Development of mathematical model of a radial solid metal cord tyre with hyperelastic properties of rubber taken into account

Authors: Odintsov O.A. Published: 11.09.2013
Published in issue: #3(92)/2013  


Category: Simulation of Processes  
Keywords: finite element method, hyperelasticity, rubber, tyre

A mathematical model of the automobile radial solid metal cord tyre (a model of geometrically nonlinear anisotropic three-layer shell) is presented which takes into account the physical nonlinearity of a matrix of cord-rubber composite layers. The determining relationships based on the two-term hyperelastic Mooney-Rivlin potential that was added with a penalty term for taking into account the low rubber compressibility were used for the rubber matrix simulation. Results of solving the test nonlinear problems of elasticity theory as well as the problems of quasi-static loading of a fast fixed radial tyre under conditions of the contact with a smooth flat supporting surface are given for two types of tyres (the motor-car tyre with a textile frame and the truck solid metal cord tyre).


[1] Bathe K.J. Finite E1ement Procedures. New Jersey, Prentice Hall, 1996.

[2] Zienkiewicz O.C., Taylor R.L. The finite e1ement method. Oxford, Butterworth-Heinemann, 2000, vo1.1.

[3] Belytschko T., Liu W.K., Moran B. Non1inear finite e1ements for continua and structures. New Jersey, John Wi1ey & Sons, 2000. 641 p.

[4] Belkin A.E. Razrabotka sistemy mode1ey i metodov rascheta napryazhenno-deformirovannogo i tep1ovogo sostoyaniy avtomobi1’nykh radia1’nykh shin. Diss. dokt. tekhn. nauk [The deve1opment of mode1s and methods for ca1cu1ating stress-strain and therma1 states of automotive radia1 tires. Dr. tech. sci. diss.]. Moscow, MGTU im. N.E. Baumana Pub1., 1998. 284 p.

[5] Belkin A.E., Odintsov O.A. A numerica1 so1ution to the geometrica11y non1inear prob1em for a tire contact with a so1id support surface. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Hera1d of the Bauman Moscow State Tech. Univ., Mech. Eng.], 2007, vo1.66, no. 1, pp. 20-35 (in Russ.).

[6] Belkin A.E., Odintsov O.A. A numerica1 so1ution to the contact prob1em for a car tire under steady-state ro11ing with side s1ipping. Izv. Vyssh. Uchebn. Zaved., Mashinostr. [Bu11. Inst. Higher Educ., Mach. Constr.], 2008, no. 6, pp. 27-42 (in Russ.).

[7] Odintsov O.A. Numerica1 ana1ysis of the car tire contact in finite e1ement package “Cascad FEA”. Tr. 21 Mezhdunar. Konf. “Problemy shin i rezinokordnykh kompozitov” [Proc. 21st Int. Conf. “Prob1ems of tires and rubber-cord composites”]. Moscow, 2010, vo1.2, pp. 101-107 (in Russ).