scholarly journals Hybrid discretization of the Signorini problem with Coulomb friction. Theoretical aspects and comparison of some numerical solvers

2006 ◽  
Vol 56 (2) ◽  
pp. 163-192 ◽  
Author(s):  
Houari Boumediène Khenous ◽  
Julien Pommier ◽  
Yves Renard
Keyword(s):  
Coulomb Friction ◽  
Signorini Problem ◽  
Hybrid Discretization

The reciprocal variational approach to the Signorini problem with friction. Approximation results

1984 ◽  
Vol 98 (3-4) ◽  
pp. 365-383 ◽  
Author(s):  
J. Haslinger ◽  
P. D. Panagiotopoulos
Keyword(s):  
Coulomb Friction ◽  
Numerical Results ◽  
Contact Boundary ◽  
Minimum Problem ◽  
Approximation Procedure ◽  
Signorini Problem ◽  
Direct Integral ◽  
Mixed Problems ◽  
Convergence Results ◽  
Integral Equation Approach

SynopsisIn this paper, a new variational formulation of the Signorini problem with friction is given in terms of the contact stresses. The method corresponds to the direct integral equation approach in classical elastostatic problems. First the displacement and mixed problems are briefly described together with some numerical results. Next the displacements are eliminated by the use of Green's function, and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived. Then the resulting approximation procedure is studied and certain convergence results are proved. Finally, some remarks on the Signorini problem with Coulomb friction are presented. Numerical results illustrate the theory.

Some Consequences of Coulomb Friction in Modeling Longitudinal Traction

1990 ◽  
Vol 18 (1) ◽  
pp. 13-65 ◽  
Author(s):  
W. W. Klingbeil ◽  
H. W. H. Witt
Keyword(s):  
Shear Force ◽  
Coulomb Friction ◽  
Interfacial Shear ◽  
Force Generation ◽  
Behavior Patterns ◽  
Inflation Pressure ◽  
Friction Law ◽  
The Coefficient Of Friction ◽  
Coulomb Friction Law ◽  
Perfect Adhesion

Abstract A three-component model for a belted radial tire, previously developed by the authors for free rolling without slip, is generalized to include longitudinal forces and deformations associated with driving and braking. Surface tractions at the tire-road interface are governed by a Coulomb friction law in which the coefficient of friction is assumed to be constant. After a brief review of the model, the mechanism of interfacial shear force generation is delineated and explored under traction with perfect adhesion. Addition of the friction law then leads to the inception of slide zones, which propagate through the footprint with increasing severity of maneuvers. Different behavior patterns under driving and braking are emphasized, with comparisons being given of sliding displacements, sliding velocities, and frictional work at the tire-road interface. As a further application of the model, the effect of friction coefficient and of test variables such as load, deflection, and inflation pressure on braking stiffness are computed and compared to analogous predictions on the braking spring rate.

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