The Non-Linear Field Theories of Mechanics

Truesdell, C.; Noll, Walter; Pipkin, A. C.

doi:10.1007/978-3-662-13183-1

Cited by 549 publications

(106 citation statements)

References 622 publications

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“…Various groups (polyestradiols) resistant to hydrolytic degradation are used to produce polyurethane (Ryszkowska et al 2010). The approach of the constitutive equation formulation presented in the paper, based on application of a potential function form ψ , is well described in the literature (Truesdell and Noll 1992;Coleman 1964;Pawlikowski 2012). It is a very convenient approach as it makes it possible to take into account various phenomena, such as ability of a material to dissipate energy, relation between reaction and deformation rate of a material, anisotropy of a material by means of structural tensors, etc.…”

Section: Introductionmentioning

confidence: 99%

Non-linear approach in visco-hyperelastic constitutive modelling of polyurethane nanocomposite

Pawlikowski

2013

Mech Time-Depend Mater

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The constitutive modelling of the polyurethane nanocomposite presented in the paper is done in the context of its possible application as one of the components of the intervertebral disc prosthesis. The constitutive study is a part of the researches aiming at creation of the new prosthetic device. The material is considered as incompressible, isotropic and visco-hyperelastic one. The focus of the work lies on the formulation of a constitutive equation for its further implementation in finite element analyses. The equation is formulated on the basis of uniaxial monotonic compression tests and relaxation tests performed at room temperature. The constants of the constitutive model are determined from the experimental data by means of the curve-fitting approach employing least-squares optimisation method. The constitutive modelling consisted of two steps. In the first one pure hyperelastic model was determined. The Mooney-Rivlin model proved to be the best one to describe hyperelastic behaviour of the material. In the second step non-linear visco-hyperelastic model was derived. Relaxation times, characteristic amplitudes and Mooney-Rivlin hyperelastic constants were calibrated on the basis of strain-stress curves (hysteresis loops) obtained experimentally at three strain rates, i.e.λ = 0.1 min −1 ,λ = 1 min −1 andλ = 10 min −1. The constitutive law is validated on the basis of relaxation test. The paper concludes with summary and plans for further investigations in the area.

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Section: Introductionmentioning

confidence: 99%

Non-linear approach in visco-hyperelastic constitutive modelling of polyurethane nanocomposite

Pawlikowski

2013

Mech Time-Depend Mater

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“…Let us point out that, although we consider here only two particular fluid models, our results remain valid for more general fluids of the Oldroyd and Rivlin-Ericksen type, for example for all the models studied in [25,32]. For the mechanical background of the rate and differential type viscoelastic fluids, we refer to [31,29,27,10].…”

Section: Introductionmentioning

confidence: 94%

Asymptotic behaviour at infinity of three-dimensional steady viscoelastic flows

Назаров¹,

Sequeira²,

Videman³

2002

Pacific J. Math.

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The steady motion of viscoelastic fluids is investigated in a three-dimensional exterior domain. Results concerning existence, uniqueness and asymptotic behaviour are obtained using appropriately constructed function spaces in which the elements are defined as a sum of the main asymptotic term and of the remainder living in a proper weighted Sobolev space. The equations are written as a coupled system that, at the first stage, can be studied as two linear problems composed of a Stokes system and a transport equation. Finally, a standard contraction argument provides existence and uniqueness of solutions for the original nonlinear coupled set of equations, when the data are sufficiently small.

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“…Their motion has been characterized by numerous models over the past 50 years, see References [1,3,[21][22][23] and the references cited therein. During the last decades, mathematicians have also started to pay attention to these models and several results concerning existence, uniqueness and the asymptotic behaviour of solutions have appeared, see References [15,17,[24][25][26].…”

Section: Non-newtonian Fluids: a Short Review And The Formulation Of mentioning

confidence: 99%

Incompressible non‐Newtonian fluids: time asymptotic behaviour of weak solutions

Nečasová

Penel

2006

Math Methods in App Sciences

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The Non-Linear Field Theories of Mechanics

Abstract: Library of Congress Cataloging-in-Publication Data Truesdell, C. (Clifford),1919-The non-linear field theories of mechanics I C. Truesdell, W. Noll-3rd ed./ edited by StuartS. Antman. p. em. Includes bibliographical references and index.

Cited by 549 publications

References 622 publications

Non-linear approach in visco-hyperelastic constitutive modelling of polyurethane nanocomposite

Non-linear approach in visco-hyperelastic constitutive modelling of polyurethane nanocomposite

Asymptotic behaviour at infinity of three-dimensional steady viscoelastic flows

Incompressible non‐Newtonian fluids: time asymptotic behaviour of weak solutions

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