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) continua. Problems of propagation of weak discontinuities in type-I MPTE continua are discussed. Geometrical and kinematical compatibility conditions due to Hadamard and Thomas are used to study possible wave surfaces of weak discontinuities. Weak discontinuities are discriminated according to spatial orientations of the discontinuities polarization vectors (DPVs). It is shown that the surfaces of weak discontinuities can propagate exist without weak discontinuities of the temperature field. Second part of the paper is concerned the 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 obtained 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.
Highlights
Problems of micropolar continua take its origin from the classical E. and F
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) continua
The special form of the first variation of the action integral is used in order to obtained 4-covariant jump conditions on wave surfaces
Summary
Problems of micropolar continua take its origin from the classical E. and F. 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) continua. These conditions are derived from the requisite equations (Sec. 2) and the geometrical and kinematical conditions due to Hadamard and Thomas [8]. Propagating surfaces of weak discontinuities are discriminated depending on the spatial orientations of DPVs. In Sec. 5 the constitutive equations for hyperbolic thermoelastic type-II micropolar continuum is derived by the field theory. Three-dimensional form of the jump conditions on the surface of a strong discontinuity of thermoelastic field are derived from 4-covariant form
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
