By P. W. Bridgman
1961 version.
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Extra info for The Nature of Thermodynamics
Example text
Xn ) is a Legendre transformation of the thermostatic energy density function of the controls, ϕ(y ˆ 1 , . . , yn ). 3 Generalized Thermodynamic Functions The conjugate relations, xi = ∂ ϕ/∂ ˆ yi , for i = 1, . . , n define a distinguished subset, Me , of 2n at each point of the system. The subset, Me , is a submanifold (Chapter 7). For example, if ϕˆ is the hyperelastic strain energy density of a solid, then Me is the set of possible equilibrium states. To model time-dependent nonequilibrium behavior, a generalized function, ϕ ∗ , of all thermodynamic variables is defined on all states rather than just those in Me such that Me is the manifold of zero gradient states of ϕ ∗ with respect to the state variables.
S. R. de Groot and P. Mazur (1984). Non-equilibrium Thermodynamics, Dover, New York. A. E. Green and P. M. Naghdi (1977). On thermodynamics and the nature of the second law. Proceedings of the Royal Society of London, Series A 357, 253–270. M. E. Gurtin (1968). On the thermodynamics of materials with memory. Archive for Rational Mechanics and Analysis 28, 40–50. R. B. Hall (2008). Combined thermodynamics approach for anisotropic, finite deformation overstress models of viscoplasticity. International Journal of Engineering Science 46, 119–130.
26 2 Thermostatics and Energy Methods Definition 4 A hyperelastic material is one that has a strain energy density function and whose state of stress is computed as the derivative of the strain energy density function by the strain. This means that the strain energy density function determines the stress-strain relation. 1 Linear Elastic The isotropic generalized Hooke’s law is, for normal stress σ , shear stress τ , normal strain , shear strain γ , the elastic modulus E, and the shear modulus G, x y z 1 [σx − ν(σ y + σz )]; E 1 = [σ y − ν(σx + σz )]; E 1 = [σz − ν(σx + σ y )]; E 1 1 1 γx y = τx y ; γx z = τx z ; γ yz = τ yz .