Overview
- Presents a unified treatment of the key points of continuum physics
- Develops a new approach to hysteresis and phase transitions
- Explores a wide range of constitutive models for non-simple materials
Part of the book series: Modeling and Simulation in Science, Engineering and Technology (MSSET)
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Table of contents (16 chapters)
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Basic Principles and Balance Equations
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Constitutive Models of Simple Materials
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Non-simple Materials
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Hysteresis and Phase Transitions
Keywords
About this book
Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics – such as reference and current configurations, transport relations, singular surfaces, objectivity, and objective time derivatives – are covered in detail. A chapter on balance equations then develops the balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the balance laws in electromagnetism.
Part II is devoted to the general requirements on constitutive models, emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed, and in this framework, detailed descriptions are given of solids (thermoelastic, elastic, and dissipative) and fluids (elastic, thermoelastic, viscous, and Newtonian).
A wide of variety of constitutive models are investigated in Part III, which consists of separate chapters focused on several types of non-simple materials: materials with memory, aging and higher-order grade materials, mixtures, micropolar media, and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity, magnetoelasticity, and plasma theory.
Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself, as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena, such as those occurring in hysteretic continua (e.g., plasticity, electromagnetism, and the physics of shape memory alloys).
Mathematical Modelling of Continuum Physics will be an important reference for mathematicians, engineers, physicists, and other scientists interested in research or applications of continuum mechanics.
Authors and Affiliations
Bibliographic Information
Book Title: Mathematical Modelling of Continuum Physics
Authors: Angelo Morro, Claudio Giorgi
Series Title: Modeling and Simulation in Science, Engineering and Technology
DOI: https://doi.org/10.1007/978-3-031-20814-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-20813-3Published: 20 March 2023
Softcover ISBN: 978-3-031-20816-4Published: 21 March 2024
eBook ISBN: 978-3-031-20814-0Published: 19 March 2023
Series ISSN: 2164-3679
Series E-ISSN: 2164-3725
Edition Number: 1
Number of Pages: XIX, 1009
Number of Illustrations: 47 b/w illustrations, 1 illustrations in colour
Topics: Mathematical Modeling and Industrial Mathematics, Classical and Continuum Physics