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Parametric nonlinear PDEs with multiple solutions: A PGD approach
Can the 'stickslip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?
1.  CNRS and UMPC Université Paris 06, Institut Jean le Rond d'Alembert, UMR 7190, 75005 Paris, France 
References:
[1] 
P. Ballard and J. Jarušek, Indentation of an elastic halfspace by a rigid flat punch as a model problem for analyzing contact problems with coulomb friction,, Journal of Elasticity, 103 (2011), 15. doi: 10.1007/s1065901092709. 
[2] 
P. Ballard, Steady sliding frictional contact problems in linear elasticity,, Journal of Elasticity, 110 (2013), 33. doi: 10.1007/s1065901293816. 
[3] 
P. Ballard, Steady sliding frictional contact problem for an elastic halfspace with a discontinuous friction coefficient and related stress singularities,, to appear in the special issue of Journal of the Mechanics and Physics of Solids in honour of Pierre Suquet, (2015). 
[4] 
R. W. Cottle, J.S. Pang and R. E. Stone, The Linear Complementarity Problem,, Society for Industrial and Applied Mathematics, (2009). doi: 10.1137/1.9780898719000.ch1. 
[5] 
P. Hild, Nonunique slipping in the Coulomb friction model in twodimensional linear elasticity,, The Quarterly Journal of Mechanics and Applied Mathematics, 57 (2004), 225. doi: 10.1093/qjmam/57.2.225. 
[6] 
J. L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, Volume 1,, Dunod, (1968). 
[7] 
J. L. Lions and G. Stampacchia, Variational Inequalities,, Communications on Pure and Applied Mathematics, 20 (1967), 493. doi: 10.1002/cpa.3160200302. 
[8] 
J. R. Rice and A. L. Ruina, Stability of steady frictional slipping,, Journal of Applied Mechanics, 50 (1983), 343. doi: 10.1115/1.3167042. 
[9] 
F. G. Tricomi, Integral Equations,, Interscience Publishers, (1957). 
show all references
References:
[1] 
P. Ballard and J. Jarušek, Indentation of an elastic halfspace by a rigid flat punch as a model problem for analyzing contact problems with coulomb friction,, Journal of Elasticity, 103 (2011), 15. doi: 10.1007/s1065901092709. 
[2] 
P. Ballard, Steady sliding frictional contact problems in linear elasticity,, Journal of Elasticity, 110 (2013), 33. doi: 10.1007/s1065901293816. 
[3] 
P. Ballard, Steady sliding frictional contact problem for an elastic halfspace with a discontinuous friction coefficient and related stress singularities,, to appear in the special issue of Journal of the Mechanics and Physics of Solids in honour of Pierre Suquet, (2015). 
[4] 
R. W. Cottle, J.S. Pang and R. E. Stone, The Linear Complementarity Problem,, Society for Industrial and Applied Mathematics, (2009). doi: 10.1137/1.9780898719000.ch1. 
[5] 
P. Hild, Nonunique slipping in the Coulomb friction model in twodimensional linear elasticity,, The Quarterly Journal of Mechanics and Applied Mathematics, 57 (2004), 225. doi: 10.1093/qjmam/57.2.225. 
[6] 
J. L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, Volume 1,, Dunod, (1968). 
[7] 
J. L. Lions and G. Stampacchia, Variational Inequalities,, Communications on Pure and Applied Mathematics, 20 (1967), 493. doi: 10.1002/cpa.3160200302. 
[8] 
J. R. Rice and A. L. Ruina, Stability of steady frictional slipping,, Journal of Applied Mechanics, 50 (1983), 343. doi: 10.1115/1.3167042. 
[9] 
F. G. Tricomi, Integral Equations,, Interscience Publishers, (1957). 
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