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Author: R. W. Dickey Publisher: Academic Press ISBN: 1483264793 Category : Mathematics Languages : en Pages : 415
Book Description
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.
Author: R. W. Dickey Publisher: Academic Press ISBN: 1483264793 Category : Mathematics Languages : en Pages : 415
Book Description
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.
Author: Gerhard A. Holzapfel Publisher: Springer Science & Business Media ISBN: 9783211004555 Category : Technology & Engineering Languages : en Pages : 360
Book Description
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.
Author: Larry Alan Taber Publisher: World Scientific ISBN: 9812387358 Category : Science Languages : en Pages : 417
Book Description
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.
Author: A.I. Lurie Publisher: Elsevier ISBN: 0444597239 Category : Science Languages : en Pages : 632
Book Description
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.
Author: A. Libai Publisher: Cambridge University Press ISBN: 9780521019767 Category : Science Languages : en Pages : 564
Book Description
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.
Author: N. Kikuchi Publisher: SIAM ISBN: 9781611970845 Category : Science Languages : en Pages : 508
Book Description
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.
Author: Gerhard A. Holzapfel Publisher: Springer Science & Business Media ISBN: 3211958754 Category : Technology & Engineering Languages : en Pages : 351
Author: Pablo Pedregal Publisher: SIAM ISBN: 9780898719529 Category : Science Languages : en Pages : 110
Book Description
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.
Author: R. W. Dickey
Author: R. W. Dickey
Author: Y. B. Fu
Author: Gerhard A. Holzapfel
Author: Larry Alan Taber
Author: A.I. Lurie
Author: A. Libai
Author: N. Kikuchi
Author: Gerhard A. Holzapfel
Author: 
Author: Pablo Pedregal