INTERNAL STATE VARIABLES IN DIPOLAR THERMOELASTIC BODIES

Abstract

The aim of our study is prove that the presence of the internal statevariables in a thermoelastic dipolar body do not influence the uniqueness of solution. After the mixed initial boundary value problem inthis context is formulated, we use the Gronwall’s inequality to provethe uniqueness of solution of this problem.

Keywords

• thermoelastic, dipolar, internal state variables, uniqueness, Gronwall’sinequality2000 AMS Classification:35A25, 35G46, 74A60, 74H25, 80A20

INTERNAL STATE VARIABLES IN DIPOLAR THERMOELASTIC BODIES

Abstract

-

Keywords

• -

References

1. Anand, L. and Gurtin, M. E. A theory of amorphous solids undergoing large deformations, Int. J. Solids Struct. 40, 1465–1487, 2003
2. Bouvard, J. L., Ward, D. K., Hossain, D., Marin, E. B., Bammann, D. J. and Horstemeyer M. F., A general inelastic internal state variable model for amorphous glassy polymers, Acta Mechanica, 213 1–2, 71-96, 2010
3. Chirita, S. On the linear theory of thermo-viscoelastic materials with internal state variables, Arch. Mech., 33, 455–464, 1982
4. Marin, M. An evolutionary equation in thermoelasticity of dipolar bodies, Journal of Mathematical Physics, 40 3, 1391–1399, 1999
5. Marin, M. A partition of energy in thermoelsticity of microstretch bodies, Nonlinear Analysis: RWA, 11 4, 2436–2447, 2010
6. Marin, M. Some estimates on vibrations in thermoelasticity of dipolar bodies, Journal of Vibration and Control, 16 1, 33–47, 2010
7. Marin, M. Lagrange identity method for microstretch thermoelastic materials J. Mathematical Analysis and Applications, 363 1, 275–286, 2010
8. Marin, M., Agarwal, R. P. and Mahmoud, S. R. Modeling a microstretch thermoelastic body with two temperature, Abstract and Applied Analysis, 2013, 1–7, 2013

9. Nachlinger, R. R. and Nunziato, J. W. Wave propagation and uniqueness theorem for elastic materials with ISV, Int. J. Engng. Sci., 14, 31-38, 1976
10. Pop, N., An algorithm for solving nonsmooth variational inequalities arising in frictional quasistatic contact problems, Carpathian Journal of Mathematics, 24 1, 110–119, 2008 Pop, N., Cioban, H. and Horvat-Marc, A., Finite element method used in contact problems with dry friction, Computational Materials Science, 50 4, 1283–1285, 2011
11. Sherburn, J. A., Horstemeyer, M. F., Bammann, D. J. and Baumgardner, R. R. Application of the Bammann inelasticity internal state variable constitutive model to geological materials, Geophysical J. Int., 184 3, 1023–1036, 2011
12. Solanki, K. N. and Bammann, D. J. A thermodynamic framework for a gradient theory of continuum damage, (American Acad.Mech.Conf., New Orleans, 2008).
13. Wei, C. and Dewoolkar, M. M. Formulation of capillary hysteresis with internal state variables, Water Resources Research, 42, 16 pp., 2006