Nonlinear Viscoelastic Materials With Fading Memory

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Nonlinear Viscoelastic Materials with Fading Memory

Author : John A. Nohel
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Nonlinear Viscoelastic Materials with Fading Memory by : John A. Nohel

Download or read book Nonlinear Viscoelastic Materials with Fading Memory written by John A. Nohel and published by . This book was released on 1986 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The equations governing the motion of viscoelastic materials with fading memory incorporate a nonlinear elastic-type response with a natural dissipative mechanical. Our purpose is to discuss the subtle effects of this mechanism in viscoelastic materials of Boltzmann type. Recent results on the global existence and decay of classical solutions for smooth and small data (in one space dimension) are reviewed for smooth and singular memory kernels; for smooth kernels a number of such results can be generalized to several space dimensions. A recent result on the development of singularities in finite time for large data is discussed; several open problems are formulated. A program for studying weak solutions for such systems, including the development of numerical algorithms, is outlined. Keywords: hyperbolic equations; Volterra equations.

Development of Singularities in Nonlinear Viscoelasticity

Author : J. A. Nohel
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Development of Singularities in Nonlinear Viscoelasticity by : J. A. Nohel

Download or read book Development of Singularities in Nonlinear Viscoelasticity written by J. A. Nohel and published by . This book was released on 1985 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper discusses the motion of nonlinear viscoelastic materials with fading memory in one space dimension. It concentrates on viscoelastic solids and briefly remark on similar results for fluids. After formulating the mathematical problems, the authors survey results for global existence of classical solutions to the initial value problem, provided the initial data are sufficiently small. They then discuss in some detail the development of singularities in initially smooth solutions for large data. Keywords: nonlinear hyperbolic problems; Volterra integrodifferential equations; dissipation; decay; shocks; viscoelastic fluids.

Asymptotic Behavior of Nonlinear Viscoelastic Model with Fading Memory and Compressible, Isentropic, Viscous 1-D Flow

Author : Yanni Zeng
Publisher :
ISBN 13 :
Total Pages : 166 pages
Book Rating : 4.:/5 (798 download)

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Book Synopsis Asymptotic Behavior of Nonlinear Viscoelastic Model with Fading Memory and Compressible, Isentropic, Viscous 1-D Flow by : Yanni Zeng

Download or read book Asymptotic Behavior of Nonlinear Viscoelastic Model with Fading Memory and Compressible, Isentropic, Viscous 1-D Flow written by Yanni Zeng and published by . This book was released on 1992 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Creep and Relaxation of Nonlinear Viscoelastic Materials

Author : William N. Findley
Publisher : Courier Corporation
ISBN 13 : 0486145174
Total Pages : 402 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Creep and Relaxation of Nonlinear Viscoelastic Materials by : William N. Findley

Download or read book Creep and Relaxation of Nonlinear Viscoelastic Materials written by William N. Findley and published by Courier Corporation. This book was released on 2013-01-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering book presents the basic theory, experimental methods, experimental results and solution of boundary value problems in a readable, useful way to designers as well as research workers and students. The mathematical background required has been kept to a minimum and supplemented by explanations where it has been necessary to introduce specialized mathematics. Also, appendices have been included to provide sufficient background in Laplace transforms and in step functions. Chapters 1 and 2 contain an introduction and historic review of creep. As an aid to the reader a background on stress, strain, and stress analysis is provided in Chapters 3 and 4, an introduction to linear viscoelasticity is found in Chapter 5 and linear viscoelastic stress analysis in Chapter 6. In the next six chapters the multiple integral representation of nonlinear creep and relaxation, and simplifications to single integral forms and incompressibility, are examined at length. After a consideration of other representations, general relations are derived, then expanded to components of stress or strain for special cases. Both constant stress (or strain) and variable states are described, together with methods of determining material constants. Conversion from creep to relaxation, effects of temperature and stress analysis problems in nonlinear materials are also treated here. Finally, Chapter 13 discusses experimental methods for creep and stress relaxation under combined stress. This chapter considers especially those experimental problems which must be solved properly when reliable experimental results of high precision are required. Six appendices present the necessary mathematical background, conversion tables, and more rigorous derivations than employed in the text. An extensive updated bibliography completes the book.

A Stability Investigation for an Incompressible Simple Fluid with Fading Memory

Author : E. F. Infante
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis A Stability Investigation for an Incompressible Simple Fluid with Fading Memory by : E. F. Infante

Download or read book A Stability Investigation for an Incompressible Simple Fluid with Fading Memory written by E. F. Infante and published by . This book was released on 1978 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the finite-linear viscoelastic theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several stability and asymptotic behavior results for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamic system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid. (Author).

Constitutive Models for Rubber

Author : Al Dorfmann
Publisher : CRC Press
ISBN 13 : 9789058091130
Total Pages : 334 pages
Book Rating : 4.0/5 (911 download)

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Book Synopsis Constitutive Models for Rubber by : Al Dorfmann

Download or read book Constitutive Models for Rubber written by Al Dorfmann and published by CRC Press. This book was released on 1999-01-01 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text aims to enable the experience accumulated by engineers and the research community in materials science, continuum mechanics and applied mathematics to be shared. In this way, the design and analysis of rubber components using the Finite Element Method should be enhanced.

Initial Value Problems in Viscoelasticity

Author : W. J. Hrusa
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Initial Value Problems in Viscoelasticity by : W. J. Hrusa

Download or read book Initial Value Problems in Viscoelasticity written by W. J. Hrusa and published by . This book was released on 1988 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document reviews some recent mathematical results concerning integrodifferential equations that model the motion of one-dimensional nonlinear viscoelastic materials. In particular, the authors discuss global (in time) existence and long-time behavior of classical solutions, as well as the formation of singularities in finite time from smooth initial data. Although the mathematical theory is comparatively incomplete, some remarks are more concerning the existence of weak solutions (i.e., solutions with shocks). Some relevant results from linear wave propagation will also be discussed. Keywords: integrodifferential equations; mathematical models; Nonlinear viscoelasticity, materials with fading memory, viscoelastic fluids, linear wave propagation, acceleration waves, smooth kernels, singular kernels, Laplace transforms, hyperbolic equations, global existence, smooth solution. (kr).

Continuum Mechanics of Single-Substance Bodies

Author : A. Cemal Eringen
Publisher : Academic Press
ISBN 13 : 1483276678
Total Pages : 635 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Continuum Mechanics of Single-Substance Bodies by : A. Cemal Eringen

Download or read book Continuum Mechanics of Single-Substance Bodies written by A. Cemal Eringen and published by Academic Press. This book was released on 2013-10-22 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuum Physics, Volume II: Continuum Mechanics of Single-Substance Bodies discusses the continuum mechanics of bodies constituted by a single substance, providing a thorough and precise presentation of exact theories that have evolved during the past years. This book consists of three parts—basic principles, constitutive equations for simple materials, and methods of solution. Part I of this publication is devoted to a discussion of basic principles irrespective of material geometry and constitution that are valid for all kinds of substances, including composites. The geometrical notions, kinematics, balance laws, and thermodynamics of continua are also deliberated. Part II focuses on materials consisting of a single substance, followed by a general theory of constitutive equations and special types of bodies. The thermoelastic solids, thermoviscous fluids, and memory-dependent materials are likewise considered. Part III is devoted to a discussion of a variety of nonlinear and linear problems, as well as nonlinear deformations of elastic solids, viscometric fluids, singular surfaces and waves, and complex function technique. This volume is a good source for researchers and students conducting work on the continuum mechanics of single-substance bodies.

Nonlinear Evolution Equations And Infinite Dimensional Dynamical Systems - Proceedings Of The Conference

Author : Tatsien Li
Publisher : World Scientific
ISBN 13 : 9814546429
Total Pages : 286 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonlinear Evolution Equations And Infinite Dimensional Dynamical Systems - Proceedings Of The Conference by : Tatsien Li

Download or read book Nonlinear Evolution Equations And Infinite Dimensional Dynamical Systems - Proceedings Of The Conference written by Tatsien Li and published by World Scientific. This book was released on 1997-01-04 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 30 research papers presenting the recent development and trend on the following subjects: nonlinear hyperbolic equations (systems); nonlinear parabolic equations (systems); infinite-dimensional dynamical systems; applications (free boundary problems, phase transitions, etc.).

Viscoelasticity and Rheology

Author : Arthur S. Lodge
Publisher : Academic Press
ISBN 13 : 1483263355
Total Pages : 456 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Viscoelasticity and Rheology by : Arthur S. Lodge

Download or read book Viscoelasticity and Rheology written by Arthur S. Lodge and published by Academic Press. This book was released on 2014-06-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation. This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws. This book will prove useful to chemical engineers, researchers, and students.

Amorphous Polymers and Non-Newtonian Fluids

Author : Constantine Dafermos
Publisher : Springer Science & Business Media
ISBN 13 : 146121064X
Total Pages : 207 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Amorphous Polymers and Non-Newtonian Fluids by : Constantine Dafermos

Download or read book Amorphous Polymers and Non-Newtonian Fluids written by Constantine Dafermos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise.

Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids

Author : A.I. Leonov
Publisher : Springer Science & Business Media
ISBN 13 : 9401112584
Total Pages : 492 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids by : A.I. Leonov

Download or read book Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids written by A.I. Leonov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents theoretical and experimental studies of flows of elastic liquids. Falling into this category are particularly the melts and concentrated solutions of such flexible-chain polymers as polyethylene, polyisobutylene and polypropylene, all of which are widely used in polymer processing. These polydisperse polymers vary greatly, from batch to batch, in their mechanical properties and 20% variation in a property is believed to be good enough. l 7 All recent books - devoted to the rheology of polymers do not answer the question of which constitutive equations should be used for solving the fluid mechanic problems of polymer processing in the usual case of an appreciable nonlinear region of deformation where nonlinear effects of shear and extensional elasticity are very important. Viscoelastic constitut ive equations cited commonly (see, e.g. Refs 5 and 6) do not describe simultaneously even the simplest cases of deformations, viz. simple shear and uniaxial extension. Moreover, some of them are internally inconsist ent and sometimes display highly unstable behaviour in simple flows without any fundamental reasons. Even more respected molecular ap free from these defects.

Research in Progress

Author :
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Research in Progress by :

Download or read book Research in Progress written by and published by . This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory of Viscoelasticity

Author : R. M. Christensen
Publisher : Courier Corporation
ISBN 13 : 0486318966
Total Pages : 386 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Theory of Viscoelasticity by : R. M. Christensen

Download or read book Theory of Viscoelasticity written by R. M. Christensen and published by Courier Corporation. This book was released on 2013-04-26 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration of theoretical developments offers complete description of linear theory of viscoelastic behavior of materials, with theoretical formulations derived from continuum mechanics viewpoint and discussions of problem solving. 1982 edition.

Transactions of the ... Army Conference on Applied Mathematics and Computing

Author :
Publisher :
ISBN 13 :
Total Pages : 898 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Transactions of the ... Army Conference on Applied Mathematics and Computing by :

Download or read book Transactions of the ... Army Conference on Applied Mathematics and Computing written by and published by . This book was released on 1986 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Viscoelastic Solids (1998)

Author : Roderic S. Lakes
Publisher : CRC Press
ISBN 13 : 1351355643
Total Pages : 476 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Viscoelastic Solids (1998) by : Roderic S. Lakes

Download or read book Viscoelastic Solids (1998) written by Roderic S. Lakes and published by CRC Press. This book was released on 2017-11-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelastic Solids covers the mathematical theory of viscoelasticity and physical insights, causal mechanisms, and practical applications. The book: presents a development of the theory, addressing both transient and dynamic aspects as well as emphasizing linear viscoelasticity synthesizes the structure of the theory with the aim of developing physical insight illustrates the methods for the solution of stress analysis problems in viscoelastic objects explores experimental methods for the characterization of viscoelastic materials describes the phenomenology of viscoelasticity in a variety of materials, including polymers, metals, high damping alloys, rock, piezoelectric materials, cellular solids, dense composite materials, and biological materials analyzes high damping and extremely low damping provides the theory of viscoelastic composite materials, including examples of various types of structure and the relationships between structure and mechanical properties contains examples on the use of viscoelastic materials in preventing and alleviating human suffering Viscoelastic Solids also demonstrates the use of viscoelasticity for diverse applications, such as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music.

Mechanical Behavior of Engineering Materials

Author : Y.M. Haddad
Publisher : Springer Science & Business Media
ISBN 13 : 9780792363545
Total Pages : 452 pages
Book Rating : 4.3/5 (635 download)

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Book Synopsis Mechanical Behavior of Engineering Materials by : Y.M. Haddad

Download or read book Mechanical Behavior of Engineering Materials written by Y.M. Haddad and published by Springer Science & Business Media. This book was released on 2000-08-31 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph consists of two volumes and provides a unified, comprehensive presentation of the important topics pertaining to the understanding and determination of the mechanical behaviour of engineering materials under different regimes of loading. The large subject area is separated into eighteen chapters and four appendices, all self-contained, which give a complete picture and allow a thorough understanding of the current status and future direction of individual topics. Volume I contains eight chapters and three appendices, and concerns itself with the basic concepts pertaining to the entire monograph, together with the response behaviour of engineering materials under static and quasi-static loading. Thus, Volume I is dedicated to the introduction, the basic concepts and principles of the mechanical response of engineering materials, together with the relevant analysis of elastic, elastic-plastic, and viscoelastic behaviour. Volume II consists of ten chapters and one appendix, and concerns itself with the mechanical behaviour of various classes of materials under dynamic loading, together with the effects of local and microstructural phenomena on the response behaviour of the material. Volume II also contains selected topics concerning intelligent material systems, and pattern recognition and classification methodology for the characterization of material response states. The monograph contains a large number of illustrations, numerical examples and solved problems. The majority of chapters also contain a large number of review problems to challenge the reader. The monograph can be used as a textbook in science and engineering, for third and fourth undergraduate levels, as well as for the graduate levels. It is also a definitive reference work for scientists and engineers involved in the production, processing and applications of engineering materials, as well as for other professionals who are involved in the engineering design process.