The Thermomechanics of Nonlinear Irreversible Behaviors
The Thermomechanics of Nonlinear Irreversible Behaviors

Author: G‚rard A. Maugin

Publisher: World Scientific

Published: 1999

Total Pages: 398

ISBN-13: 9789810233754

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In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of ?irreversible thermodynamics? behaviors which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework.The book is intended for all students and researchers whose main concern is the rational modeling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, fracture, nonlinear-diffusion, and phase-transformation phenomena.

Thermomechanical Behavior of Dissipative Composite Materials
Thermomechanical Behavior of Dissipative Composite Materials

Author: George Chatzigeorgiou

Publisher: Elsevier

Published: 2018-01-16

Total Pages: 298

ISBN-13: 0081025521

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Thermomechanical Behavior of Dissipative Composite Materials presents theoretical and numerical tools for studying materials and structures under fully coupled thermomechanical conditions, focusing primarily on composites. The authors cover many aspects of the modeling process and provide the reader with the knowledge required to identify the conservation laws and thermodynamic principles that must be respected by most solid materials. The book also covers construct constitutive laws for various types of dissipative processes, both rate-independent and rate-dependent, by utilizing a rigorous thermodynamic framework. Topics explored are useful for graduate students and advanced researchers who wish to strengthen their knowledge of the application of thermodynamic principles. - Identifies the conservation laws and thermodynamic principles that need to be respected by any solid material - Presents construct, proper constitutive laws for various types of dissipative processes, both rate-independent and rate-dependent, by utilizing an appropriate thermodynamic framework - Includes robust numerical algorithms that permit accuracy and efficiency in the calculations of very complicated constitutive laws - Uses rigorous homogenization theories for materials and structures with both periodic and random microstructure

Thermodynamics of Fluids Under Flow
Thermodynamics of Fluids Under Flow

Author: D. Jou

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 242

ISBN-13: 3662044145

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Based on the authors’ successful theory for extended irreversible thermodynamics, the book analyzes the thermodynamic aspects of several phenomena induced by the flow in fluid systems.

Internal Variables in Thermoelasticity
Internal Variables in Thermoelasticity

Author: Arkadi Berezovski

Publisher: Springer

Published: 2017-05-05

Total Pages: 222

ISBN-13: 3319569341

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This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are, as a rule, inhomogeneous. The thermoelastic theory with internal variables presented here provides a general framework for predicting a material’s reaction to external loading. The basic physical principles provide the primary theoretical information, including the evolution equations of the internal variables. The cornerstones of this framework are the material representation of continuum mechanics, a weak nonlocality, a non-zero extra entropy flux, and a consecutive employment of the dissipation inequality. Examples of thermoelastic phenomena are provided, accompanied by detailed procedures demonstrating how to simulate them.

Beyond Equilibrium Thermodynamics
Beyond Equilibrium Thermodynamics

Author: Hans Christian Öttinger

Publisher: John Wiley & Sons

Published: 2005-05-13

Total Pages: 651

ISBN-13: 0471727911

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Beyond Equilibrium Thermodynamics fills a niche in the market by providing a comprehensive introduction to a new, emerging topic in the field. The importance of non-equilibrium thermodynamics is addressed in order to fully understand how a system works, whether it is in a biological system like the brain or a system that develops plastic. In order to fully grasp the subject, the book clearly explains the physical concepts and mathematics involved, as well as presenting problems and solutions; over 200 exercises and answers are included. Engineers, scientists, and applied mathematicians can all use the book to address their problems in modelling, calculating, and understanding dynamic responses of materials.

Generalized Models and Non-classical Approaches in Complex Materials 1
Generalized Models and Non-classical Approaches in Complex Materials 1

Author: Holm Altenbach

Publisher: Springer

Published: 2018-03-24

Total Pages: 799

ISBN-13: 3319724401

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This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Continuum Thermomechanics
Continuum Thermomechanics

Author: Gérard A. Maugin

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 428

ISBN-13: 0306469464

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Contributed by world-renowned specialists on the occasion of Paul Germain's 80th birthday, this unique book reflects the foundational works and the intellectual influence of this author. It presents the realm of modern thermomechanics with its extraordinary wealth of applications to the behaviour of materials, whether solid or fluid. The thirty-one contributions follow an easygoing autobiographical sketch by Paul Germain, and highlight the power and richness of a methodological approach to the phenomenology of many materials. This approach combines harmoniously thermodynamics and continuum theory in order to provide exploitable, thermodynamically admissible models of a large variety of behaviours and phenomena, including those of diffusion, thermoelasticity, viscoplasticity, relaxation, hysteresis, wetting, shape-memory effects, growth, phase transitions, stability, fracture, shocks, machining of materials, microstructured solids, complex fluids, etc. Especially aimed at graduate students, researchers, and engineers in mechanical engineering and materials science, this book also presents the state of the art in an active field of research and opens new horizons in other scientific fields, such as applied mathematics and applied physics, because of the intellectual satisfaction and remarkable efficiency provided by the advocated approach.

Applied Wave Mathematics
Applied Wave Mathematics

Author: Ewald Quak

Publisher: Springer Science & Business Media

Published: 2009-08-29

Total Pages: 467

ISBN-13: 3642005853

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This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

Spatial and Material Forces in Nonlinear Continuum Mechanics
Spatial and Material Forces in Nonlinear Continuum Mechanics

Author: Paul Steinmann

Publisher: Springer Nature

Published: 2022-03-28

Total Pages: 418

ISBN-13: 3030890708

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This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the related configurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.

Configurational Mechanics of Materials
Configurational Mechanics of Materials

Author: Reinhold Kienzler

Publisher: Springer

Published: 2014-05-04

Total Pages: 313

ISBN-13: 3709125766

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These lecture notes cover numerous elements of configurational mechanics, including mathematical foundations, linear and nonlinear elasticity and continuum mechanics, coupled fields, fracture mechanics, as well as strength of materials.