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Finite element modeling has developed into one of the most important tools at an engineer's disposal, especially in applications involving nonlinearity. While engineers coping with such applications may have access to powerful computers and finite element codes, too often they lack the strong foundation in finite element analysis (FEA) that nonline
Thermomechanics of Solids and Structures: Physical Mechanisms, Continuum Mechanics, and Applications covers kinematics, balance equations, the strict thermodynamic frameworks of thermoelasticity, thermoplasticity, creep covering constitutive equations, the physical mechanisms of deformation, along with computational aspects. The book concludes with coverage of the thermodynamics of solids and applications of the constitutive three-dimensional model to both one-dimensional homogeneous and composite beam structures. Practical applications of the theories and techniques covered are emphasized throughout the book, with analytical solutions provided for various problems. - Provides foundational knowledge on continuum mechanics, covering kinematics, balance equations, isothermal elasticity and plasticity, variational principles, and more - Presents applications of constitutive 3D models to homogeneous and composite beams, including equations for stress and displacement estimation in thermoelastic beam problems - Reviews experimental results of thermoelastic material behavior, along with case studies to support reviews - Covers the inelastic behavior of materials at elevated temperatures, with experimental results for both monotonic and cyclic tensile tests presented - Looks at the physical mechanisms, experimental results, and constitutive modeling of creep
In this book basic and some more advanced thermodynamics and phase as well as stability diagrams relevant for diffusion studies are introduced. Following, Fick’s laws of diffusion, atomic mechanisms, interdiffusion, intrinsic diffusion, tracer diffusion and the Kirkendall effect are discussed. Short circuit diffusion is explained in detail with an emphasis on grain boundary diffusion. Recent advances in the area of interdiffusion will be introduced. Interdiffusion in multi-component systems is also explained. Many practical examples will be given, such that researches working in this area can learn the practical evaluation of various diffusion parameters from experimental results. Large number of illustrations and experimental results are used to explain the subject. This book will be appealing for students, academicians, engineers and researchers in academic institutions, industry research and development laboratories.
The first part of this textbook presents the mathematical background needed to precisely describe the basic problem of continuum thermomechanics. The book then concentrates on developing governing equations for the problem dealing in turn with the kinematics of material continuum, description of the state of stress, discussion of the fundamental conservation laws of underlying physics, formulation of initial-boundary value problems and presenting weak (variational) formulations. In the final part the crucial issue of developing techniques for solving specific problems of thermomechanics is addressed. To this aim the authors present a discretized formulation of the governing equations, discuss the fundamentals of the finite element method and develop some basic algorithms for solving algebraic and ordinary differential equations typical of problems on hand. Theoretical derivations are followed by carefully prepared computational exercises and solutions.
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.
The main objective of the contributions contained in this volume is to present the thermodynamic foundations of the response of elastic and dissipative materials. In particular, the governing equations of non linear thermoelasticity and thermoinelasticity as well as the basic properties of these equations as resulting from the primary assumptions of continuum thermodynamics are derived. The global formulation of thermodynamics of continua is discussed. A special attention is paid to the properties of the balance equations on a singular surface. The possible forms of the second law of thermodynamics are discussed within the frame work ofaxiomatic thermodynamics. Furthermore, the thermodynamiG requirements for differ ent kinds of materials are examined. The secondary purpose of the Course was to discuss some connections between rational and classical formulations of the principles of thermodynamics. The present volume contains the texts of three (of the four delivered) Course lectures. I hope it will constitute a useful source of information on the problems presented and discussed in Udine. Special thanks are due to the International Centre for Mechanical Sciences whose direction encouraged us to prepare and to deliver the lectures.
The notion of continuum thermodynamics, adopted in this book, is primarily understood as a strategy for development of continuous models of various physical systems. The examples of such a strategy presented in the book have both the classical character (e. g. thermoelastic materials, viscous fluids, mixtures) and the extended one (ideal gases, Maxwellian fluids, thermoviscoelastic solids etc. ). The latter has been limited intentionally to non-relativistic models; many important relativistic applications of the true extended thermodynamics will not be considered but can be found in the other sources. The notion of extended thermodynamics is also adopted in a less strict sense than suggested by the founders. For instance, in some cases we allow the constitutive dependence not only on the fields themselves but also on some derivatives. In this way, the new thermodynamical models may have some features of the usual nonequilibrium models and some of those of the extended models. This deviation from the strategy of extended thermodynamics is motivated by practical aspects; frequently the technical considerations of extended thermodynamics are so involved that one can no longer see important physical properties of the systems. This book has a different form from that usually found in books on continuum mechanics and continuum thermodynamics. The presentation of the formal structure of continuum thermodynamics is not always as rigorous as a mathematician might anticipate and the choice of physical subjects is too disperse to make a physicist happy.
This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.