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Thermodynamic Foundations of Tbermoelasticity
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acoustic wave Anal arbitrary assumptions axiom balance equation balance laws body boundary conditions called Clausius-Duhem inequality consider constitutive equations constitutive relations continuum defined definition deformation deformation gradient deformation-temperature denotes derivative described differential equation dislocation dissipation principle elastic elastic-plastic entropy equilibrium Euler-Lagrange equations evolution equation evolution function finite formulation Galilean invariance given heat conduction heat flux Helmholtz free energy inequality initial value integral internal dissipation internal friction internal state variables intrinsic state space introduce Lagrange multipliers law of thermodynamics linear M.E.Gurtin mapping Mech method of preparation momentum motion non-linear obtained parameter particle PERZYNA phonon Phys plastic preparation space problem propagation properties rate type respect response function satisfied second law singular surface strain rate stress tensor subbody theorem theory thermally activated thermodynamic process thermoelastic materials tion trial function unique material structure unit mass vanishes variational principle vector velocity field viscoplastic viscosity yields