References
- E. Cosserat and F. Cosserat, Théorie Des Corps Déformables. Paris: Librairie Scientifique A. Hermann et Fils, 2009.
- A. C. Eringen, “Linear theory of micropolar viscoelasticity,” Int. J. Eng. Sci, vol. 5, no. 2, pp. 191–204, 1967. DOI: 10.1016/0020-7225(67)90004-3.
- A. C. Eringen, “Balance laws of micromorphic mechanics,” Int. J. Eng. Sci, vol. 8, no. 10, pp. 819–828, 1970.
- R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Rational Mech. Anal, vol. 16, no. 1, pp. 51–78, 1964. DOI: 10.1007/BF00248490.
- A. C. Eringen, Microcontinuum Field Theories: I. Foundations and Solids, New York, USA: Springer, 2012.
- P. Neff, I.-D. Ghiba, A. Madeo, L. Placidi and G. Rosi, “A unifying perspective: The relaxed linear micromorphic continuum,” Continuum Mech. Thermodyn, vol. 26, no. 5, pp. 639–681, 2014. DOI: 10.1007/s00161-013-0322-9.
- I.-D. Ghiba, P. Neff, A. Madeo, L. Placidi and G. Rosi, “The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics,” Math. Mech. Solids, vol. 20, no. 10, pp. 1171–1197, 2015. DOI: 10.1177/1081286513516972.
- A. Madeo, P. Neff, I.-D. Ghiba, L. Placidi and G. Rosi, “Wave propagation in relaxed micromorphic continua: Modeling metamaterials with frequency band-gaps,” Continuum Mech. Thermodyn, vol. 27, no. 4-5, pp. 551–570, 2015. DOI: 10.1007/s00161-013-0329-2.
- A. Madeo, P. Neff, I.-D. Ghiba, L. Placidi and G. Rosi, “Band gaps in the relaxed linear micromorphic continuum,” Z. Angew. Math. Mech, vol. 95, no. 9, pp. 880–887, 2015. DOI: 10.1002/zamm.201400036.
- A. Khurana, S. Bala, H. Khan, S. K. Tomar and P. Neff, “On the dispersion of waves for the linear thermoelastic relaxed micromorphic model,” J. Therm. Stresses, vol. 43, no. 1, pp. 3–20, 2020. DOI: 10.1080/01495739.2019.1679056.
- E. Betti, “Teoria della ‘elasticitia’,” Il Nuovo Cim, vol. 7-8, no. 1, pp. 158–180, 1872. DOI: 10.1007/BF02824604.
- V. M. Maizel, “Generalization of the Betti—Maxwell theorem to the case of thermal stresses and some applications,”' (in Russian) DAN SSSR, vol. 30, pp. 115–118, 1941.
- Y. C. Fung and P. Tong, Classical and Computational Solid Mechanics, Singapore: World Scientific, 2001,
- V. Ionescu-Cazimir, “Problem of linear coupled thermoelasticity: Theorems on reciprocity for dynamic problem of coupled thermoelasticity. I,” Bull. Acad. Polon. Sci. Ser. Sci. Tech, vol. 12, no. 9, pp. 473–480, 1964.
- W. Nowacki, “Couple-Stresses in the theory of thermoelasticity,” in irreversible aspects of continuum mechanics and transfer of physical characteristics in moving fluids,” H. Parkus and L.I. Sedov, Eds. Vienna, IUTAM Symposia, Vienna: Springer, 1966.
- D. S. Chandrasekharaiah, “A reciprocal theorem in generalized thermoelasticity,” J Elasticity, vol. 14, no. 2, pp. 223–226, 1984. DOI: 10.1007/BF00041669.
- D. S. Chandrasekharaiah, “Variational and reciprocal principles in micropolar thermoelasticity,” Int. J. Eng. Sci, vol. 25, no. 1, pp. 55–63, 1987. DOI: 10.1016/0020-7225(87)90134-0.
- D. Ieşan, “Sur la Théorie de la Thermoélasticité Micropolaire Couplée,” C. R. Acad. Sci. Paris, vol. 265A, no. 9, pp. 271–274, 1967.
- D. Ieşan, “On the linear coupled thermoelasticity with two temperatures,” J. Appl. Math. Phys., vol. 21, no. 4, pp. 583–591, 1970. DOI: 10.1007/BF01587687.
- D. Ieşan, “Reciprocity, uniqueness, and minimum principles in the dynamic theory of thermoelasticity,” J. Therm. Stresses, vol. 12, no. 4, pp. 465–481, 1989. DOI: 10.1080/01495738908961978.
- A. C. Eringen and E. S. Suhubi, Elastodynamics: Linear Theory, Vol. II, New York: Academic Press, 1974,
- J. D. Achenbach, Reciprocity in Elastodynamics. Cambridge, UK: Cambridge University Press, 2003,
- J. D. Achenbach, “Application of the reciprocity theorem to analyze ultrasound generated by high-intensity surface heating of elastic bodies,” J. Therm. Stresses, vol. 30, no. 8, pp. 841–853, 2007. DOI: 10.1080/01495730701462782.
- L. Brun, “Methodes Energetiques dans les Systemes Evolutifs Lineares. Theormes d’Unicite,” J. Méc., vol. 8, pp. 167–192, 1969.
- R. J. Knops and L. E. Payne, “Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics,” Arch. Rational Mech. Anal, vol. 41, no. 5, pp. 363–398, 1971. DOI: 10.1007/BF00281873.
- P. M. Naghdi and J. A. Trapp, “A uniqueness theorem in the theory of Cosserat surface,” J Elasticity, vol. 2, no. 1, pp. 9–20, 1972. DOI: 10.1007/BF00045690.
- A. E. Green and K. A. Lindsay, “Thermoelasticity,” J Elasticity, vol. 2, no. 1, pp. 1–7, 1972. no DOI: 10.1007/BF00045689.
- A. E. Green, “A note on linear thermoelasticity,” Mathematika, vol. 19, no. 1, pp. 69–75, 1972. DOI: 10.1112/S0025579300004952.
- G. P. Galdi, R. J. Knops and S. Rionero, “Uniqueness and continuous dependence in the linear elastodynamic exterior and half-space problems,” Math. Proc. Camb. Phil. Soc, vol. 99, no. 2, pp. 357–366, 1986. DOI: 10.1017/S0305004100064276.
- S. Chiriţă, “Some applications of the Lagrange identity in thermoelasticity with one relaxation time,” J. Therm. Stresses, vol. 11, no. 3, pp. 207–231, 1988.
- S. Rionero and S. Chiriţă, “New reciprocal and continuous dependence theorems in linear theory of viscoelasticity,” Int. J. Eng. Sci, vol. 27, no. 9, pp. 1023–1036, 1989. DOI: 10.1016/0020-7225(89)90081-5.
- M. Marin, “The Lagrange identity method in thermoelasticity of bodies with microstructure,” Int. J. Eng. Sci, vol. 32, no. 8, pp. 1229–1240, 1994. DOI: 10.1016/0020-7225(94)90034-5.
- M. Marin, “Lagrange identity method for microstretch thermoelastic materials,” J. Math. Anal. Appl, vol. 363, no. 1, pp. 275–286, 2010. DOI: 10.1016/j.jmaa.2009.08.045.
- M. Marin, S. R. Mahmoud and K. S. Al-Basyouni, “Problems of micromorphic elastic bodies approached by Lagrange identity method,” CMC-Comput Mat. Con, vol. 37, no. 1, pp. 23–37, 2013.
- D. Ieşan, “On the micromorphic thermoelasticity,” Int. J. Eng. Sci, vol. 40, no. 5, pp. 549–567, 2002. DOI: 10.1016/S0020-7225(01)00061-1.
- D. Ieşan, “On some theorems in thermoelastodynamics,” Rev. Roum. Sci. Ser. Techn. Me´c. Appl, vol. 34, pp. 101–111, 1989.
- M. Marin, I. Abbas and C. Cârstea, “On continuous dependence for the mixed problem of microstretch bodies,” Analele Universitatii “Ovidius” Constanta-Seria Matematica, vol. 25, no. 1, pp. 131–143, 2017. 2017. DOI: 10.1515/auom-2017-0011.