Mathematical Modelling Of Continuum Physics
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Mathematical Modelling Of Continuum Physics
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Author : Angelo Morro
language : en
Publisher: Springer Nature
Release Date : 2023-03-19
Mathematical Modelling Of Continuum Physics written by Angelo Morro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-19 with Mathematics categories.
This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive equations for wide-ranging classes of materials. Derivations of results are detailed through careful proofs, and the contents have been developed to ensure a self-contained and consistent presentation. 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.
Mathematical Modeling In Continuum Mechanics
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Author : Roger Temam
language : en
Publisher: Cambridge University Press
Release Date : 2005-05-19
Mathematical Modeling In Continuum Mechanics written by Roger Temam and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-19 with Science categories.
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
Mathematical Methods In Continuum Mechanics Of Solids
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Author : Martin Kružík
language : en
Publisher: Springer
Release Date : 2019-03-02
Mathematical Methods In Continuum Mechanics Of Solids written by Martin Kružík and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-02 with Science categories.
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.
Continuum Methods Of Physical Modeling
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Author : Kolumban Hutter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Continuum Methods Of Physical Modeling written by Kolumban Hutter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
This book is a considerable outgrowth of lecture notes on Mechanics of en vironmentally related systems I, which I hold since more than ten years in the Department of Mechanics at the Darmstadt University of Technology for upper level students majoring in mechanics, mathematics, physics and the classical engineering sciences. These lectures form a canon of courses over three semesters in which I present the foundations of continuum physics (first semester), those of physical oceanography and limnology (second semester) and those of soil, snow and ice physics in the geophysical context (third semester). The intention is to build an understanding of the mathemati cal foundations of the mentioned geophysical research fields combined with a corresponding understanding of the regional, but equally also the global, processes that govern the climate dynamics of our globe. The present book contains the material (and extensions of it) of the first semester; it gives an introduction into continuum thermomechanics, the methods of dimensional analysis and turbulence modeling. All these themes belong today to the every day working methods of not only environmental physicists but equally also those engineers, who are confronted with continuous systems of solid and fluid mechanics, soil mechanics and generally the mechanics and thermody namics of heterogeneous systems. The book addresses a broad spectrum of researchers, both at Universities and Research Laboratories who wish to fa miliarize themselves with the methods of "rational" continuum physics, and students from engineering and classical continuum physics.
Continuum Mechanics
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Author : Myron B. Allen, III
language : en
Publisher: John Wiley & Sons
Release Date : 2015-06-24
Continuum Mechanics written by Myron B. Allen, III and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Mathematics categories.
Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.
Mathematical Modelling And Biomechanics Of The Brain
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Author : Corina Drapaca
language : en
Publisher: Springer Nature
Release Date : 2019-09-06
Mathematical Modelling And Biomechanics Of The Brain written by Corina Drapaca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-06 with Mathematics categories.
This monograph aims to provide a rigorous yet accessible presentation of some fundamental concepts used in modeling brain mechanics and give a glimpse of the insights and advances that have arisen as a result of the nascent interaction of the mathematical and neurosurgical sciences. It begins with some historical perspective and a brief synopsis of the biomedical/biological manifestations of the clinical conditions/diseases considered. Each chapter proceeds with a discussion of the various mathematical models of the problems considered, starting with the simplest models and proceeding to more complex models where necessary. A detailed list of relevant references is provided at the end of each chapter. With the beginning research student in mind, the chapters have been crafted to be as self-contained as possible while addressing different clinical conditions and diseases. The book is intended as a brief introduction to both theoreticians and experimentalists interested in brain mechanics, with directions and guidance for further reading, for those who wish to pursue particular topics in greater depth. It can also be used as a complementary textbook in a graduate level course for neuroscientists and neuroengineers.
Mathematical Modelling In Solid Mechanics
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Author : Francesco dell'Isola
language : en
Publisher: Springer
Release Date : 2017-03-10
Mathematical Modelling In Solid Mechanics written by Francesco dell'Isola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Science categories.
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.
Mathematical Models And Integration Methods
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Author : Oleg V. Kaptsov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Mathematical Models And Integration Methods written by Oleg V. Kaptsov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
The book compiles works presented at a seminar aiming to attract global experts in differential equations, mathematical modeling, and integration methods. It covers classical and contemporary integration techniques for partial differential equations, including Monge and Darboux's approaches and their extensions. Additionally, it introduces a novel theoretical model for plane turbulent flows, presents gravitational equations derived from the principle of least action, and explores symmetry-preserving conservative finite-difference schemes for hydrodynamic-type equations. Analytical solutions for Maxwell's equations in incompressible viscoelastic mediums are examined, alongside theoretical-group analysis of wake mathematical models and reduction to ordinary differential equations. The book also delves into special classes of two-dimensional ideal fluid motion and advancements in discrete orthogonal polynomial theory, showcasing rapid decay properties near interval boundaries. In conclusion, this comprehensive collection is indispensable for researchers and practitioners in applied mathematics, fluid dynamics, and computational modeling, providing valuable insights into cutting-edge methods and solutions in the field.
Mathematical Modeling And Simulation
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Author : Kai Velten
language : en
Publisher: John Wiley & Sons
Release Date : 2009-06-01
Mathematical Modeling And Simulation written by Kai Velten and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-01 with Science categories.
This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).
Mathematical Modelling In Continuum Mechanics
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Author : Roger Temam
language : en
Publisher:
Release Date : 2005
Mathematical Modelling In Continuum Mechanics written by Roger Temam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.