The Estimation of Firmness in Soft Materials

Blair, G. W. Scott; Coppen, F. M. V.

doi:10.2307/1417506

Cited by 34 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consequently, only some specific cases have a desired solution, making this approach not sufficiently flexible. Alternatively, Scott Blair and Coppen [21,22] and Rabotnov [23] suggested to use fraction-exponential operators to describe viscoelastic behaviour and demonstrated their advantages of sufficient accuracy in description of experimental data of real materials together with convenience of solving analytical Laplace transformations. Thanks to that, the use of fraction-exponential operators in recent years attracted a growing interest in the field of solid mechanics, especially mechanics of heterogeneous materials [24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Through-thickness stress relaxation in bacterial cellulose hydrogel

Gao

Kuśmierczyk

Shi

et al. 2016

Journal of the Mechanical Behavior of Biomedical Materials

View full text Add to dashboard Cite

Biological hydrogels, e.g. bacterial cellulose (BC) hydrogel, attracted increasing interest in recent decades since they show a good potential for biomedical engineering as replacements of real tissues thanks mainly to their good biocompatibility and fibrous structure. To select potential candidates for such applications, a comprehensive understanding of their performance under application-relevant conditions is needed. Most hydrogels demonstrate time-dependent behaviour due to the contribution of their liquid phase and reorientation of fibres in a process of their deformation. To quantify such time-dependent behaviour is crucial due to their exposure to complicated loading conditions in body environment. Some hydrogel-based biomaterials with a multi-layered fibrous structure demonstrate a promise as artificial skin and blood vessels. The results show a good potential to use a fraction-exponential model to describe such behaviour of multi-layered hydrogels, especially at stages of stress decay at low forces and of stress equilibrium at high forces.

show abstract

Section: Introductionmentioning

confidence: 99%

Through-thickness stress relaxation in bacterial cellulose hydrogel

Gao

Kuśmierczyk

Shi

et al. 2016

Journal of the Mechanical Behavior of Biomedical Materials

View full text Add to dashboard Cite

show abstract

“…It was suggested in [61] that, in considered cases, comparative firmness is judged neither by σ, nor byσ, nor by any mixture of these two magnitude, but by some intermediate entity, namely by fractional derivative ∂ ν σ ∂t ν . 3 More exactly, he wrote: The general constitutive equation "... is applicable to integral values of n but a more general equation may be used even n is a fraction.The numerical coefficient is expressed as a quotient of Γ-functions and may be written…”

Section: Scott Blair's Fractional Modelmentioning

confidence: 99%

“…where proportionality coefficient ψ is a constant. Derived in this way the equation (2) looks entirely empirical, tough the fundamental significance of α (which is called the dissipation coefficient) is shown in psychophysical experiments described by Scott Blair and Coppen (see [58], [59], [61]). A comparison of the partially differentiated Nutting equation and Maxwell's equation may be written (see [51]), namely, for Nutting: 2…”

Section: Nutting's Lawmentioning

confidence: 99%

See 1 more Smart Citation

George William Scott Blair – the pioneer of fractional calculus in rheology

Rogosin¹,

Mainardi²

2014

Communications in Applied and Industrial Mathematics

View full text Add to dashboard Cite

The article shows the pioneering role of the British scientist, Professor G.W.Scott Blair, in the creation of the application of fractional modelling in rheology. Discussion of his results is presented. His approach is highly recognized by the rheological society and is adopted and generalized by his successors. Further development of this branch of Science is briefly described in this article too.

show abstract

“…Perhaps suitable mathematical techniques could be developed that would reduce these difficulties. Appendix Note on fractional differential and the gamma-function (See Coppen, 1943, andHarper, 1947) It is elementary that, if we consider a length, I, then the rate of change of I with time (t) (the velocity) is written as dZ/dt and the rate of change of velocity with time (the acceleration), as d21/dt ' . There is no limit to the possible number of differentiations (dnl/dt ").…”

Section: Conclasionsmentioning

confidence: 99%

Psychorheology: Links Between the Past and the Present*

Blair¹

1974

Journal of Texture Studies

Self Cite

View full text Add to dashboard Cite

A brief discussion is given concerning the validity of psychophysics as a science with special reference to psychorheology. Some early work on psychorheology concerned mainly with cutaneous and kinaesthetic sensations is discussed. A distinction is made between connotative and denotative concepts; difficulties in defining the latter are stressed, with special reference to translating into other languages.Denotative concepts are to be regarded as processes rather than as properties; i.e., properties changing with time often as a result of the testing. It was suggested long ago that these time-differentials should be fractional, and it is proposed thatin spite of mathematical difficultiesfractional differential equations might serve as a useful adjunct to the 'consistency profiling' now in wide use.

show abstract

The Estimation of Firmness in Soft Materials

Cited by 34 publications

References 0 publications

Through-thickness stress relaxation in bacterial cellulose hydrogel

Through-thickness stress relaxation in bacterial cellulose hydrogel

George William Scott Blair – the pioneer of fractional calculus in rheology

Psychorheology: Links Between the Past and the Present*

Contact Info

Product

Resources

About