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Author: Alagappan Ponnalagu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The aim of this work is to study the impact response of multilayered polymers using a thermodynamically consistent framework. Rather than integral type viscoelastic model, the approach here is based on the idea of two inter penetrating networks, one is permanent and other is transient together with the rate equations for the time evolution of the transient network. The primary hypothesis is that, it is possible to use a two network theory to capture the essential features of a impact response of multilayered polymers and solve the resulting boundary value problem using finite volume scheme. We first study the impact of layered polymer plate involving small deformation using a thermodynamic framework. The constitutive equations are nonlinear even though the strains are small. Six different protocols involving PU and PC, namely pure PC, pure PU, bilayer(PU/PC and PC/PU) and trilayer(PU/PC/PU and PC/PU/PC) were considered to evaluate the performance of the layering sequence based on the kinetic energy transferred on the wall. The interfaces are assumed to be fully bonded. The material parameters for the model was obtained from the experimental creep data from the literature. The layering of polymers improved the performance of plate depending upon the type of layering sequence. In the one and two dimensional study carried out, the performance was best when a compliant layer is placed between two stiff layers. Whereas, when a stiff layer was placed between two less compliant layer, the performance was worse than bilayer. Finally, a thermodynamically consistent finite deformation model was used to evaluate the impact performance of layered plate involving large deformation. A full scale three dimensional impact analysis was carried out with the thermal phenomena suppressed. Similar to the small deformation study, six different protocols were considered. The material parameters were obtained from the experimental data from the literature involving strain values above 50%. The overall performance was similar to what has been observed in the small strain model. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155588.
Author: Alagappan Ponnalagu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The aim of this work is to study the impact response of multilayered polymers using a thermodynamically consistent framework. Rather than integral type viscoelastic model, the approach here is based on the idea of two inter penetrating networks, one is permanent and other is transient together with the rate equations for the time evolution of the transient network. The primary hypothesis is that, it is possible to use a two network theory to capture the essential features of a impact response of multilayered polymers and solve the resulting boundary value problem using finite volume scheme. We first study the impact of layered polymer plate involving small deformation using a thermodynamic framework. The constitutive equations are nonlinear even though the strains are small. Six different protocols involving PU and PC, namely pure PC, pure PU, bilayer(PU/PC and PC/PU) and trilayer(PU/PC/PU and PC/PU/PC) were considered to evaluate the performance of the layering sequence based on the kinetic energy transferred on the wall. The interfaces are assumed to be fully bonded. The material parameters for the model was obtained from the experimental creep data from the literature. The layering of polymers improved the performance of plate depending upon the type of layering sequence. In the one and two dimensional study carried out, the performance was best when a compliant layer is placed between two stiff layers. Whereas, when a stiff layer was placed between two less compliant layer, the performance was worse than bilayer. Finally, a thermodynamically consistent finite deformation model was used to evaluate the impact performance of layered plate involving large deformation. A full scale three dimensional impact analysis was carried out with the thermal phenomena suppressed. Similar to the small deformation study, six different protocols were considered. The material parameters were obtained from the experimental data from the literature involving strain values above 50%. The overall performance was similar to what has been observed in the small strain model. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155588.
Author: Roderic S. Lakes
Publisher: CRC Press
ISBN: 9780849396588
Category : Technology & Engineering
Languages : en
Pages : 494
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Book Description
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.
Author: Roderic S. Lakes
Publisher: CRC Press
ISBN: 1351355651
Category : Technology & Engineering
Languages : en
Pages : 490
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Book Description
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.
Author: W. D. Pilkey
Publisher:
ISBN:
Category :
Languages : en
Pages : 70
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Book Description
A comprehensive theory for the dynamic response of linear continuous viscoelastic structural members is formulated with a modal analysis. The constitutive relation is in the form of a hereditary integral. A general set of formulas is derived that may be used for both non-self-adjoint and self-adjoint systems of governing equations of motion. Applications include a Voigt-Kelvin beam and a viscoelastic circular plate. (Author)
Author: Gerald Lee Goudreau
Publisher:
ISBN:
Category : Elasticity
Languages : en
Pages : 250
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Book Description
Author: A.C. Pipkin
Publisher: Springer Science & Business Media
ISBN: 146121078X
Category : Science
Languages : en
Pages : 199
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Book Description
This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely detailed explanation. Furthermore, much of the content of the course is in the problems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not give, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA II, 291 (I962ยป remains the best reference for proofs of theorems.
Author: R. M. Christensen
Publisher: Courier Corporation
ISBN: 0486318966
Category : Technology & Engineering
Languages : en
Pages : 386
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Book Description
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.
Author: Arthur S. Lodge
Publisher: Academic Press
ISBN: 1483263355
Category : Technology & Engineering
Languages : en
Pages : 456
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Book Description
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.
Author: F. J. Lockett
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 216
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Book Description
Author: W.N. Findley
Publisher: Elsevier
ISBN: 0444601929
Category : Science
Languages : en
Pages : 382
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Book Description
Creep and Relaxation of Nonlinear Viscoelastic Materials with an Introduction to Linear Viscoelasticity deals with nonlinear viscoelasticity, with emphasis on creep and stress relaxation. It explains the concepts of elastic, plastic, and viscoelastic behavior, along with creep, recovery, relaxation, and linearity. It also describes creep in a variety of viscoelastic materials, such as metals and plastics. Organized into 13 chapters, this volume begins with a historical background on creep, followed by discussions about strain and stress analysis, linear viscoelasticity, linear viscoelastic stress analysis, and oscillatory stress and strain. It methodically walks the reader through topics such as the multiple integral theory with simplifications to single integrals, incompressibility and linear compressibility, and the responses of viscoelastic materials to stress boundary conditions (creep), strain boundary conditions (relaxation), and mixed stress and strain boundary conditions (simultaneous creep and relaxation). The book also looks at the problem of the effect of temperature, especially variable temperature, on nonlinear creep, and describes methods for the characterization of kernel functions, stress analysis of nonlinear viscoelastic materials, and experimental techniques for creep and stress relaxation under combined stress. This book is a useful text for designers, students, and researchers.
