On the finite element solution of the three-dimensional tire contact problem

Rothert, H.; Idelberger, H.; Jacobi, William J.; Laging, G.

doi:10.1016/0029-5493(84)90200-0

Cited by 24 publications

(11 citation statements)

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“…Finite element simulation of a tire is a difficult task. The major numerical difficulties include geometric nonlinearity due to large deformation, material nonlinearity, incompressibility constraint on the deformation of elastomers, and the nonlinear boundary conditions (contact boundary) [1][2][3]. Among these difficulties, the disposal of contact boundary is the most important, and has attracted much attention [1][2][3][4]7,11].…”

Section: Introductionmentioning

confidence: 99%

“…The major numerical difficulties include geometric nonlinearity due to large deformation, material nonlinearity, incompressibility constraint on the deformation of elastomers, and the nonlinear boundary conditions (contact boundary) [1][2][3]. Among these difficulties, the disposal of contact boundary is the most important, and has attracted much attention [1][2][3][4]7,11]. In many circumstances penalty term [3,4] or gap element [1,11] is employed to describe the interaction of two contacting bodies.…”

Section: Introductionmentioning

confidence: 99%

“…Among these difficulties, the disposal of contact boundary is the most important, and has attracted much attention [1][2][3][4]7,11]. In many circumstances penalty term [3,4] or gap element [1,11] is employed to describe the interaction of two contacting bodies. Unfortunately, neither of these methods can give an exact contact boundary.…”

Section: Introductionmentioning

confidence: 99%

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Finite Element Formulation of Tire with Static Foundation Contact and Its Application

Yan

2005

Journal of Reinforced Plastics and Composites

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Tire's are made up of a typical fiber–rubber composite structure. A finite element model of a tire with foundation contact is developed in this study. In this model, the rubber compounds are simulated by incompressible elements, which are treated using the Lagrangian multipliers method. The nonlinear mechanical properties of the elastomers are modeled by the Mooney–Rivlin model. The belts, carcass, and bead are modeled by an equivalent orthotropic material model in which the effective moduli are determined from the individual material properties of the rubber compound and cord based on the Halpin–Tsai equations. For composite elements consisting of multi-ply cord–rubber composites, three-dimensional effective elastic constants can be determined using the material model presented by Sun and Li. The contact constraint of the tire with a flat foundation and rigid rim is treated using the variable constraint method. For the large deformation description of the tire, the Lagrangian method is used here. The strain tensor and the stress tensor are selected as, respectively, the Green–Lagrangian strain tensor and the second Piola– Kirchhoff stress tensor. In finite element code, two kinds of three-dimensional elements are used – an eight-node brick isoparametric element (hexahedral element) and a six-node isoparametric element (pentahedral element). The present numerical results show that the reliability and convergence of the model are fairly good. Moreover, three groups of radial tires with different belt widths under inflation and static footprint loading are analyzed using the finite element method. Based on the detailed analysis for stress analysis parameters in the critical regions in the tires, the relative belt edge endurance is predicted.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite Element Formulation of Tire with Static Foundation Contact and Its Application

Yan

2005

Journal of Reinforced Plastics and Composites

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“…With the development of computer science and numerical computational techniques, finite element analysis techniques are widely used in the analysis, evaluation and optimum design of complex engineering structures (for example, a tire structure [3,19,[26][27][28][29][30]32]). Due to the complexity of the tire structure analysis mentioned above, at present, finite element analysis techniques are usually used in the tire structure analysis [3,[13][14][15][16][17][18][19]. Computational fracture mechanics techniques [1,2,[4][5][6][7][8][9][10][11][12][13][20][21][22][23][24] and analysis techniques [2,3,5,6,[13][14][15][16][17][18][19] on composite structures make [1,2,[9]…”

Section: Introductionmentioning

confidence: 99%

“…Due to the complexity of the tire structure analysis mentioned above, at present, finite element analysis techniques are usually used in the tire structure analysis [3,[13][14][15][16][17][18][19]. Computational fracture mechanics techniques [1,2,[4][5][6][7][8][9][10][11][12][13][20][21][22][23][24] and analysis techniques [2,3,5,6,[13][14][15][16][17][18][19] on composite structures make [1,2,[9][10][11][12][13] the delamination crack growth analysis possible in complex structures. As far as the delamination crack growth analysis of a radial tire structure is concerned, Wei [13] and Ebbt [2] use computational fracture mechanics techniques in simulating the delamination crack growth between belts and at the tire body turn-up region, respectively.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Finite Element Modeling of Delamination Crack Growth Process between Belts of a Radial Tire

Feng

Yan

Wei

et al. 2004

Journal of Reinforced Plastics and Composites

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A radial tire is a very complex structure made from rubber elastomers and fiber rubber composite materials. During its use, a delamination crack growth between belts can occur, which obviously affects its durability and life. In the present paper, a new numerical model of the delamination crack growth in complex structures is presented. The model can reveal the crack growth dependence on the relative size of energy release rates at the left and right crack tips and the interfacial material property. The crack growth model, the Irwin’s virtual crack close technique and finite element analysis method are together used in simulating numerically the growth process of the delamination crack between belts of a radial tire. The numerical results show that the crack growth model proposed in the present paper can more really characterize the complexity of the delamination crack growth process in complex composite structures.

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The solution of large displacement frictionless contact problems using a sequence of linear complementarity problems

Björkman

1991

Numerical Meth Engineering

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SUMMARYA Newton method for solution of frictionless contact problems is presented. A finite element discretization is performed and the contact constraints are given as complementarity conditions. The resulting equations, which represent the equilibrium of the system, are formulated as a generalized equation. Generalized equations, from the discipline of Mathematical Programming, are a way of writing multi-valued relations, such as complementarity conditions, in a way that is similar to ordinary equations. Newton's method is then used, in a straightforward way, to solve the present non-linear generalized equation, resulting in a sequence of Linear Complementarity Problems (LCP's).

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On the finite element solution of the three-dimensional tire contact problem

Cited by 24 publications

References 0 publications

Finite Element Formulation of Tire with Static Foundation Contact and Its Application

Finite Element Formulation of Tire with Static Foundation Contact and Its Application

Nonlinear Finite Element Modeling of Delamination Crack Growth Process between Belts of a Radial Tire

The solution of large displacement frictionless contact problems using a sequence of linear complementarity problems

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