Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure
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-equilibri
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Henry W. Haslach Jr.
Maximum Dissipation Non-Equilibrium Thermodynamics and its Geometric Structure
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Henry W. Haslach Jr. Department of Mechanical Engineering University of Maryland Glenn L. Martin Hall College Park, MD 20742-3035, USA [email protected]
ISBN 978-1-4419-7764-9 e-ISBN 978-1-4419-7765-6 DOI 10.1007/978-1-4419-7765-6 Springer New York Dordrecht Heidelberg London c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This work explicates a geometric model for non-equilibrium thermodynamics and a maximum dissipation criterion assumed to supplement the second law of thermodynamics. The evolution equations resulting from the author’s maximum dissipation construction provide a constitutive model for non-equilibrium processes. The construction can account for the effect of loads, heat, electromagnetic effects, chemical effects, and transport processes on fluids and solids. In the process of producing a mathematical construction describing the evolution of non-equilibrium processes, some insight is also obtained about the foundations of thermodynamics. A further goal is to put this model in the context of the history of thermodynamics and constitutive modeling of solids. A constitutive model is a mathematical construct that describes the inter-relations of a set of variables that are presumed to describe the physical state and behavior of the particular materials making up the body. The model might be a system of algebraic equations, a system of differential equations, a combination of algebraic and differential equations, a geometric structure, a statistical description, etc. Constitutive models may be based on a phenomenological characterization of experimental results or may be based on fundamental physical laws. A phenomenological (or empirical) model is one that simply describes data, but is not necessarily derived from physical principles. Such models are commonly used in solid mechanics to describe the equilibrium stress-strain response. An example is the Mooney-Rivlin stress-stretch relation for rubber. No one has yet successfully derived such a model for rubber from the laws governing the molecular response of polymers. Alternatively, the mathematical model could be chosen by anal
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