Nonlinear Elasticity
Nonlinear Elasticity

Author: R. W. Dickey

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 415

ISBN-13: 1483264793

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Nonlinear Elasticity presents a description of research and result on various nonlinear problems arising in elasticity. This book covers a variety of topics, including shallow elastic membranes, nonlinear elasticity, finite deformations of elastic solids, and nonlinear thermoelasticity. Organized into 11 chapters, this book begins with an overview of the nonlinear theory of buckling of elastic shells. This text then examines the ways in which the energy criterion supplies a necessary condition for asymptotic stability. Other chapters consider some of the phenomena, both physical and mathematical, that typify the large deformation of a nonlinearly elastic body. This book discusses as well the concepts leading to a criterion for instabilities and discusses how the criterion applies to some well-known ideal materials. The final chapter deals with the structure of strong shocks and studies the evolution of such a shock produced by a suddenly-applied strain. This book is a valuable resource for mathematicians.

Nonlinear Elasticity
Nonlinear Elasticity

Author: Y. B. Fu

Publisher: Cambridge University Press

Published: 2001-05-07

Total Pages: 541

ISBN-13: 0521796954

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Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.

Biomechanics of Soft Tissue in Cardiovascular Systems
Biomechanics of Soft Tissue in Cardiovascular Systems

Author: Gerhard A. Holzapfel

Publisher: Springer Science & Business Media

Published: 2003-05-06

Total Pages: 360

ISBN-13: 9783211004555

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The book is written by leading experts in the field presenting an up-to-date view of the subject matter in a didactically sound manner. It presents a review of the current knowledge of the behaviour of soft tissues in the cardiovascular system under mechanical loads, and the importance of constitutive laws in understanding the underlying mechanics is highlighted. Cells are also described together with arteries, tendons and ligaments, heart, and other biological tissues of current research interest in biomechanics. This includes experimental, continuum mechanical and computational perspectives, with the emphasis on nonlinear behaviour, and the simulation of mechanical procedures such as balloon angioplasty.

Non-Linear Theory of Elasticity
Non-Linear Theory of Elasticity

Author: A.I. Lurie

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 632

ISBN-13: 0444597239

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This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

Nonlinear Theory of Elasticity
Nonlinear Theory of Elasticity

Author: Larry Alan Taber

Publisher: World Scientific

Published: 2004

Total Pages: 417

ISBN-13: 9812387358

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Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.

The Nonlinear Theory of Elastic Shells
The Nonlinear Theory of Elastic Shells

Author: A. Libai

Publisher: Cambridge University Press

Published: 2005-12-15

Total Pages: 564

ISBN-13: 9780521019767

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Elastic shells are pervasive in everyday life. Examples of these thin-walled structures range from automobile hoods to basketballs, veins and arteries, and soft drink cans. This book explains shell theory, with numerous examples and applications. This second edition not only brings all the material of the first edition entirely up to date; it also adds two entirely new chapters on general shell theory and general membrane theory. Aerospace, mechanical, and civil engineers, as well as applied mathematicians, will find this book a clearly written and thorough information source on shell theory.

Contact Problems in Elasticity
Contact Problems in Elasticity

Author: N. Kikuchi

Publisher: SIAM

Published: 1988-01-01

Total Pages: 508

ISBN-13: 9781611970845

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The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

Variational Methods in Nonlinear Elasticity
Variational Methods in Nonlinear Elasticity

Author: Pablo Pedregal

Publisher: SIAM

Published: 2000-01-01

Total Pages: 110

ISBN-13: 9780898719529

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This book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity.