Modeling via the internal energy balance and analysis of adhesive contact with friction in thermoviscoelasticity

Eck, 2005, vol. 270 Sofonea, 2006, vol. 276 Shillor, 2004, vol. 655 Frémond, 1996, Damage, gradient of damage and priciple of virtual power, Internat J. Solids Struct., 33, 1083, 10.1016/0020-7683(95)00074-7 Freddi, 2006, Damage in domains and interfaces: a coupled predictive theory, J. Mech. Mater. Struct., 7, 1205, 10.2140/jomms.2006.1.1205 Bonetti, 2011, Analytical results on a model for damaging in domains and interfaces, ESAIM Control Optim. Calc. Var., 17, 955, 10.1051/cocv/2010033 Frémond, 2002 Frémond, 2012 Point, 1998, Unilateral contact with adherence, Math. Methods Appl. Sci., 10, 367, 10.1002/mma.1670100403 Kočvara, 2006, A rate-independent approach to the delamination problem, Math. Mech. Solids, 11, 423, 10.1177/1081286505046482 Rossi, 2011, Thermodynamics and analysis of rate-independent adhesive contact at small strains, Nonlinear Anal., 74, 3159, 10.1016/j.na.2011.01.031 Raous, 1999, A consistent model coupling adhesion, friction, and unilateral contact, Comput. Methods Appl. Mech. Engrg., 177, 383, 10.1016/S0045-7825(98)00389-2 Chau, 2003, Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion, J. Comput. Appl. Math., 159, 431, 10.1016/S0377-0427(03)00547-8 Fernández, 2003, Analysis and numerical simulations of a dynamic contact problem with adhesion, Math. Comput. Modelling, 37, 1317, 10.1016/S0895-7177(03)90043-4 Bonetti, 2008, Global existence for a contact problem with adhesion, Math. Methods Appl. Sci., 31, 1029, 10.1002/mma.957 Bonetti, 2007, Well-posedness and long-time behaviour for a model of contact with adhesion, Indiana Univ. Math. J., 56, 2787, 10.1512/iumj.2007.56.3079 Bonetti, 2009, Thermal effects in adhesive contact: modelling and analysis, Nonlinearity, 22, 2697, 10.1088/0951-7715/22/11/007 Bonetti, 2011, Long-time behaviour of a thermomechanical model for adhesive contact, Discrete Contin. Dyn. Syst. Ser. S, 4, 273 Bonetti, 2012, Analysis of a unilateral contact problem taking into account adhesion and friction, J. Differential Equations, 253, 438, 10.1016/j.jde.2012.03.017 Bonetti, 2014, Analysis of a temperature-dependent model for adhesive contact with friction, Physica D, 285, 42, 10.1016/j.physd.2014.06.008 Bonetti, 2015, Analysis of a model coupling volume and surface processes in thermo- viscoelasticity, Discrete Contin. Dyn. Syst. Ser. A, 35, 10.3934/dcds.2015.35.2349 Bonetti, 2007, Global solution to a singular integrodifferential system related to the entropy balance, Nonlinear Anal., 66, 1949, 10.1016/j.na.2006.02.035 Bonetti, 2006, Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity, Discrete Contin. Dyn. Syst. Ser. B, 6, 1001, 10.3934/dcdsb.2006.6.1001 Duvaut, 1980, Équilibre d’un solide élastique avec contact unilatéral et frottement de Coulomb, C. R. Acad. Sci., Paris Sér. A–B, 290, 263 Boccardo, 1989, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87, 149, 10.1016/0022-1236(89)90005-0 Roubíček, 2010, Thermodynamics of rate independent processes in viscous solids at small strains, SIAM J. Math. Anal., 40, 256, 10.1137/080729992 Mielke, 2004, On rate-independent hysteresis models, NoDEA Nonlinear Differential Equations Appl., 11, 151, 10.1007/s00030-003-1052-7 Nirenberg, 1959, On elliptic partial differential equations, Ann. Sc. Norm. Super. Pisa, 13, 115 Bonfanti, 2000, Global solution to a nonlinear system for irreversible phase changes, Adv. Math. Sci. Appl., 10, 1 Barbu, 1976 Brézis, 1973, vol. 5 Roubíček, 2005, vol. 153 E. Rocca, R. Rossi, “Entropic” solutions to a thermodynamically consistent PDE system for phase transitions and damage, 2014. Preprint arxiv:1403.2577. Feireisl, 2006, On the Navier–Stokes equations with temperature-dependent transport coefficients, Differ. Equ. Nonlinear Mech., 14 Simon, 1987, Compact sets in the space Lp(0,T;B), Ann. Mat. Pura Appl. (4), 146, 65, 10.1007/BF01762360 Roubíček, 2015, Stress-driven local-solution approach to quasistatic brittle delamination, Nonlinear Anal., 22, 645, 10.1016/j.nonrwa.2014.09.011