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An Introduction To Continuum Mechanics

Author: J. N. Reddy
Publisher: Cambridge University Press
ISBN: 1107025435
Size: 62.20 MB
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This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.

Nonlinear Continuum Mechanics And Large Inelastic Deformations

Author: Yuriy I. Dimitrienko
Publisher: Springer Science & Business Media
ISBN: 9789400700345
Size: 41.20 MB
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The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Geometric Continuum Mechanics And Induced Beam Theories

Author: Simon Eugster
Publisher: Springer
ISBN: 3319164953
Size: 50.68 MB
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This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

An Introduction To The Mechanics Of Fluids

Author: Clifford Truesdell
Publisher: Springer Science & Business Media
ISBN: 9780817640149
Size: 47.83 MB
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This reference provides a general foundation of the mechanics of continual, and examines some select applications that illustrate the principle. Applications special to fluids and non-linear fluids are presented, such as: Navier-Stokes fluids, and incompressible and compressible Euler fluids.

Continuum Mechanics Through The Ages From The Renaissance To The Twentieth Century

Author: Gérard A. Maugin
Publisher: Springer
ISBN: 3319265938
Size: 56.34 MB
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Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on continuum mechanics is key: these provide the most valuable documentary basis on which a revival of continuum mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of continuum mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom continuum mechanics as a vividly evolving science still has its own mysteries.

Understanding Viscoelasticity

Author: Nhan Phan-Thien
Publisher: Springer Science & Business Media
ISBN: 366210704X
Size: 42.62 MB
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In this book, the necessary background for understanding viscoelasticity is covered; both the continuum and microstructure approaches to modelling viscoelastic materials are discussed, since neither approach alone is sufficient.

Continuum Mechanics Through The Twentieth Century

Author: Gerard A Maugin
Publisher: Springer Science & Business Media
ISBN: 9400763530
Size: 62.58 MB
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This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.