Reflection and Transmission at the Boundary of Two Couple Stress Generalized Thermoelastic Solids
Subject Areas : EngineeringR Kumar 1 , K Kumar 2 , R.C Nautiyal 3
1 - Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, 136119, India
2 - Department of Mathematics, DeenBandhu Chhotu Ram University of Science and Technology, Sonipat, Haryana, 131001, India
3 - Department of Mathematics, DeenBandhu Chhotu Ram University of Science and Technology, Sonipat, Haryana, 131001, India
Keywords:
Abstract :
[1] Voigt W., 1887, Theoretische studien uber die elastizitastsverhaltnisse der kristalle, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 34:3-51.
[2] Cosserat E., Cosserat F., 1909, Theorie des Corps Deformables, Hermann et Fils, Paris.
[3] Toupin R.A., 1962, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis 11(1): 385-414.
[4] Mindlin R.D., Tiersten H.F., 1962, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415-448.
[5] Mindlin R.D., 1963, Influence of couple-stresses on stress-concentrations, Experimental Mechanics 3: 1-7.
[6] Koiter W.T., 1964, Couple-stresses in the theory of elasticity, Proceedings of the Koninklijke Nederlandse Academie van Wetenschappen, Amsterdam.
[7] Yang J.F.C., Lakes R.S., 1982, Experimental study of micropolar and couple stress elasticity in compact bone in bending, Journal of Biomechanics 15: 91-98.
[8] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory of elasticity, International Journal of Solids and Structures 39: 2731-2743.
[9] Sengupta P.R., Ghosh B., 1974, Effects of couple stresses on the surface waves in elastic media, Gerlands Beitr Geophys 83:1-18.
[10] Sengupta P.R., Ghosh B., 1974, Effects of couple stresses on the propagation of waves in an elastic layer, Pure and Applied Geophysics 112:331-338.
[11] Sengupta P.R., Benerji D.K., 1978, Effects of couple-stresses on propagation of waves in an elastic layer immersed in an infinite liquid, International Journal of Pure and Applied Mathematics 9:17-28.
[12] Georgiadis H.G., Velgaki E.G., 2003, High-frequency rayleigh waves in materials with micro-structure and couple-stress effects, International Journal of Solids and Structures 40:2501-2520.
[13] Lubarda V.A., Markenscoff X., 2000, Conservation integrals in couple stress elasticity, Journal of the Mechanics and Physics of Solids 48:553-564.
[14] Bardet J.P., Vardoulakis I., 2001, The asymmetry of stress in granular media, International Journal of Solids and Structures 38:353-367.
[15] Lubarda V.A., 2003, Circular inclusions in anti-plane strain couple stress elasticity, International Journal of Solids and Structures 40:3827-3851.
[16] Jasiuk I., Ostoja-Starzewski M., 1995, Planar cosserat elasticity of materials with holes and intrusions, Applied Mechanics Reviews 48(11):S11-S18.
[17] Akgoz B., Civalek O., 2013, Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory, Meccanica 48(4):863-873.
[18] Sharma V., Kumar S., 2014, Velocity dispersion in an elastic plate with microstructure: effects of characteristic length in a couple stress model, Meccanica 49:1083-1090.
[19] Biot M., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[20] Lord H., Shulman Y., 1967, A generalized dynamical theory of elasticity, Journal of the Mechanics and Physics 15: 299-309.
[21] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[22] Ram P., Sharma N., 2008, Reflection and transmission of micropolar thermoelastic waves with an imperfect bonding, International Journal of Applied Mathematics and Mechanics 4(3): 1-23.
[23] Xue B.B., Xu H.Y., Fu Z.M., Sun Q.Y., 2010, Reflection and refraction of longitudinal displacement wave at interface between two micropolar elastic solid, Advanced Materials Research 139-141: 214-217.
[24] Kumar R., Kaur M., Rajvanshi S.C., 2014, Reflection and transmission between two micropolar thermoelastic half-spaces with three-phase-lag model, Journal of Engineering Physics and Thermophysics 87(2): 295-307.