Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure
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Beschreibung
Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique to construct nonlinear evolution equations describing non-equilibrium processes, while also developing a geometric context for non-equilibrium thermodynamics. Solid materials are the main focus in this volume, but the construction is shown to also apply to fluids. This volume also:
• Explains the theory behind a thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes, based on supplementing the second law with a maximum dissipation criterion
• Provides a geometric setting for non-equilibrium thermodynamics in differential topology and, in particular, contact structures that generalize Gibbs
• Models processes that include thermoviscoelasticity, thermoviscoplasticity, thermoelectricity and dynamic fracture
• Recovers several standard time-dependent constitutive models as maximum dissipation processes
• Produces transport models that predict finite velocity of propagation
• Emphasizes applications to the time-dependent modeling of soft biological tissue
Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure will be valuable for researchers, engineers and graduate students in non-equilibrium thermodynamics and the mathematical modeling of material behavior.
Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique created in order to construct nonlinear evolution equations describing non-equilibrium processes, while also developing a geometric context for non-equilibrium thermodynamics. Solid materials are the main focus in this volume, but the construction is shown to also apply to fluids. This volume also: • Explains the theory behind thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes • Provides a geometric setting for non-equilibrium thermodynamics through several standard models, which are defined as maximum dissipation processes • Emphasizes applications to the time-dependent modeling of soft biological tissue Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure will be valuable for researchers, engineers and graduate students in non-equilibrium thermodynamics and the mathematical modeling of material behavior.
Explains the theory behind thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes Provides a geometric setting for non-equilibrium thermodynamics through several standard models, which are defined as maximum dissipation processes Emphasizes applications to the time-dependent modeling of soft biological tissue Includes supplementary material: sn.pub/extras
Autor*in
Henry W. Haslach Jr.
Themen in »Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure«
Bifurcations Biomaterials Continuum thermodynamics Homogeneous thermodynamics Hyperelastic energy density Joule heating Non-equilibrium thermodynamics Nonlinear dynamical systems Onsager Tensors Viscoelasticity Viscoplasticity
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From the reviews:
“The author presents his construction of a geometric model for non-equilibrium thermodynamics and his maximum dissipation criterion which is assumed to complement the second law of thermodynamics. … the author explores different concrete situations where his construction of a maximum dissipation criterion may be applied. … This book will be interesting for researchers involved either in applied mathematics or in mechanics.” (Alain Brillard, Zentralblatt MATH, Vol. 1222, 2011)
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