniadakis and C. -W. Shu: The development of discontinuous galerkin methods. In Cockburn (ed. ): Discontinuous Galerkin Methods, Springer, (1999).

DOI: 10.1007/978-3-642-59721-3_1

[6] L. O. Faria, J. T. Oden, B. Yavari, W. Tworzydlo, J. M. Bass and E. B. Becker: Tire modeling by finite elements. Tire Science & Technology, 20, 33-56, (1992).

DOI: 10.2346/1.2139507

[7] S. Godunov: Finite difference method for numerical computation of discontinuous solutions of the equation of fluid dynamics. Math. Sbornik, 47, 272-306, (1959).

[8] M. Kaliske, D. Zheng, M. Andre and C. Bertram: Efficient Steady-State Simulations up to High Speed of Dissipative Tire Chracteristics. Vehicle Systems Dynamics Journal, Supplement 40, 175-194, (2003).

[9] O. Kolditz: Computational Methods in Environmental Fluid Mechanics, Springer, (2002).

[10] U. Nackenhorst: On the finite element analysis of steady state rolling contact. In M. H. Aliabadi and C. A. Brebbia (eds. ): Contact Mechanics - Computational Techniques, CMP, Southamption, Boston, 53-60, (1993).

[11] U. Nackenhorst, The ALE-Formulation of Bodies in Rolling Contact - Theoretical Foundations and Finite Element Approach -. Computer Methods in Applied Mechanics and Engineering. 193, 4299-4322, (2004).

DOI: 10.1016/j.cma.2004.01.033

[12] U. Nackenhorst and M. Ziefle: Finite element modelling of rolling tires. Kautschuk, Gummi, Kunststoffe (KGK), 6, 322-326, (2005).

[13] J. T. Oden and T. L. Lin: On the general rolling contact problem for finite deformations of a viscoelastic cylinder. Computer Methods in Applied Mechanics and Engineering, 57, 297-367, (1986).

DOI: 10.1016/0045-7825(86)90143-x

[14] S. Reese: Thermomechanische Modellierung gummiartiger Polymerstrukturen, Universit¨at Hannover, (2000).

[15] A. Rodriguez-Ferran, F. Casadei and A. Huerta: ALE Stress Update For Transient And Quasistatic Processes. Int. J. Num. Meth. Engng. 43, 241-262, (1998).

DOI: 10.1002/(sici)1097-0207(19980930)43:2<241::aid-nme389>;2-d

[16] F. Shakib and T. J. R. Hughes: A new finite element formulation for computational fluid dynamics: IX. Fourier analysis of space-time Galerkin/least-squares algorithms. Computer Methods in Applied Mechanics and Engineering, 87, 35-58, (1991).

DOI: 10.1016/0045-7825(91)90145-v

[17] J. C. Simo and T. J. R. Hughes: Computational Inelasticity. Springer, (1998).

[18] C. Stoker: Developments of the Arbitrary Lagrangian-Eulerian Method in non-linear Solid Mechanics, University Twente, (1999).

[19] P. Le Tallec and C. Rahier: Numerical models of steady rolling for non-linear viscoelastic structures in finite deformations. Int. J. Num. Meth. Engng. 37, 1159-1186, (1994).

DOI: 10.1002/nme.1620370705

Fetching data from Crossref.
This may take some time to load.