Compatibility conditions in models of semi-isotropic thermoelastic solids

E. V. Murashkin, T. K. Nesterov, N. E. Stadnik

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

Abstract: In this paper, we discuss the compatibility conditions on the surfaces of weak and strong discontinuities propagating in continuous semi-isotropic thermoelastic media. To derive such boundary conditions, the well-known Yugonio–Hadamar theory, substantially developed by G. I. Bykovtsev, and generalized to the case of pseudotensor physical fields, is used. The questions of differentiation with respect to pseudoscalar time and its transformation under mirror reflections and space inversions are considered. First-order geometric and kinematic compatibility conditions are obtained in terms of pseudotensors. Compatibility conditions are derived for weak discontinuities of displacements and microrotations in a hemitropic micropolar continuum. Compatibility conditions are obtained for strong discontinuities in a semi-isotropic thermoelastic continuum.

Keywords: pseudotensor, fundamental orienting pseudoscalar, constitutive pseudoscalars, micropolar hemitropic continuum, elastic potential, primary wave mode, mirror mode.

Received: 20.02.2023
Revised: 06.06.2023
Accepted: 01.06.2023

DOI: 10.37972/chgpu.2023.55.1.011