Geodesic
On Strong and Weak Discontinuities of the Coupled Thermomechanical Field in Micropolar Thermoelastic Type-II Continua
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 85-97

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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.
Keywords: micropolar thermoelasticity, type-II continuum, weak discontinuity, strong discontinuity, shock wave, longitudinal wave, compatibility condition, jump.
Mots-clés : transverse wave 
@article{VSGTU_2014_4_a7,
     author = {E. V. Murashkin and Yu. N. Radayev},
     title = {On {Strong} and {Weak} {Discontinuities} of the {Coupled} {Thermomechanical} {Field} in {Micropolar} {Thermoelastic} {Type-II} {Continua}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {85--97},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
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E. V. Murashkin; Yu. N. Radayev. On Strong and Weak Discontinuities of the Coupled Thermomechanical Field in Micropolar Thermoelastic Type-II Continua. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 85-97. http://geodesic.mathdoc.fr/item/VSGTU_2014_4_a7/