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Existence of rotational waves in non-classical thermoelastic solid continua incorporating internal rotations

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Abstract

In this work, we demonstrate the existence of rotational waves in deforming thermoelastic non-classical solid continua in which the conservation and balance laws consider internal rotations due to the deformation gradient tensor (Jacobian of deformation) as well as their time varying rates. In this non-classical continuum theory, time dependent deformation of solid continua results in time dependent varying rotations, angular velocities and angular accelerations at material points. Resistance to these by deforming continua results in additional moments due to rotations, angular momenta due to rotation rates and rotational inertial effects due to angular accelerations at the material points. Currently this physics is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM) based on internal and/or Cosserat rotations. In this paper, we present derivation of conservation and balance laws in Lagrangian description: conservation of mass, balance of linear momentum, balance of angular momentum, balance of moment of moments, first and second laws of thermodynamics that include: (i) physics due to internal rotations resulting from the displacement gradient tensor (ii) new physics associated with rotation rates (angular velocities) and angular accelerations resulting from the varying, time dependent internal rotations at the material points. The balance laws derived here are compared with those that only consider internal rotations and their rates in the absence of rotational inertial effects (Surana et al. in J Therm Eng 1(6):446–459, 2015; Int J Eng Res Ind Appl 8(2):77–106, 2015) to demonstrate the influence of new physics. Constitutive variables and their argument tensors are established using the conjugate pairs in the entropy inequality, additional desired physics and the principle of equipresence. The constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity. It is shown that the mathematical model consisting of the conservation and balance laws and the constitutive theories has closure. Existence of rotational waves is demonstrated due to the presence of angular velocities and angular accelerations arising from the time varying rotations and their rates when deforming solid continua offer rotational inertial resistance. In this paper, we only consider isotropic and homogeneous solid continua with small strain, small deformation physics and reversible mechanical deformation. Model problem studies are presented in a follow up paper.

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References

  1. Surana, K.S., Powell, M.J., Reddy, J.N.: A more complete thermodynamic framework for solid continua. J. Therm. Eng. 1(6), 446–459 (2015)

    Google Scholar 

  2. Surana, K.S., Reddy, J.N., Nunez, D., Powell, M.J.: A polar continuum theory for solid continua. Int. J. Eng. Res. Ind. Appl. 8(2), 77–106 (2015)

    Google Scholar 

  3. Surana, K.S., Powell, M.J., Reddy, J.N.: Constitutive theories for internal polar thermoelastic solid continua. J. Pure Appl. Math. Adv. Appl. 14(2), 89–150 (2015)

    Google Scholar 

  4. Surana, K.S., Mohammadi, F., Reddy, J.N., Dalkilic, A.S.: Ordered rate constitutive theories for non-classical internal polar thermoviscoelastic solids without memory. Int. J. Math. Sci. Eng. Appl. 10(2), 99–131 (2016)

    Google Scholar 

  5. Surana, K.S., Shanbhag, R.S., Reddy, J.N.: Necessity of law of balance of moment of moments in non-classical continuum theories for solid continua. Meccanica 53(11), 2939–2972 (2018)

    MathSciNet  MATH  Google Scholar 

  6. Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)

    MATH  Google Scholar 

  7. Surana, K.S., Reddy, J.N., Mysore, D.: Thermodynamic consistency of beam theories in the context of classical and non-classical continuum mechanics and a kinematic assumption free new formulation. (in the process of being submitted for publication) (2018)

  8. Surana, K.S., Reddy, J.N., Mysore, D.: Non-classical continuum theories for solid and fluent continua and some applications. Int. J. Smart Nano Mater. 10, 28–89 (2018)

    Google Scholar 

  9. Bayada, G., Łukaszewicz, G.: On micropolar fluids in the theory of lubrication. Rigorous derivation of an analogue of the Reynolds equation. Int. J. Eng. Sci. 34(13), 1477–1490 (1996)

    MathSciNet  MATH  Google Scholar 

  10. Eringen, A.C.: Simple microfluids. Int. J. Eng. Sci. 2(2), 205–217 (1964)

    MathSciNet  MATH  Google Scholar 

  11. Eringen, A.C.: Mechanics of Micromorphic Materials. In: Gortler, H. (ed.) Proceeding of 11th International Congress of Applied Mechanics, Munich, pp. 131–138. Springer, Berlin (1964)

    Google Scholar 

  12. Eringen, A.C.: Theory of micropolar fluids. J. Math. Mech. 16(1), 1–18 (1966)

    MathSciNet  Google Scholar 

  13. Eringen, A.C.: Mechanics of generalized continua. In: Kroner, E. (ed.) Mechanics of Micromorphic Continua, pp. 18–35. Springer, New York (1968)

    MATH  Google Scholar 

  14. Eringen, A.C.: Theory of micropolar elasticity. In: Liebowitz, H. (ed.) Fracture, pp. 621–729. Academic Press, New York (1968)

    Google Scholar 

  15. Eringen, A.C.: Micropolar fluids with stretch. Int. J. Eng. Sci. 7(1), 115–127 (1969)

    MATH  Google Scholar 

  16. Eringen, A.C.: Balance laws of micromorphic mechanics. Int. J. Eng. Sci. 8(10), 819–828 (1970)

    MathSciNet  MATH  Google Scholar 

  17. Eringen, A.C.: Theory of thermomicrofluids. J. Math. Anal. Appl. 38(2), 480–496 (1972)

    MATH  Google Scholar 

  18. Eringen, A.C.: Micropolar theory of liquid crystals. Liq. Cryst. Ordered Fluids 3, 443–473 (1978)

    Google Scholar 

  19. Eringen, A.C.: Theory of thermo-microstretch fluids and bubbly liquids. Int. J. Eng. Sci. 28(2), 133–143 (1990)

    MathSciNet  MATH  Google Scholar 

  20. Eringen, A.C.: Balance laws of micromorphic continua revisited. Int. J. Eng. Sci. 30(6), 805–810 (1992)

    MathSciNet  MATH  Google Scholar 

  21. Eringen, A.C.: Continuum theory of microstretch liquid crystals. J. Math. Phys. 33, 4078 (1992)

    MathSciNet  MATH  ADS  Google Scholar 

  22. Eringen, A.C.: Theory of Micropolar Elasticity. Springer, Berlin (1999)

    MATH  Google Scholar 

  23. Franchi, F., Straughan, B.: Nonlinear stability for thermal convection in a micropolar fluid with temperature dependent viscosity. Int. J. Eng. Sci. 30(10), 1349–1360 (1992)

    MathSciNet  MATH  Google Scholar 

  24. Kirwan, A.D.: Boundary conditions for micropolar fluids. Int. J. Eng. Sci. 24(7), 1237–1242 (1986)

    MATH  Google Scholar 

  25. Koiter, W.T.: Couple stresses in the theory of elasticity, I and II. Nederl. Akad. Wetensch. Proc. Ser. B 67, 17–44 (1964)

    MathSciNet  MATH  Google Scholar 

  26. Oevel, W., Schröter, J.: Balance equations for micromorphic materials. J. Stat. Phys. 25(4), 645–662 (1981)

    MathSciNet  ADS  Google Scholar 

  27. Eringen, A.C.: A unified theory of thermomechanical materials. Int. J. Eng. Sci. 4(2), 179–202 (1966)

    MathSciNet  MATH  Google Scholar 

  28. Eringen, A.C.: Linear theory of micropolar viscoelasticity. Int. J. Eng. Sci. 5(2), 191–204 (1967)

    MATH  Google Scholar 

  29. Eringen, A.C.: Theory of micromorphic materials with memory. Int. J. Eng. Sci. 10(7), 623–641 (1972)

    MATH  Google Scholar 

  30. Reddy, J.N.: Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45(2–8), 288–307 (2007)

    MATH  Google Scholar 

  31. Reddy, J.N., Pang, S.D.: Nonlocal continuum theories of beams for the analysis of carbon nanotubes. J. Appl. Phys. 103(2), 023511 (2008)

    ADS  Google Scholar 

  32. Reddy, J.N.: Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. Int. J. Eng. Sci. 48(11), 1507–1518 (2010)

    MathSciNet  MATH  Google Scholar 

  33. Lu, P., Zhang, P.Q., Leo, H.P., Wang, C.M., Reddy, J.N.: Nonlocal elastic plate theories. Proc. R. Soc. A 463, 3225–3240 (2007)

    MathSciNet  MATH  ADS  Google Scholar 

  34. Yang, J.F.C., Lakes, R.S.: Experimental study of micropolar and couple stress elasticity in compact bone in bending. J. Biomech. 15(2), 91–98 (1982)

    Google Scholar 

  35. Lubarda, V.A., Markenscoff, X.: Conservation integrals in couple stress elasticity. J. Mech. Phys. Solids 48, 553–564 (2000)

    MathSciNet  MATH  ADS  Google Scholar 

  36. Ma, H.M., Gao, X.L., Reddy, J.N.: A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. J. Mech. Phys. Solids 56, 3379–3391 (2008)

    MathSciNet  MATH  ADS  Google Scholar 

  37. Ma, H.M., Gao, X.L., Reddy, J.N.: A nonclassical Reddy–Levinson beam model based on modified couple stress theory. J. Multiscale Comput. Eng. 8(2), 167–180 (2010)

    Google Scholar 

  38. Reddy, J.N.: Microstructure dependent couple stress theories of functionally graded beams. J. Mech. Phys. Solids 59, 2382–2399 (2011)

    MathSciNet  MATH  ADS  Google Scholar 

  39. Reddy, J.N., Arbind, A.: Bending relationship between the modified couple stress-based functionally graded timoshenko beams and homogeneous bernoulli-euler beams. Ann. Solid Struct. Mech. 3, 15–26 (2012)

    Google Scholar 

  40. Srinivasa, A.R., Reddy, J.N.: A model for a constrained, finitely deforming elastic solid with rotation gradient dependent strain energy and its specialization to Von Kármán plates and beams. J. Mech. Phys. Solids 61(3), 873–885 (2013)

    MathSciNet  ADS  Google Scholar 

  41. Mora, R.J., Waas, A.M.: Evaluation of the micropolar elasticity constants for honeycombs. Acta Mech. 192, 1–16 (2007)

    MATH  Google Scholar 

  42. Onck, P.R.: Cosserat modeling of cellular solids. C. R. Mec. 330, 717–722 (2002)

    MathSciNet  MATH  ADS  Google Scholar 

  43. Segerstad, P.H., Toll, S., Larsson, R.: A micropolar theory for the finite elasticity of open-cell cellular solids. Proc. R. Soc. A 465, 843–865 (2009)

    MathSciNet  MATH  ADS  Google Scholar 

  44. Altenbach, H., Eremeyev, V.A.: On the linear theory of micropolar plates. ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Mech. 89(4), 242–256 (2009)

    MathSciNet  MATH  Google Scholar 

  45. Altenbach, H., Eremeyev, V.A.: Strain rate tensors and constitutive equations of inelastic micropolar materials. Int. J. Plast 63, 3–17 (2014)

    Google Scholar 

  46. Altenbach, H., Eremeyev, V.A., Lebedev, L.P., Rendón, L.A.: Acceleration waves and ellipticity in thermoelastic micropolar media. Arch. Appl. Mech. 80(3), 217–227 (2010)

    MATH  ADS  Google Scholar 

  47. Altenbach, H., Maugin, G.A., Erofeev, V.: Mechanics of Generalized Continua, vol. 7. Springer, Berlin (2011)

    MATH  Google Scholar 

  48. Altenbach, H., Naumenko, K., Zhilin, P.A.: A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions. Contin. Mech. Thermodyn. 15(6), 539–570 (2003)

    MathSciNet  MATH  ADS  Google Scholar 

  49. Ebert, F.: A similarity solution for the boundary layer flow of a polar fluid. Chem. Eng. J. 5(1), 85–92 (1973)

    Google Scholar 

  50. Eremeyev, V.A., Lebedev, L.P., Altenbach, H.: Kinematics of micropolar continuum. In: Eremeyev, V.A., Lebedev, L.P., Altenbach, H. (eds.) Foundations of Micropolar Mechanics, pp. 11–13. Springer, Berlin (2013)

    MATH  Google Scholar 

  51. Eremeyev, V.A., Pietraszkiewicz, W.: Material symmetry group and constitutive equations of anisotropic Cosserat continuum. In: Generalized Continua as Models for Materials. p. 10 (2012)

  52. Eremeyev, V.A., Pietraszkiewicz, W.: Material symmetry group of the non-linear polar-elastic continuum. Int. J. Solids Struct. 49(14), 1993–2005 (2012)

    Google Scholar 

  53. Grekova, E.F.: Ferromagnets and Kelvin’s medium: basic equations and wave processes. J. Comput. Acoust. 9(02), 427–446 (2001)

    MATH  Google Scholar 

  54. Grekova, E.F.: Linear reduced Cosserat medium with spherical tensor of inertia, where rotations are not observed in experiment. Mech. Solids 47(5), 538–543 (2012)

    ADS  Google Scholar 

  55. Grekova, E.F., Kulesh, M.A., Herman, G.C.: Waves in linear elastic media with microrotations, part 2: Isotropic reduced Cosserat model. Bull. Seismol. Soc. Am. 99(2B), 1423–1428 (2009)

    Google Scholar 

  56. Grioli, G.: Linear micropolar media with constrained rotations. In: Micropolar elasticity, Springer, Berlin, pp 45–71 (1974)

  57. Grekova, E.F., Maugin, G.A.: Modelling of complex elastic crystals by means of multi-spin micromorphic media. Int. J. Eng. Sci. 43(5), 494–519 (2005)

    MathSciNet  MATH  Google Scholar 

  58. Grioli, G.: Microstructures as a refinement of cauchy theory. Problems of physical concreteness. Contin. Mech. Thermodyn. 15(5), 441–450 (2003)

    MathSciNet  MATH  ADS  Google Scholar 

  59. Altenbach, J., Altenbach, H., Eremeyev, V.A.: On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Arch. Appl. Mech. 80(1), 73–92 (2010)

    MATH  ADS  Google Scholar 

  60. Lazar, M., Maugin, G.A.: Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. Int. J. Eng. Sci. 43(13), 1157–1184 (2005)

    MathSciNet  MATH  Google Scholar 

  61. Lazar, M., Maugin, G.A.: Defects in gradient micropolar elasticity—I: screw dislocation. J. Mech. Phys. Solids 52(10), 2263–2284 (2004)

    MathSciNet  MATH  ADS  Google Scholar 

  62. Maugin, G.A.: A phenomenological theory of ferroliquids. Int. J. Eng. Sci. 16(12), 1029–1044 (1978)

    MathSciNet  MATH  Google Scholar 

  63. Maugin, G.A.: Wave motion in magnetizable deformable solids. Int. J. Eng. Sci. 19(3), 321–388 (1981)

    MathSciNet  MATH  Google Scholar 

  64. Maugin, G.A.: On the structure of the theory of polar elasticity. Philos. Trans. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 356(1741), 1367–1395 (1998)

    MathSciNet  MATH  ADS  Google Scholar 

  65. Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3), 774–787 (2009)

    MathSciNet  MATH  Google Scholar 

  66. Cosserat, E., Cosserat, F.: Théorie des Corps Déformables. Hermann, Paris (1909)

    MATH  Google Scholar 

  67. Zakharov, A.V., Aero, E.L.: Statistical mechanical theory of polar fluids for all densities. Phys. A 160(2), 157–165 (1989)

    Google Scholar 

  68. Green, A.E.: Micro-materials and multipolar continuum mechanics. Int. J. Eng. Sci. 3(5), 533–537 (1965)

    MathSciNet  Google Scholar 

  69. Green, A.E., Rivlin, R.S.: The relation between director and multipolar theories in continuum mechanics. Z. für angew. Math.k und Phys. ZAMP 18(2), 208–218 (1967)

    MATH  ADS  Google Scholar 

  70. Green, A.E., Rivlin, R.S.: Multipolar continuum mechanics. Arch. Ration. Mech. Anal. 17(2), 113–147 (1964)

    MathSciNet  MATH  Google Scholar 

  71. Martins, L.C., Oliveira, R.F., Podio-Guidugli, P.: On the vanishing of the additive measures of strain and rotation for finite deformations. J. Elast. 17(2), 189–193 (1987)

    MathSciNet  MATH  Google Scholar 

  72. Martins, L.C., Podio-Guidugli, P.: On the local measures of mean rotation in continuum mechanics. J. Elast. 27(3), 267–279 (1992)

    MathSciNet  MATH  Google Scholar 

  73. Nowacki, W.: Theory of Micropolar Elasticity. Springer, Berlin (1970)

    MATH  Google Scholar 

  74. Surana, K.S., Joy, A.D., Reddy, J.N.: Ordered rate constitutive theories for thermoviscoelastic solids without memory incorporating internal and cosserat rotations. Acta Mech. 229(8), 3189–3213 (2018)

    MathSciNet  MATH  Google Scholar 

  75. Surana, K.S., Joy, A.D., Reddy, J.N.: Ordered rate constitutive theories for non-classical thermoviscoelastic solids with memory incorporating internal and cosserat rotations. Continuum Mechanics and Thermodynamics. (in press) (2018). https://doi.org/10.1007/s00161-018-0697-8

  76. Surana, K.S., Mysore, D., Reddy, J.N.: Ordered rate constitutive theories for non-classical thermoviscoelastic solids with dissipation and memory incorporating internal rotations. Polytechnica (in press) (2018). https://doi.org/10.1007/s41050-018-0004-2:17

  77. Surana, K.S., Joy, A.D., Reddy, J.N.: Non-classical continuum theory for fluids incorporating internal and cosserat rotation rates. Continuum Mech. Thermodyn. 29(6), 1249–1289 (2017)

    MathSciNet  MATH  ADS  Google Scholar 

  78. Surana, K.S., Joy, A.D., Reddy, J.N.: Ordered rate constitutive theories for non-classical thermoviscoelastic fluids incorporating internal and cosserat rotation rates. Int. J. Appl. Mech. 10(2), 1850012 (2018). https://doi.org/10.1142/S1758825118500126

    Article  Google Scholar 

  79. Surana, K.S., Powell, M.J., Reddy, J.N.: A more complete thermodynamic framework for fluent continua. J. Therm. Eng. 1(6), 460–475 (2015)

    Google Scholar 

  80. Surana, K.S., Powell, M.J., Reddy, J.N.: A polar continuum theory for fluent continua. Int. J. Eng. Res. Ind. Appl. 8(2), 107–146 (2015)

    Google Scholar 

  81. Surana, K.S., Powell, M.J., Reddy, J.N.: Ordered rate constitutive theories for internal polar thermofluids. Int. J. Math. Sci. Eng. Appl. 9(3), 51–116 (2015)

    Google Scholar 

  82. Surana, K.S., Long, S.W., Reddy, J.N.: Rate constitutive theories of orders \(n\) and \(^1\!n\) for internal polar non-classical thermofluids without memory. Appl. Math. 7(16), 2033–2077 (2016)

    Google Scholar 

  83. Surana, K.S.: Advanced Mechanics of Continua. CRC/Taylor and Francis, Boca Raton (2015)

    MATH  Google Scholar 

  84. Surana, K.S., Joy, A.D., Reddy, J.N.: Non-classical continuum theory for solids incorporating internal rotations and rotations of cosserat theories. Contin. Mech. Thermodyn. 29(2), 665–698 (2017)

    MathSciNet  MATH  ADS  Google Scholar 

  85. Eringen, A.C.: Mechanics of Continua. Wiley, New York (1967)

    MATH  Google Scholar 

  86. Reddy, J.N.: An Introduction to Continuum Mechanics: with Application. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  87. Surana, K.S., Long, S.W., Reddy, J.N.: Necessity of law of balance/equilibrium of moment of moments in non-classical continuum theories for fluent continua. Acta Mech. 22(7), 2801–2833 (2018)

    MathSciNet  MATH  Google Scholar 

  88. Prager, W.: Strain hardening under combined stresses. J. Appl. Phys. 16, 837–840 (1945)

    MathSciNet  ADS  Google Scholar 

  89. Reiner, M.: A mathematical theory of dilatancy. Am. J. Math. 67, 350–362 (1945)

    MathSciNet  MATH  ADS  Google Scholar 

  90. Todd, J.A.: Ternary quadratic types. Philos. Trans. R. Soc. Lond. Ser. A: Math. Phys. Sci. 241, 399–456 (1948)

    MathSciNet  MATH  ADS  Google Scholar 

  91. Rivlin, R.S., Ericksen, J.L.: Stress-deformation relations for isotropic materials. J. Ration. Mech. Anal. 4, 323–425 (1955)

    MathSciNet  MATH  Google Scholar 

  92. Rivlin, R.S.: Further remarks on the stress-deformation relations for isotropic materials. J. Ration. Mech. Anal. 4, 681–702 (1955)

    MathSciNet  MATH  Google Scholar 

  93. Wang, C.C.: On representations for isotropic functions, Part I. Arch. Ration. Mech. Anal. 33, 249 (1969)

    Google Scholar 

  94. Wang, C.C.: On representations for isotropic functions, Part II. Arch. Ration. Mech. Anal. 33, 268 (1969)

    Google Scholar 

  95. Wang, C.C.: A new representation theorem for isotropic functions, Part I and Part II. Arch. Ration. Mech. Anal. 36, 166–223 (1970)

    Google Scholar 

  96. Wang, C.C.: Corrigendum to ‘Representations for isotropic functions’. Arch. Ration. Mech. Anal. 43, 392–395 (1971)

    Google Scholar 

  97. Smith, G.F.: On a fundamental error in two papers of C.C. Wang, ‘On representations for isotropic functions, Part I and Part II’. Arch. Ration. Mech. Anal. 36, 161–165 (1970)

    Google Scholar 

  98. Smith, G.F.: On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9, 899–916 (1971)

    MathSciNet  MATH  Google Scholar 

  99. Spencer, A.J.M., Rivlin, R.S.: The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch. Ration. Mech. Anal. 2, 309–336 (1959)

    MathSciNet  MATH  Google Scholar 

  100. Spencer, A.J.M., Rivlin, R.S.: Further results in the theory of matrix polynomials. Arch. Ration. Mech. Anal. 4, 214–230 (1960)

    MathSciNet  MATH  Google Scholar 

  101. Spencer, A.J.M.: Theory of Invariants. Chapter 3 ‘Treatise on Continuum Physics, I’ Edited by A. C. Eringen, Academic Press (1971)

  102. Boehler, J.P.: On irreducible representations for isotropic scalar functions. J. Appl. Math. Mech. / Z. für Angew. Math. und Mech. 57, 323–327 (1977)

    MathSciNet  MATH  ADS  Google Scholar 

  103. Zheng, Q.S.: On the representations for isotropic vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions. Int. J. Eng. Sci. 31, 1013–1024 (1993)

    MathSciNet  MATH  Google Scholar 

  104. Zheng, Q.S.: On transversely isotropic, orthotropic and relatively isotropic functions of symmetric tensors, skew-symmetric tensors, and vectors. Int. J. Eng. Sci. 31, 1399–1453 (1993)

    MATH  Google Scholar 

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Acknowledgements

First author is grateful for his endowed professorship and the department of mechanical engineering of the University of Kansas for providing financial support to the second author. The computational facilities provided by the Computational Mechanics Laboratory of the mechanical engineering department are also acknowledged.

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    K. S. Surana & J. K. Kendall

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Surana, K.S., Kendall, J.K. Existence of rotational waves in non-classical thermoelastic solid continua incorporating internal rotations. Continuum Mech. Thermodyn. 32, 1659–1683 (2020). https://doi.org/10.1007/s00161-020-00872-6

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