On strong and weak discontinuities of the coupled thermomechanical field in micropolar thermoelastic type-II continua


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Abstract

The present study is devoted to problem of propagating surfaces of weak and strong discontinuities of translational displacements, microrotations and temperature in micropolar (MP) thermoelastic (TE) type-II continua. First part of the paper is concerned to discussions of the propagating surfaces of strong discontinuities of field variables in type-II MPTE continua. Constitutive relations for hyperbolic thermoelastic type-II micropolar continuum is derived by the field theory. The special form of the first variation of the action integral is used in order to obtain 4-covariant jump conditions on wave surfaces. Three-dimensional form of the jump conditions on the surface of a strong discontinuity of thermoelastic field are derived from 4-covariant form. Problems of propagation of weak discontinuities in type-II MPTE continua are discussed too. Geometrical and kinematical compatibility conditions due to Hadamard and Thomas are used to study possible wave surfaces of weak discontinuities. It is shown that the surfaces of weak discontinuities can propagate exist without weak discontinuities of the temperature field.

About the authors

Evgenii V Murashkin

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Email: murashkin@ipmnet.ru
(Cand. Phys. & Math. Sci.; murashkin@ipmnet.ru), Researcher, Lab. of Modeling in Solid Michanics 101, pr. Vernadskogo, Moscow, 119526, Russian Federation

Yuri N Radayev

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Email: radayev@ipmnet.ru
Dr. Phys. & Math. Sci.; radayev@ipmnet.ru; Corresponding Author, Leader Researcher, Lab. of Modeling in Solid Michanics 101, pr. Vernadskogo, Moscow, 119526, Russian Federation

References

  1. Мурашкин E. В., Радаев Ю. Н. О сильных и слабых разрывах связанного термомеханического поля в термоупругих микрополярных континуумах второго типа / Четвертая международная конференция «Математическая физика и ее приложения»: материалы конф.; ред. чл.-корр. РАН И. В. Волович; д.ф.-м.н., проф. В. П. Радченко. Самара: СамГТУ, 2014. С. 261-262.
  2. Ковалев В. А., Радаев Ю. Н. Волновые задачи теории поля и термомеханика. Саратов: Изд-во Сарат. ун-та, 2010. 328 с.
  3. Cosserat E. et F. Théorie des corps déformables. Paris: Librairie Scientifique A. Hermann et Fils, 1909. 226 pp.
  4. Toupin R. A. Theories of elasticity with couple-stress // Arch. Rational Mech. Anal., 1964. vol. 17, no. 2. pp. 85-112. doi: 10.1007/bf00253050.
  5. Green A. E., Naghdi P. M. On undamped heat waves in an elastic solid // Journal of Thermal Stresses, 1992. vol. 15, no. 2. pp. 253-264. doi: 10.1080/01495739208946136.
  6. Green A. E., Naghdi P. M. Thermoelasticity without energy dissipation // J. Elasticity, 1993. vol. 31, no. 3. pp. 189-208. doi: 10.1007/BF00044969.
  7. Thomas T. Plastic flow and fracture in solids. New York: Academic Press, 1961. ix+267 pp.
  8. Rankine W. J. M. On the thermodynamic theory of waves of finite longitudinal disturbance // Proceedings of the Royal Society of London, 1869. vol. 18, no. 114-122. pp. 80-83. doi: 10.1098/rspl.1869.0025
  9. Rankine W. J. M. On the thermodynamic theory of waves of finite longitudinal disturbance // Philosophical Transactions of the Royal Society of London. vol. 160. pp. 277-288. doi: 10.1098/rstl.1870.0015
  10. Rankine W. J. M. On the thermodynamic theory of waves of finite longitudinal disturbance / Classic Papers in Shock Compression Science / Shock Wave and High Pressure Phenomena, 1998. pp. 133-148. doi: 10.1007/978-1-4612-2218-7_5.
  11. Hugoniot P. H. Sur la propagation du mouvement dans les corps et spécialement dans lesgaz parfaits (première partie) // Journal de l'Ecole Polytechnique, 1887. vol. 57. pp. 3-97 (In French).
  12. Ковалев В. А., Мурашкин Е. В., Радаев Ю. Н. Математическая теория связанных плоских гармонических термоупругих волн в микрополярных континуумах первого типа // Изв. Сарат. ун-та. Нов. сер. Сер. Математика. Механика. Информатика, 2014. Т. 14, № 1. С. 77-87.
  13. Nowacki W. Theory of Asymmetric Elasticity. Oxford: Pergamon Press, 1986. viii+383 pp.

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