References
- Bonetti E, Bonfanti G, Rossi R. Analysis of a unilateral contact problem taking into account adhesion and friction. J. Differ. Equ. 2012;253:438–462.
- Drozdov AD. Finite elasticity and viscoelasticity: a course in the nonlinear mechanics of solids. Singapore: World Scientific Publishing Co Inc.; 1996.
- Han W, Sofonea M. Quasistatic contact problems in viscoelasticity and viscoplasticity. Vol. 30, Studies in advanced mathematics. Somerville: American Mathematical Society--International Press; 2002.
- Kikuchi N, Oden JT. Contact problems in elasticity: a study of variational inequalities and finite element methods. Philadelphia: SIAM; 1988.
- Nassar SA, Andrews KT, Kruk S, et al. Modelling and simulations of a bonded rod. Math. Comput. Model. 2002;42:553–572.
- Pătrulescu F, Ramadan A. Convergence results for contact problems with memory term. Math. Rep. 2015;17:24–41.
- Raous M, Cangémi L, Cocu M. A consistent model coupling adhesion, friction and unilateral contact. Comput. Methods Appl. Mech. Eng. 1999;177:383–399.
- Shillor M, Sofonea M, Telega JJ. Models and analysis of quasistatic contact. Vol. 655, Lecture notes in physics. Berlin: Springer-Verlag; 2004.
- Sofonea M, Han W, Shillor M. Analysis and approximation of contact problems with adhesion or damage. Vol. 276, Pure and applied mathematics. New York (NY): Chapman-Hall/CRC Press; 2006.
- Wriggers P. Computational contact mechanics. Chichester: Wiley; 2002.
- Sofonea M, Pătrulescu F. A viscoelastic contact problem with adhesion and surface memory effects. Math. Model. Anal. 2014;19:607–626.
- Céa J. Optimization. Théorie et algorithmes. Paris: Dunond Gauthier-Villars; 1971.
- Ekeland I, Temam R. Convex analysis and variational problems. Vol. 28, Classics in applied mathematics. Philadelphia (PA): SIAM; 1999.
- Hueber S, Matei A, Wohlmuth B. A mixed variational formulation and optimal a priori error estimate for a frictional contact problem in elasto-piezoelectricity. Bull. Math. Soc. Sci. Math. Roumanie (N.S.). 2005;48:209–232.
- Lions J-L, Glowinski R, Trémoli\‘{e}res R. Numerical analysis of variational inegalities. Amsterdam: North-Holland; 1981.
- Matei A, Ciurcea R. Contact problems for nonlinearly elastic materials: weak solvability involving dual Lagrange multipliers. ANZIAM J. 2010;52:160–178.
- Sofonea M, Matei A. History-dependent mixed variational problems in contact mechanics. J. Glob. Optim. 2015;61:591–614.
- Sofonea M, Pătrulescu F. Analysis of a history-dependent frictionless contact problem. Math. Mech. Solids. 2013;18:409–430.
- Chau O, Fernández JR, Shillor M, et al. Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion. J. Comput. Appl. Math. 2003;159:431–465.
- Cocu M, Rocca R. Existence results for unilateral quasistatic contact problems with friction and adhesion. ESAIM Math. Model Numer. Anal. 2000;34:981–1001.
- Frémond M. Non-smooth thermomechanics. Berlin: Springer-Verlag; 2002.
- Han J, Li Y, Migorski S. Analysis of an adhesive contact problem for viscoelastic materials with long memory. J. Math. Anal. Appl. 2015;427:646–668.
- Dumont Y, Goeleven D, Rochdi M, et al. A dynamic model with friction and adhesion with applications to rocks. J. Math. Anal. Appl. 2000;247:87–109.
- Rojek J, Telega JJ. Contact problems with friction, adhesion and wear in orthopaedic biomechanics. Part I: general developments. J. Theor. Appl. Mech. 2001;39:655–677.
- Rojek J, Telega JJ, Stupkiewicz S. Contact problems with friction, adhesion and wear in orthopaedic biomechanics. Part II: numerical implementation and application to implanted knee joints. J. Theor. Appl. Mech. 2001;39:679–706.
- Oden JT, Martins JAC. Models and computational methods for dynamic friction phenomena. Comput. Methods Appl. Mech. Eng. 1985;52:527–634.
- Klarbring A, Mikelič A, Shillor M. Frictional contact problems with normal compliance. Int. J. Eng. Sci. 1988;26:811–832.
- Klarbring A, Mikelič A, Shillor M. On friction problems with normal compliance. Nonlinear Anal. 1989;13:935–955.
- Signorini A. Sopra alcune questioni di elastostatica, Atti della Società Italiana per il Progresso delle Scienze; 1933.
- Barboteu M, Matei A, Sofonea M. On the behavior of the solution of a viscoplastic contact problem. Quart. Appl. Math. 2014;72:625–647.
- Sofonea M, Danan D, Zheng C. Primal and dual variational formulation of a frictional contact problem. Mediterr. J. Math. 2014. doi: 10.1007/s00009-014-0504-0.
- Barboteu M, Matei A, Sofonea M. Analysis of quasistatic viscoplastic contact problems with normal compliance. Q. J. Mech. Appl. Math. 2012;65:555–579.
- Barboteu M, Pătrulescu F, Ramadan A, et al. History-dependent contact models for viscoplastic materials. IMA J. Appl. Math. 2014;79:1180–1200.
- Ciarlet PhG. Linear and nonlinear functional analysis with applications. Philadelphia: SIAM; 2013.