MATEC Web Conf.
Volume 95, 20172016 the 3rd International Conference on Mechatronics and Mechanical Engineering (ICMME 2016)
|Number of page(s)||7|
|Section||Applied Mechanics and Dynamics|
|Published online||09 February 2017|
Compatibility Conditions in Continua with Microstrusture
1 Institute for Problems in Mechanics of the Russian Academy of Sciences, Vernadsky Ave 101 Bldg 1, Moscow, 119526, Russia
2 Bauman Moscow State Technical University, 2nd Baumanskaya Str 5/1, Moscow, 105005, Russia
3 National Research Nuclear University T«MEPhITї, Kashirskoye shosse 31, Moscow, 115409, Russia
4 Moscow Technological University, Vernadsky Ave 78, Moscow, 119454, Russia
The present study is devoted to the statement of compatibility conditions on propagating wave sur- faces of strong and weak discontinuities in thermoelastic continua with microstructure. The field formalism is used to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are stated for a varying domain. A special form of the first variation of the action is employed to obtain 4-covariant boundary conditions on the wave surfaces. These are given by jumps of the Piola–Kirchhoff stress 4-tensor and the energy–momentum tensor. Problems of propagation of weak discontinuities in type-II MPTE continua are considered. Geometrical and kinematical compatibility conditions are used to study possi- ble wave surfaces of weak discontinuities. It is shown that the surfaces of weak discontinuities can propagate without weak discontinuities of the temperature displacement.
© The Authors, published by EDP Sciences, 2017
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