Ideal asymmetric dissipative 4d-medium as a model of irreversible dynamic thermalelasticity
A model of the irreversible dynamic thermoelasticity of ideal media is
constructed in the work as the theory of elasticity of an asymmetric,
transversally isotropic in the direction of time, a dissipative defect-free 4D
medium. In this model, the fourth component of the 4D displacement vector is
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The kinematic model unites a 3D distortion tensor, a 3D velocity vector, a 3D
gradient vector of
the local non-uniform time and the entropy into a single tensor object-an
asymmetric 4D distortion tensor of the
second rank. Accordingly, the power model combines a 3D stress tensor, a 3D
pulse vector, a 3D heat flux vector and temperature into a single tensor
object-an asymmetric 4D stress tensor of the second rank. The Hooke's law
equations connecting the components of asymmetric 4D stress tensors and
distortions are formulated. Physical interpretations of the components of the
thermomechanical tensors of the formulated medium are given. Accordingly, an attempt is made to
formulate a general covariant model of the irreversible dynamic thermoelasticity
of ideal (defect-free) media in which components of common tensor objects are basic kinematic and force variables,
and the theory is described by the 4D-vector equation. The variational Sedov
equation, from which the Euler equations follow, the spatial projections of
which determine the equations of motion, and the temporal projection determines the heat equation, the entire spectrum of initial-boundary value
problems, is constructed.
