Abstract
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.
Highlights
Problems of micropolar continua take its origin from the classical E. and F
There are several phenomena being beyond the scope of the conventional thermoelasticity (CTE) and piezoelectroelasticity, the finite propagation velocity of thermal waves known as second sound waves
The micropolar thermoelastic (MPTE) continuum may be described in terms of field formalism, for example, from positions of the Green–Naghdi thermoelasticity (GN-theory) [15, 16]
Summary
Problems of micropolar continua take its origin from the classical E. and F. There are several phenomena (for example, additive manufacturing design [4, 5], biomechanics, nematic liquid crystals [7, 8] behavior, the anomalous piezoelectric effect in quartz, the dispersion of elastic waves, as well as a number of other experimentally observed elastic properties of the pure crystals) being beyond the scope of the conventional thermoelasticity (CTE) and piezoelectroelasticity, the finite propagation velocity of thermal waves known as second sound waves. The micropolar thermoelastic (MPTE) continuum may be described in terms of field formalism, for example, from positions of the Green–Naghdi thermoelasticity (GN-theory) [15, 16] Such mathematical frame- works of the thermoelastic behavior of solids are rapidly refined [17,18,19,20]. GNIII-theory obviously encircles a wider range of phenomena, as compared with the classical Fourier heat conduction (CTE) theory
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