American Institute of Mathematical Sciences

Advanced
January  1998, 4(1): 55-72. doi: 10.3934/dcds.1998.4.55

Analysis of a quasistatic viscoplastic problem involving tresca friction law

Amina Amassad 1, and  Mircea Sofonea 1,

1. 

Department of Mathematics, University of Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France, France

Received  May 1996 Revised  January 1997 Published  October 1997

The quasistatic evolution of an elastic-viscoplastic body in bilateral contact with a rigid foundation is considered. The contact involves viscous friction of Tresca type. Two variational formulations of the problem are proposed, followed by existence and uniqueness results. Some properties involving the equivalence between the previous variational formulations, the continuous dependence of the solution with respect to the data as well as a convergence result with respect to the friction yield limit are also obtained.
Keywords: implicite scheme, Viscoplasticity, variational inequalities, Tresca friction law, nonlinear evolution equations, fixed point..
Mathematics Subject Classification: 73E60, 49J40, 47H1.
Citation: Amina Amassad, Mircea Sofonea. Analysis of a quasistatic viscoplastic problem involving tresca friction law. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 55-72. doi: 10.3934/dcds.1998.4.55
[1]

Amina Amassad, Mircea Sofonea. Analysis of some nonlinear evolution systems arising in rate-type viscoplasticity. Conference Publications, 1998, 1998 (Special) : 58-71. doi: 10.3934/proc.1998.1998.58
[2]

Francis Akutsah, Akindele Adebayo Mebawondu, Hammed Anuoluwapo Abass, Ojen Kumar Narain. A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021046
[3]

Lateef Olakunle Jolaoso, Maggie Aphane. Bregman subgradient extragradient method with monotone self-adjustment stepsize for solving pseudo-monotone variational inequalities and fixed point problems. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020178
[4]

Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692
[5]

Tiziana Cardinali, Paola Rubbioni. Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result. Discrete & Continuous Dynamical Systems - S, 2020, 13 (7) : 1947-1955. doi: 10.3934/dcdss.2020152
[6]

Filippo Dell'Oro, Olivier Goubet, Youcef Mammeri, Vittorino Pata. A semidiscrete scheme for evolution equations with memory. Discrete & Continuous Dynamical Systems, 2019, 39 (10) : 5637-5658. doi: 10.3934/dcds.2019247
[7]

Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023
[8]

Vyacheslav Maksimov. The method of extremal shift in control problems for evolution variational inequalities under disturbances. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021048
[9]

Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4927-4962. doi: 10.3934/dcdsb.2020320
[10]

Timilehin Opeyemi Alakoya, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo. A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020152
[11]

Abd-semii Oluwatosin-Enitan Owolabi, Timilehin Opeyemi Alakoya, Adeolu Taiwo, Oluwatosin Temitope Mewomo. A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021004
[12]

Wolfgang Walter. Nonlinear parabolic differential equations and inequalities. Discrete & Continuous Dynamical Systems, 2002, 8 (2) : 451-468. doi: 10.3934/dcds.2002.8.451
[13]

Samir Adly, Tahar Haddad. On evolution quasi-variational inequalities and implicit state-dependent sweeping processes. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1791-1801. doi: 10.3934/dcdss.2020105
[14]

Nassif Ghoussoub. A variational principle for nonlinear transport equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 735-742. doi: 10.3934/cpaa.2005.4.735
[15]

Md. Golam Hafez, Sayed Allamah Iqbal, Asaduzzaman, Zakia Hammouch. Dynamical behaviors and oblique resonant nonlinear waves with dual-power law nonlinearity and conformable temporal evolution. Discrete & Continuous Dynamical Systems - S, 2021, 14 (7) : 2245-2260. doi: 10.3934/dcdss.2021058
[16]

Nicholas Long. Fixed point shifts of inert involutions. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297
[17]

Bertram Düring, Daniel Matthes, Josipa Pina Milišić. A gradient flow scheme for nonlinear fourth order equations. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 935-959. doi: 10.3934/dcdsb.2010.14.935
[18]

Stanislaw Migórski. A class of hemivariational inequalities for electroelastic contact problems with slip dependent friction. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 117-126. doi: 10.3934/dcdss.2008.1.117
[19]

Risei Kano, Yusuke Murase. Solvability of nonlinear evolution equations generated by subdifferentials and perturbations. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 75-93. doi: 10.3934/dcdss.2014.7.75
[20]

Matthieu Alfaro, Isabeau Birindelli. Evolution equations involving nonlinear truncated Laplacian operators. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3057-3073. doi: 10.3934/dcds.2020046

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (104)
  • HTML views (0)
  • Cited by (29)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy