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Comparison between Borel-Padé summation and factorial series, as time integration methods
Modelling contact with isotropic and anisotropic friction by the bipotential approach
1. | Laboratoire de Mécanique de Lille, UMR CNRS 8107, Université des Sciences et Technologies de Lille, bâtiment Boussinesq, Cité Scientifique, 59655 Villeneuve d'Ascq cedex |
References:
[1] |
G. Bodovillé, On damage and implicit standard materials,, C. R. Acad. Sci. Paris, 327 (1999), 715. Google Scholar |
[2] |
G. Bodovillé and G. de Saxcé, Plasticity with non linear kinematic hardening: Modelling and shakedown analysis by the bipotential approach,, Eur. J. Mech., 20 (2001), 99. Google Scholar |
[3] |
L. Bousshine, A. Chaaba and G. de Saxcé, Plastic limit load of plane frames with frictional contact supports,, Int. J. Mech. Sci., 44 (2002), 2189.
doi: 10.1016/S0020-7403(02)00135-2. |
[4] |
M. Buliga, G. de Saxcé and C. Vallée, Existence and construction of bipotentials for graphs of multivalued laws,, J. Convex Analysis, 15 (2008), 87.
|
[5] |
M. Buliga, G. de Saxcé and C. Vallée, Bipotentials for non monotone multivalued operators: Fundamental results and applications,, Acta Applicandae Mathematicae, 110 (2010), 955.
doi: 10.1007/s10440-009-9488-3. |
[6] |
M. Buliga, G. de Saxcé and C. Vallée, Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law,, J. Convex Analysis, 17 (2010), 81.
|
[7] |
G. de Saxcé, Une généralisation de l'inégalité de Fenchel et ses applications aux lois constitutives,, C. R. Acad. Sci. Paris, 314 (1992), 125. Google Scholar |
[8] |
G. de Saxcé, The bipotential method, a new variational and numerical treatment of the dissipative laws of materials,, 10th Int. Conf. on Mathematical and Computer Modelling and Scientific Computing, (1995). Google Scholar |
[9] |
G. de Saxcé and L. Bousshine, Implicit standard materials,, D. Weichert G. Maier eds. Inelastic behaviour of structures under variable repeated loads, (2002). Google Scholar |
[10] |
G. de Saxcé and L. Bousshine, On the extension of limit analysis theorems to the non associated flow rules in soils and to the contact with Coulomb's friction,, XI Polish Conference on Computer Methods in Mechanics. Kielce, (1993), 815. Google Scholar |
[11] |
G. de Saxcé and Z. Q. Feng, New inequality and functional for contact friction: The implicit standard material approach,, Mechanics of Structures and Machines, 19 (1991), 301.
doi: 10.1080/08905459108905146. |
[12] |
G. de Saxcé and Z. Q. Feng, The bi-potential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms,, Mathematical and Computer Modelling, 28 (1998), 225.
doi: 10.1016/S0895-7177(98)00119-8. |
[13] |
W. Fenchel, On conjugate convex functions,, Canadian Journal of Mathematics, 1 (1949), 73.
doi: 10.4153/CJM-1949-007-x. |
[14] |
Z.-Q. Feng, M. Hjiaj, G. de Saxcé and Z. Mróz, Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface,, Comput. Mech., 37 (2006), 349.
doi: 10.1007/s00466-005-0674-5. |
[15] |
Z.-Q. Feng, M. Hjiaj, G. de Saxcé and Z. Mróz, Influence of frictional anisotropy on contacting surfaces during loading/unloading cycles,, International Journal of Non-Linear Mechanics, 41 (2006), 936.
doi: 10.1016/j.ijnonlinmec.2006.08.002. |
[16] |
J. Fortin, M. Hjiaj and G. de Saxcé, An improved discrete element method based on a variational formulation of the frictional contact law,, Comput. Geotech., 29 (2002), 609.
doi: 10.1016/S0266-352X(02)00016-2. |
[17] |
B. Halphen and S. Nguyen Quoc, Sur les matériaux standard généralisés,, C. R. Acad. Sci. Paris 14 (1975), 14 (1975), 39.
|
[18] |
M. Hjiaj, G. Bodovillé and G. de Saxcé, Matériaux viscoplastiques et loi de normalité implicites,, C. R. Acad. Sci. Paris, 328 (2000), 519.
doi: 10.1016/S1620-7742(00)00007-6. |
[19] |
M. Hjiaj, G. de Saxcé and Z. Mróz, A variational-inequality based formulation of the frictional contact law with a non-associated sliding rule,, European Journal of Mechanics A/Solids, 21 (2002), 49.
doi: 10.1016/S0997-7538(01)01183-4. |
[20] |
M. Hjiaj, Z.-Q. Feng, G. de Saxcé and Z. Mróz, Three dimensional finite element computations for frictional contact problems with on-associated sliding rule,, Int. J. Numer. Methods Eng., 60 (2004), 2045.
doi: 10.1002/nme.1037. |
[21] |
P. Laborde and Y. Renard, Fixed points strategies for elastostatic frictional contact problems,, Math. Meth. Appl. Sci., 31 (2008), 415.
doi: 10.1002/mma.921. |
[22] |
R. Michałowski and Z. Mróz, Associated and non-associated sliding rules in contact friction problems,, Archives of Mechanics, 11 (1978), 259. Google Scholar |
[23] |
J. J. Moreau, Fonctionnelles Convexes,, Istituto Poligrafico e zecca dello stato, (2003). Google Scholar |
[24] |
Z. Mróz and S. Stupkiewicz, An anisotropic fricition and wear model,, International Journal of Solids and Structures, 31 (1994), 1113. Google Scholar |
[25] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1997).
|
[26] |
C. Vallée, C. Lerintiu, D. Fortuné, M. Ban and G. de Saxcé, Hill's bipotential,, M. Mihailescu-Suliciu eds. New Trends in Continuum Mechanics, (2005), 339. Google Scholar |
show all references
References:
[1] |
G. Bodovillé, On damage and implicit standard materials,, C. R. Acad. Sci. Paris, 327 (1999), 715. Google Scholar |
[2] |
G. Bodovillé and G. de Saxcé, Plasticity with non linear kinematic hardening: Modelling and shakedown analysis by the bipotential approach,, Eur. J. Mech., 20 (2001), 99. Google Scholar |
[3] |
L. Bousshine, A. Chaaba and G. de Saxcé, Plastic limit load of plane frames with frictional contact supports,, Int. J. Mech. Sci., 44 (2002), 2189.
doi: 10.1016/S0020-7403(02)00135-2. |
[4] |
M. Buliga, G. de Saxcé and C. Vallée, Existence and construction of bipotentials for graphs of multivalued laws,, J. Convex Analysis, 15 (2008), 87.
|
[5] |
M. Buliga, G. de Saxcé and C. Vallée, Bipotentials for non monotone multivalued operators: Fundamental results and applications,, Acta Applicandae Mathematicae, 110 (2010), 955.
doi: 10.1007/s10440-009-9488-3. |
[6] |
M. Buliga, G. de Saxcé and C. Vallée, Non maximal cyclically monotone graphs and construction of a bipotential for the Coulomb's dry friction law,, J. Convex Analysis, 17 (2010), 81.
|
[7] |
G. de Saxcé, Une généralisation de l'inégalité de Fenchel et ses applications aux lois constitutives,, C. R. Acad. Sci. Paris, 314 (1992), 125. Google Scholar |
[8] |
G. de Saxcé, The bipotential method, a new variational and numerical treatment of the dissipative laws of materials,, 10th Int. Conf. on Mathematical and Computer Modelling and Scientific Computing, (1995). Google Scholar |
[9] |
G. de Saxcé and L. Bousshine, Implicit standard materials,, D. Weichert G. Maier eds. Inelastic behaviour of structures under variable repeated loads, (2002). Google Scholar |
[10] |
G. de Saxcé and L. Bousshine, On the extension of limit analysis theorems to the non associated flow rules in soils and to the contact with Coulomb's friction,, XI Polish Conference on Computer Methods in Mechanics. Kielce, (1993), 815. Google Scholar |
[11] |
G. de Saxcé and Z. Q. Feng, New inequality and functional for contact friction: The implicit standard material approach,, Mechanics of Structures and Machines, 19 (1991), 301.
doi: 10.1080/08905459108905146. |
[12] |
G. de Saxcé and Z. Q. Feng, The bi-potential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms,, Mathematical and Computer Modelling, 28 (1998), 225.
doi: 10.1016/S0895-7177(98)00119-8. |
[13] |
W. Fenchel, On conjugate convex functions,, Canadian Journal of Mathematics, 1 (1949), 73.
doi: 10.4153/CJM-1949-007-x. |
[14] |
Z.-Q. Feng, M. Hjiaj, G. de Saxcé and Z. Mróz, Effect of frictional anisotropy on the quasistatic motion of a deformable solid sliding on a planar surface,, Comput. Mech., 37 (2006), 349.
doi: 10.1007/s00466-005-0674-5. |
[15] |
Z.-Q. Feng, M. Hjiaj, G. de Saxcé and Z. Mróz, Influence of frictional anisotropy on contacting surfaces during loading/unloading cycles,, International Journal of Non-Linear Mechanics, 41 (2006), 936.
doi: 10.1016/j.ijnonlinmec.2006.08.002. |
[16] |
J. Fortin, M. Hjiaj and G. de Saxcé, An improved discrete element method based on a variational formulation of the frictional contact law,, Comput. Geotech., 29 (2002), 609.
doi: 10.1016/S0266-352X(02)00016-2. |
[17] |
B. Halphen and S. Nguyen Quoc, Sur les matériaux standard généralisés,, C. R. Acad. Sci. Paris 14 (1975), 14 (1975), 39.
|
[18] |
M. Hjiaj, G. Bodovillé and G. de Saxcé, Matériaux viscoplastiques et loi de normalité implicites,, C. R. Acad. Sci. Paris, 328 (2000), 519.
doi: 10.1016/S1620-7742(00)00007-6. |
[19] |
M. Hjiaj, G. de Saxcé and Z. Mróz, A variational-inequality based formulation of the frictional contact law with a non-associated sliding rule,, European Journal of Mechanics A/Solids, 21 (2002), 49.
doi: 10.1016/S0997-7538(01)01183-4. |
[20] |
M. Hjiaj, Z.-Q. Feng, G. de Saxcé and Z. Mróz, Three dimensional finite element computations for frictional contact problems with on-associated sliding rule,, Int. J. Numer. Methods Eng., 60 (2004), 2045.
doi: 10.1002/nme.1037. |
[21] |
P. Laborde and Y. Renard, Fixed points strategies for elastostatic frictional contact problems,, Math. Meth. Appl. Sci., 31 (2008), 415.
doi: 10.1002/mma.921. |
[22] |
R. Michałowski and Z. Mróz, Associated and non-associated sliding rules in contact friction problems,, Archives of Mechanics, 11 (1978), 259. Google Scholar |
[23] |
J. J. Moreau, Fonctionnelles Convexes,, Istituto Poligrafico e zecca dello stato, (2003). Google Scholar |
[24] |
Z. Mróz and S. Stupkiewicz, An anisotropic fricition and wear model,, International Journal of Solids and Structures, 31 (1994), 1113. Google Scholar |
[25] |
R. T. Rockafellar, Convex Analysis,, Princeton University Press, (1997).
|
[26] |
C. Vallée, C. Lerintiu, D. Fortuné, M. Ban and G. de Saxcé, Hill's bipotential,, M. Mihailescu-Suliciu eds. New Trends in Continuum Mechanics, (2005), 339. Google Scholar |
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