Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
thermo-elasto-viscoplastic material; dynamic process; bilateral contact; friction; damage; frictional heat generation; weak solution; fixed point
thermo-elasto-viscoplastic material; dynamic process; bilateral contact; friction; damage; frictional heat generation; weak solution; fixed point
Summary:
We consider a dynamic problem describing frictional contact between a thermo-elasto-viscoplastic body and a foundation. The contact is frictional and bilateral with a moving rigid foundation that results in the wear of the contacting surface. The constitutive law includes a temperature effect described by the first-order evolution equation and a damage effect described by the parabolic inclusion with the homogeneous Neumann boundary condition. We present a variational formulation of the problem and establish the existence and uniqueness of the weak solution. The proof is based on parabolic variational inequalities, first order evolutionary variational equations, and fixed point arguments.
References:
[1] Barbu, V.: Optimal Control of Variational Inequalities. Research Notes in Mathematics 100. Pitman, Boston (1984). MR 0742624 | Zbl 0574.49005
[2] Chadi, K., Selmani, M.: Dynamic frictional thermoviscoelastic contact problem with normal compliance and damage. Bull. Belg. Math.Soc. - Simon Stevin 28 (2021), 195-215. DOI 10.36045/j.bbms.191105 | MR 4355684 | Zbl 1483.74072
[3] Cocu, M., Pratt, E., Raous, M.: Formulation and approximation of a quasistatic frictional contact. Int. J. Eng. Sci. 34 (1996), 783-798. DOI 10.1016/0020-7225(95)00121-2 | MR 1397607 | Zbl 0900.73684
[4] Duvaut, G., Lions, J. L.: Inequalities in Mechanics and Physics. Grundlehren der mathematischen Wissenschaften 219. Springer, Berlin (1976). DOI 10.1007/978-3-642-66165-5 | MR 0521262 | Zbl 0331.35002
[5] Figueiredo, I., Trabucho, L.: A class of contact and friction dynamic problems in thermoelasticity and in thermoviscoelasticity. Int. J. Eng. Sci. 33 (1995), 45-66. DOI 10.1016/0020-7225(94)E0042-H | MR 1309740 | Zbl 0899.73473
[6] Frémond, M.: Non-Smooth Thermomechanics. Springer, Berlin (2002). DOI 10.1007/978-3-662-04800-9 | MR 1885252 | Zbl 0990.80001
[7] Frémond, M., Kuttler, K. L., Nedjar, B., Shillor, M.: One-dimensional models of damage. Adv. Math. Sci. Appl. 8 (1998), 541-570. MR 1657215 | Zbl 0915.73041
[8] Frémond, M., Nedjar, B.: Damage in concrete: The unilateral phenomenon. Nucl. Eng. Design 156 (1995), 323-335. DOI 10.1016/0029-5493(94)00970-A
[9] Frémond, M., Nedjar, B.: Damage, gradient of damage and principle of virtual work. Int. J. Solids Stuct. 33 (1996), 1083-1103. DOI 10.1016/0020-7683(95)00074-7 | MR 1370124 | Zbl 0910.73051
[10] Gasiński, L., Ochal, A.: Dynamic thermoviscoelastic problem with friction and damage. Nonlinear Anal., Real World Appl. 21 (2015), 63-75. DOI 10.1016/j.nonrwa.2014.06.004 | MR 3261579 | Zbl 1334.74062
[11] Gasiński, L., Ochal, A., Shillor, M.: Quasistatic thermoviscoelastic problem with normal compliance, multivalued friction and wear diffusion. Nonlinear Anal., Real World Appl. 27 (2016), 183-202. DOI 10.1016/j.nonrwa.2015.07.006 | MR 3400523 | Zbl 1331.74042
[12] Gu, R. J., Kuttler, K. L., Shillor, M.: Frictional wear of a thermoelastic beam. J. Math. Anal. Appl. 242 (2000), 212-236. DOI 10.1006/jmaa.1999.6652 | MR 1737847 | Zbl 0970.74048
[13] Gu, R. J., Shillor, M.: Thermal and wear analysis of an elastic beam in sliding contact. Int. J. Solids Struct. 38 (2001), 2323-2333. DOI 10.1016/S0020-7683(00)00121-9 | Zbl 0977.74038
[14] Johansson, L., Klarbring, A.: Thermoelastic frictional contact problems: Modeling, finite element approximation and numerical realization. Comput. Methods Appl. Mech. Eng. 105 (1993), 181-210. DOI 10.1016/0045-7825(93)90122-E | MR 1220080 | Zbl 0772.73076
[15] Kuttler, K. L., Renard, Y., Shillor, M.: Models and simulations of dynamic frictional contact of a beam. Comput. Methods Appl. Mech. Eng. 177 (1999), 259-272. DOI 10.1016/S0045-7825(98)00384-3 | MR 1710454 | Zbl 0959.74047
[16] Nečas, J., Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Studies in Applied Mechanics 3. Elsevier, Amsterdam (1981). DOI 10.1016/c2009-0-12554-0 | MR 0600655 | Zbl 0448.73009
[17] Rochdi, M., Shillor, M.: Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity. Q. Appl. Math. 58 (2000), 543-560. DOI 10.1090/qam/1770654 | MR 1770654 | Zbl 1151.74397
[18] Rochdi, M., Shillor, M., Sofonea, M.: Quasistatic viscoelastic contact with normal compliance and friction. J. Elasticity 51 (1998), 105-126. DOI 10.1023/A:1007413119583 | MR 1664496 | Zbl 0921.73231
[19] Selmani, M., Selmani, L.: A frictional contact problem with normal damped response and damage for elastic-visco-plastic materials. Rend. Circ. Mat. Palermo (2) 59 (2010), 67-85. DOI 10.1007/s12215-010-004-4 | MR 2639438 | Zbl 1425.74348
[20] Shillor, M., Sofonea, M.: A quasistatic viscoelastic contact problem with friction. Int. J. Eng. Sci. 38 (2000), 1517-1533. DOI 10.1016/S0020-7225(99)00126-3 | MR 1763038 | Zbl 1210.74132
[21] Shillor, M., Sofonea, M., Telega, J. J.: Models and Analysis of Quasistatic Contact: Variational Methods. Lecture Notes in Physics 655. Springer, Berlin (2004). DOI 10.1007/b99799 | Zbl 1069.74001
[22] Shillor, M., Sofonea, M., Telega, J. J.: Quasistatic viscoelastic contact with friction and wear diffusion. Q. Appl. Math. 62 (2004), 379-399. DOI 10.1090/qam/2054605 | MR 2054605 | Zbl 1180.74046
[23] Sofonea, M., Han, W., Shillor, M.: Analysis and Approximation of Contact Problems with Adhesion or Damage. Pure and Applied Mathematics 276. Chapman & Hall/CRC Press, New York (2006). DOI 10.1201/9781420034837 | MR 2183435 | Zbl 1089.74004
[24] Sofonea, M., Shillor, M.: Variational analysis of quasistatic viscoplastic contact problems with friction. Commun. Appl. Anal. 5 (2001), 135-151. MR 1844677 | Zbl 1084.74541
[25] Strömberg, N.: Continuum Thermodynamics of Contact, Friction and Wear: Thesis No. 491. Department of Mechanical Engineering, Linköping Institute of Technology, Linköping (1995).
[26] Strömberg, N., Johansson, L., Klarbring, A.: Derivation and analysis of a generalized standard model for contact, friction and wear. Int. J. Solids Struct. 33 (1996), 1817-1836. DOI 10.1016/0020-7683(95)00140-9 | MR 1392130 | Zbl 0926.74012
Search
Partner of
