2 edition of **Mathematical structure of the theories of viscoelasticity** found in the catalog.

Mathematical structure of the theories of viscoelasticity

Bernhard Gross

- 76 Want to read
- 18 Currently reading

Published
**1953**
by Hermann in Paris
.

Written in English

- Viscoelasticity,
- Rheology,
- Mathematical physics

**Edition Notes**

Bibliography: p.[69]-71

Series | Actualités scientifiques et industrielles, 1190, Rhéologie, 1 |

Classifications | |
---|---|

LC Classifications | Q111 .A3 no. 1190 |

The Physical Object | |

Pagination | 74 p. |

Number of Pages | 74 |

ID Numbers | |

Open Library | OL205224M |

LC Control Number | a 53007567 |

OCLC/WorldCa | 14059289 |

1. Introduction The general mathematical structure of the linear theory of viscoelasticity has been established almost fifty years ago by Gross (1 ), with more details elaborated by Bland (). In accordance with these texts, modeling solid-like linear viscoelasticity should. Viscoelastic response is often used as a probe in polymer science, since it is sensitive to thematerial’s chemistry andmicrostructure. Theconcepts andtechniques presentedhereare.

Tegmark responds (sec VI.A.1) that "The notion of a mathematical structure is rigorously defined in any book on Model Theory", and that non-human mathematics would only differ from our own "because we are uncovering a different part of what is in fact a consistent and unified picture, so math is converging in this sense." In his book on. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing s materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

Viscoelastic Structures covers the four basic problems in the mechanics of viscoelastic solids and structural members: construction of constitutive models for the description of thermoviscoelastic behavior of polymers; mathematical modeling of manufacturing advanced composite materials; optimal-design of structural members and technological processes of their fabrication; and stability. This introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed sections present examples of stress-related problems, including sinusoidal oscillation problems, quasi-static problems, and dynamic problems. Concise and still universally referenced, the text also explains procedures for model fitting to measured values of complex modulus or compliance. edition.

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Mathematical Structure of the Theories of Viscoelasticity [Bernhard Gross, E.L. Fonseca Costa] on *FREE* shipping on qualifying offers. Mathematical Structure of the Theories of ViscoelasticityAuthor: Bernhard Gross.

Book Search tips Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for the Publisher/Society Mathematical Physics; Optics and Optical Physics; Physical Chemistry; Plasma Physics Mathematical Structure of the Theories of Viscoelasticity.

Bernhard Gross Cited by: Get this from a library. Mathematical structure of the theories of viscoelasticity. [Bernhard Gross; E L da Fonseca Costa]. Additional Physical Format: Online version: Gross, Bernhard, Mathematical structure of the theories of viscoelasticity.

Paris Hermann (OCoLC) Shareable Link. Use the link below to share a full-text version of this article with your friends and colleagues. Learn : F. Grün. Theory of Viscoelasticity: An Introduction, Second Edition discusses the integral form of stress strain constitutive relations.

The book presents the formulation of the boundary value problem and demonstrates the separation of variables condition.

The text describes the mathematical framework to predict material behavior. The mathematical structure of viscoelasticity is discussed with some care because it clarifies the basic concepts and has important consequences in computa tional applications.

Basic ideas are exemplified using the simplest problems and constitutive models in. Mathematical Structure of the Theories of Viscoelasticity. the proofs of our results use only the structure theory of reductive groups, in particular the notion of "stem" of a reduced root. 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. 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. This option allows users to search by Publication, Volume and Page Selecting this option will search the current publication in context.

Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for the Publisher/Society in context. Mathematical structure of the theories of viscoelasticity. BERNHARD GROSS Hermann & Cie, Paris, 74 pp., francs.

Foundations of the Theory of Elasticity, Plasticity, and Viscoelasticity details fundamental and practical skills and approaches for carrying out research in the field of modern problems in the mechanics of deformed solids, which involves the theories of elasticity, plasticity, and viscoelasticity.

The book includes all modern methods of research as well as the results of the authors’ recent. This is a compact book for a first year graduate course in viscoelasticity and modelling of viscoelastic multiphase fluids.

The Dissipative Particle Dynamics (DPD) is introduced as a particle-based method, relevant in modelling of complex-structured fluids.

This chapter presents the hypotheses and some of the conclusions of the theory of fading memory to make clear the way Navier–Stokes and second-order fluids approximate fluids with memory and to show how those approximations are related to others, such as that behind the Boltzmann–Volterra theory of linear viscoelasticity.

The main aim is to provide a still compact book, sufficient at the level of first year graduate course for those who wish to understand viscoelasticity and to embark in modeling of viscoelastic multiphase fluids. To this end, a new chapter on Dissipative Particle Dynamics (DPD) was introduced which is relevant to model complex-structured fluids.

Outstanding among them are the theories of ide ally plastic and of viscoelastic materials. While plastic behavior is essentially nonlinear (piecewise linear at best), viscoelasticity, like elasticity, permits a linear theory.

This theory of linear visco elasticity is the subject of tbe present book. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Book Search tips Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for the Publisher/Society in context.

Pure Appl. Math. 43, 63 Mathematical Structure of the Theories of Viscoelasticity (Herman, Paris. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.

Comparative study of physical theories has revealed the presence of a common topological and geometric structure. The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as.A.

E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover, S. P. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw-Hill, The following notation will be used in Volume II though there will be some lapses (for reasons of tradition): Greek letters will denote real numbers; lowercase boldface Latin letters.

Equations are established for the deformation of a viscoelastic porous solid containing a viscous fluid under the most general assumptions of anisotropy. The particular cases of transverse and complete isotropy are discussed.

General solutions are also developed for the equations in the isotropic case. As an example the problem of the settlement of a loaded column is treated.