Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations

Ellad B. Tadmor; Ronald E. Miller; Ryan S. Elliott

ISBN 10: 1107008263 / ISBN 13: 9781107008267

Published by Cambridge University Press, 2012

About this Item

Oversized hardcover, xxii + 350 pages, shipping weight over 1kg, NOT ex-library. A gentle crease on the front endpaper. Book is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Issued without a dust jacket. -- This book presents a unified and foundational treatment of continuum mechanics and thermodynamics, exploring the fundamental concepts and mathematical structures that govern the macroscopic behavior of materials under mechanical and thermal loading. Beginning with the rigorous definitions of scalars, vectors, and tensors, it develops the kinematics of finite deformation, elucidating concepts such as deformation gradients, strain measures, and kinematic rates. The text then establishes the balance laws of mechanics (conservation of mass, linear and angular momentum) and thermodynamics (first and second laws), deriving the local forms of the energy equation and the Clausius-Duhem inequality. A central focus is the constitutive theory, where constraints imposed by the second law, material frame-indifference, and material symmetry are systematically applied to restrict the forms of constitutive relations, culminating in discussions of hyperelasticity, generalized Hooke's law, and nonlinear material models. Variational principles, notably the principle of stationary potential energy (PSPE) and principle of minimum potential energy (PMPE), are introduced to characterize equilibrium states and stability. The second part of the book shifts from theory to solutions, first exploring universal equilibrium solutions applicable to all materials within certain classes, then detailing the finite element method (FEM) as a numerical approach to solving nonlinear boundary-value problems through energy minimization. The text concludes by demonstrating how linearization of kinematics and constitutive relations reduces the general theory to classical engineering disciplines like heat transfer, fluid mechanics, and elasticity. Bridging abstract mathematical formalism with practical problem-solving, this work provides a self-contained graduate-level introduction to the nonlinear thermomechanics of solids.

Seller Inventory # 011090

Bibliographic Details

• Title: Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations
• Publisher: Cambridge University Press
• Publication Date: 2012
• Language: English
• ISBN 10: 1107008263
• ISBN 13: 9781107008267
• Binding: Hardcover
• Edition: 1st Edition
• Condition: Very Good

About this title

Synopsis

Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.

About the Authors

Ellad B. Tadmor is a Professor of Aerospace Engineering and Mechanics at the University of Minnesota. He received his BSc and MSc in Mechanical Engineering from the Technion - Israel Institute of Technology in 1987 and 1991, and his PhD from Brown University in 1996. His research focuses on the development of multiscale theories and computational methods for predicting the behavior of materials directly from the interactions of the atoms making up the material. He has published over 40 papers in this area and two textbooks (see http://modelingmaterials.org for information on the books). Professor Tadmor is the Director of the Knowledgebase of Interatomic Models project (https://openkim.org) which is tasked with developing standards for atomistic simulations and improving transferability of interatomic potentials. He has been a Postdoctoral Research Fellow at Harvard University, Associate Professor at the Technion (Israel), and Erasmus Mundus Scholar at the Ecole Normale Superieure in Lyon (France). He received the MRS Graduate Student Award in 1995 for his work on developing the quasicontinuum method, one of the leading multiscale methods, and has received numerous awards for excellence in teaching, including the Salomon Simon Mani Award in 2001. Professor Tadmor is on the editorial board of the Journal of Elasticity.

Ronald E. Miller is Professor of Mechanical and Aerospace Engineering at Carleton University. He has worked in the area of multiscale materials modeling for over 15 years and has published more than 40 scientific articles in the area.

Ryan S. Elliott is Associate Professor of Aerospace Engineering and Mechanics at the University of Minnesota. An expert in stability of continuum and atomistic systems, he has received many awards for his work.