By Henry W. Haslach Jr.
Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium procedures in fabrics. The e-book develops a basic strategy to build nonlinear evolution equations describing non-equilibrium methods, whereas additionally constructing a geometrical context for non-equilibrium thermodynamics. sturdy fabrics are the focus during this quantity, however the development is proven to additionally follow to fluids. This quantity additionally:
• Explains the idea in the back of a thermodynamically-consistent building of non-linear evolution equations for non-equilibrium techniques, according to supplementing the second one legislation with a greatest dissipation criterion
• presents a geometrical surroundings for non-equilibrium thermodynamics in differential topology and, specifically, touch constructions that generalize Gibbs
• types procedures that come with thermoviscoelasticity, thermoviscoplasticity, thermoelectricity and dynamic fracture
• Recovers numerous normal time-dependent constitutive types as greatest dissipation tactics
• Produces delivery types that are expecting finite pace of propagation
• Emphasizes functions to the time-dependent modeling of sentimental organic tissue
Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure could be helpful for researchers, engineers and graduate scholars in non-equilibrium thermodynamics and the mathematical modeling of fabric behavior.
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Extra info for Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure
Sample 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.
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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 .