TY - JOUR T1 - INTERNAL STATE VARIABLES IN DIPOLAR THERMOELASTIC BODIES TT - INTERNAL STATE VARIABLES IN DIPOLAR THERMOELASTIC BODIES AU - Marin, M. AU - Mahmoud, S.r. AU - Stan, G. PY - 2014 DA - January JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 15 EP - 26 VL - 43 IS - 1 LA - tr N2 - 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. CR - Anand, L. and Gurtin, M. E. A theory of amorphous solids undergoing large deformations, Int. J. Solids Struct. 40, 1465–1487, 2003 CR - 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 CR - Chirita, S. On the linear theory of thermo-viscoelastic materials with internal state variables, Arch. Mech., 33, 455–464, 1982 CR - Marin, M. An evolutionary equation in thermoelasticity of dipolar bodies, Journal of Mathematical Physics, 40 3, 1391–1399, 1999 CR - Marin, M. A partition of energy in thermoelsticity of microstretch bodies, Nonlinear Analysis: RWA, 11 4, 2436–2447, 2010 CR - Marin, M. Some estimates on vibrations in thermoelasticity of dipolar bodies, Journal of Vibration and Control, 16 1, 33–47, 2010 CR - Marin, M. Lagrange identity method for microstretch thermoelastic materials J. Mathematical Analysis and Applications, 363 1, 275–286, 2010 CR - 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 CR - 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 CR - 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 CR - 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 CR - Solanki, K. N. and Bammann, D. J. A thermodynamic framework for a gradient theory of continuum damage, (American Acad.Mech.Conf., New Orleans, 2008). CR - Wei, C. and Dewoolkar, M. M. Formulation of capillary hysteresis with internal state variables, Water Resources Research, 42, 16 pp., 2006 UR - https://dergipark.org.tr/en/pub/hujms/issue//101225 L1 - https://dergipark.org.tr/en/download/article-file/86159 ER -