-
Previous Article
Few remarks on the use of Love waves in non destructive testing
- DCDS-S Home
- This Issue
-
Next Article
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, Sér. II, Fasc. b, Méc. Phys. Astron., 327 (1999), 715-720. |
[2] |
G. Bodovillé and G. de Saxcé, Plasticity with non linear kinematic hardening: Modelling and shakedown analysis by the bipotential approach, Eur. J. Mech., A/Solids, 20 (2001), 99-112. |
[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), 2189-2216.
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), 87-104. |
[5] |
M. Buliga, G. de Saxcé and C. Vallée, Bipotentials for non monotone multivalued operators: Fundamental results and applications, Acta Applicandae Mathematicae, 110 (2010), 955-972.
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), 81-94. |
[7] |
G. de Saxcé, Une généralisation de l'inégalité de Fenchel et ses applications aux lois constitutives, C. R. Acad. Sci. Paris, Sér. II, 314 (1992), 125-129. |
[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, Boston, Massachusetts, 1995. |
[9] |
G. de Saxcé and L. Bousshine, Implicit standard materials, D. Weichert G. Maier eds. Inelastic behaviour of structures under variable repeated loads, CISM Courses and Lectures 432, Springer, Wien, 2002. |
[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, Poland, (1993), 815-822. |
[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), 301-325.
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), 225-245.
doi: 10.1016/S0895-7177(98)00119-8. |
[13] |
W. Fenchel, On conjugate convex functions, Canadian Journal of Mathematics, 1 (1949), 73-77.
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), 349-361.
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), 936-948.
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), 609-640.
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), 39-63. |
[18] |
M. Hjiaj, G. Bodovillé and G. de Saxcé, Matériaux viscoplastiques et loi de normalité implicites, C. R. Acad. Sci. Paris, Sér. II, Fasc. b, Méc. Phys. Astron., 328 (2000), 519-524.
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), 49-59.
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), 2045-2076.
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), 415-441.
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), 259-276. |
[23] |
J. J. Moreau, Fonctionnelles Convexes, Istituto Poligrafico e zecca dello stato, Roma, Italy, 2003. |
[24] |
Z. Mróz and S. Stupkiewicz, An anisotropic fricition and wear model, International Journal of Solids and Structures, 31 (1994), 1113-1131. |
[25] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 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, Theta Series in Advanced Mathematics, Theta Foundation, Bucarest, Roumania, (2005), 339-351. |
show all references
References:
[1] |
G. Bodovillé, On damage and implicit standard materials, C. R. Acad. Sci. Paris, Sér. II, Fasc. b, Méc. Phys. Astron., 327 (1999), 715-720. |
[2] |
G. Bodovillé and G. de Saxcé, Plasticity with non linear kinematic hardening: Modelling and shakedown analysis by the bipotential approach, Eur. J. Mech., A/Solids, 20 (2001), 99-112. |
[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), 2189-2216.
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), 87-104. |
[5] |
M. Buliga, G. de Saxcé and C. Vallée, Bipotentials for non monotone multivalued operators: Fundamental results and applications, Acta Applicandae Mathematicae, 110 (2010), 955-972.
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), 81-94. |
[7] |
G. de Saxcé, Une généralisation de l'inégalité de Fenchel et ses applications aux lois constitutives, C. R. Acad. Sci. Paris, Sér. II, 314 (1992), 125-129. |
[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, Boston, Massachusetts, 1995. |
[9] |
G. de Saxcé and L. Bousshine, Implicit standard materials, D. Weichert G. Maier eds. Inelastic behaviour of structures under variable repeated loads, CISM Courses and Lectures 432, Springer, Wien, 2002. |
[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, Poland, (1993), 815-822. |
[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), 301-325.
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), 225-245.
doi: 10.1016/S0895-7177(98)00119-8. |
[13] |
W. Fenchel, On conjugate convex functions, Canadian Journal of Mathematics, 1 (1949), 73-77.
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), 349-361.
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), 936-948.
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), 609-640.
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), 39-63. |
[18] |
M. Hjiaj, G. Bodovillé and G. de Saxcé, Matériaux viscoplastiques et loi de normalité implicites, C. R. Acad. Sci. Paris, Sér. II, Fasc. b, Méc. Phys. Astron., 328 (2000), 519-524.
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), 49-59.
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), 2045-2076.
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), 415-441.
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), 259-276. |
[23] |
J. J. Moreau, Fonctionnelles Convexes, Istituto Poligrafico e zecca dello stato, Roma, Italy, 2003. |
[24] |
Z. Mróz and S. Stupkiewicz, An anisotropic fricition and wear model, International Journal of Solids and Structures, 31 (1994), 1113-1131. |
[25] |
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 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, Theta Series in Advanced Mathematics, Theta Foundation, Bucarest, Roumania, (2005), 339-351. |
[1] |
Stanislaw Migórski, Anna Ochal, Mircea Sofonea. Analysis of a dynamic Elastic-Viscoplastic contact problem with friction. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 887-902. doi: 10.3934/dcdsb.2008.10.887 |
[2] |
Hailing Xuan, Xiaoliang Cheng. Numerical analysis and simulation of an adhesive contact problem with damage and long memory. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2781-2804. doi: 10.3934/dcdsb.2020205 |
[3] |
Hailing Xuan, Xiaoliang Cheng. Numerical analysis and simulations of a frictional contact problem with damage and memory. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021037 |
[4] |
Hailing Xuan, Xiaoliang Cheng. Numerical analysis of a thermal frictional contact problem with long memory. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1521-1543. doi: 10.3934/cpaa.2021031 |
[5] |
Marx Chhay, Aziz Hamdouni. On the accuracy of invariant numerical schemes. Communications on Pure and Applied Analysis, 2011, 10 (2) : 761-783. doi: 10.3934/cpaa.2011.10.761 |
[6] |
Leszek Gasiński, Piotr Kalita. On dynamic contact problem with generalized Coulomb friction, normal compliance and damage. Evolution Equations and Control Theory, 2020, 9 (4) : 1009-1026. doi: 10.3934/eect.2020049 |
[7] |
Alain Léger, Elaine Pratt. On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 501-527. doi: 10.3934/dcdss.2016009 |
[8] |
Marius Cocou. A dynamic viscoelastic problem with friction and rate-depending contact interactions. Evolution Equations and Control Theory, 2020, 9 (4) : 981-993. doi: 10.3934/eect.2020060 |
[9] |
Stanislaw Migórski. A class of hemivariational inequalities for electroelastic contact problems with slip dependent friction. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 117-126. doi: 10.3934/dcdss.2008.1.117 |
[10] |
Krzysztof Bartosz. Numerical analysis of a nonmonotone dynamic contact problem of a non-clamped piezoelectric viscoelastic body. Evolution Equations and Control Theory, 2020, 9 (4) : 961-980. doi: 10.3934/eect.2020059 |
[11] |
Anna Ochal, Michal Jureczka. Numerical treatment of contact problems with thermal effect. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 387-400. doi: 10.3934/dcdsb.2018027 |
[12] |
P. Smoczynski, Mohamed Aly Tawhid. Two numerical schemes for general variational inequalities. Journal of Industrial and Management Optimization, 2008, 4 (2) : 393-406. doi: 10.3934/jimo.2008.4.393 |
[13] |
Amina Amassad, Mircea Sofonea. Analysis of a quasistatic viscoplastic problem involving tresca friction law. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 55-72. doi: 10.3934/dcds.1998.4.55 |
[14] |
Nelly Point, Silvano Erlicher. Convex analysis and thermodynamics. Kinetic and Related Models, 2013, 6 (4) : 945-954. doi: 10.3934/krm.2013.6.945 |
[15] |
Oanh Chau, R. Oujja, Mohamed Rochdi. A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 61-70. doi: 10.3934/dcdss.2008.1.61 |
[16] |
George W. Patrick. The geometry of convergence in numerical analysis. Journal of Computational Dynamics, 2021, 8 (1) : 33-58. doi: 10.3934/jcd.2021003 |
[17] |
María Teresa Cao-Rial, Peregrina Quintela, Carlos Moreno. Numerical solution of a time-dependent Signorini contact problem. Conference Publications, 2007, 2007 (Special) : 201-211. doi: 10.3934/proc.2007.2007.201 |
[18] |
Roberto Avanzi, Nicolas Thériault. A filtering method for the hyperelliptic curve index calculus and its analysis. Advances in Mathematics of Communications, 2010, 4 (2) : 189-213. doi: 10.3934/amc.2010.4.189 |
[19] |
Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators. Kinetic and Related Models, 2013, 6 (3) : 625-648. doi: 10.3934/krm.2013.6.625 |
[20] |
Nikolaos Halidias. Construction of positivity preserving numerical schemes for some multidimensional stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 153-160. doi: 10.3934/dcdsb.2015.20.153 |
2020 Impact Factor: 2.425
Tools
Metrics
Other articles
by authors
[Back to Top]