The Subjective Conception of the Firmness of Soft Materials

Blair, Gregory; Coppen, F. M. V.

doi:10.2307/1417080

Cited by 37 publications

(20 citation statements)

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“…Using Eqs. (46), (47) and (49) we obtain the asymptotic behavior of the penetration depth for compressional waves in low frequency and high frequency regimes as:…”

Section: Compressional Wave Equationmentioning

confidence: 99%

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

Pandey

Holm

2016

The Journal of the Acoustical Society of America

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The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815(2000] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials. Rather, it can also be derived from real physical processes as illustrated in this work by the example of grain-shearing.

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“…Using Eqs. (46), (47) and (49) we obtain the asymptotic behavior of the penetration depth for compressional waves in low frequency and high frequency regimes as:…”

Section: Compressional Wave Equationmentioning

confidence: 99%

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

Pandey

Holm

2016

The Journal of the Acoustical Society of America

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“…It may thus be argued that they are not true material properties because they contain noninteger powers of the fundamental dimensions of space and time. However, such quasi-properties appear to compactly describe textural parameters such as the 'firmness' of a material [24]. They are numerical measures of a dynamical process such as creep in a material rather than of an equilibrium state.…”

mentioning

confidence: 99%

“…We first briefly outline the basic definitions of fractional calculus in a form most useful for applications in rheology. We then connect the framework to the studies of Scott-Blair and co-workers [24,31], and show, using Scott-Blair et al's [31] original data on 'highly anomalous butyl rubber', how the use of the FMM to extract the quasi-properties of this material is superior to the use of conventional spring-dashpot models that characterize creep and stress relaxation. Next, we emphasize the utility of fractional constitutive models, and highlight the shortcomings of linear constitutive models for describing complex fluid interfaces using interfacial rheology data obtained from highly viscoelastic bovine serum albumin (BSA) and Acacia gum interfaces.…”

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confidence: 99%

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

2013

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Consumer products, such as foods, contain numerous polymeric and particulate additives that play critical roles in maintaining their stability, quality and function. The resulting materials exhibit complex bulk and interfacial rheological responses, and often display a distinctive power-law response under standard rheometric deformations. These power laws are not conveniently described using conventional rheological models, without the introduction of a large number of relaxation modes. We present a constitutive framework using fractional derivatives to model the power-law responses often observed experimentally. We first revisit the concept of quasiproperties and their connection to the fractional Maxwell model (FMM). Using Scott-Blair's original data, we demonstrate the ability of the FMM to capture the power-law response of 'highly anomalous' materials. We extend the FMM to describe the viscoelastic interfaces formed by bovine serum albumin and solutions of a common food stabilizer, Acacia gum. Fractional calculus allows us to model and compactly describe the measured frequency response of these interfaces in terms of their quasiproperties. Finally, we demonstrate the predictive ability of the FMM to quantitatively capture the behaviour of complex viscoelastic interfaces by combining the measured quasi-properties with the equation of motion for a complex fluid interface to describe the damped inertio-elastic oscillations that are observed experimentally.

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“…Despite this complexity, the spring-pot still lies in the linear viscoelastic framework, enabling us to greatly simplify the analysis of the data and make predictions. For dimensional consistency, the unit of the constant c β is (Pa s −β ), and therefore it does not have a straightforward physical meaning, although, it has been argued that it may represent a measurement of the firmness of the material [30].…”

Section: A Constitutive Model For Epithelial Monolayersmentioning

confidence: 99%

A unified rheological model for cells and cellularised materials

Bonfanti

Fouchard

Khalilgharibi

et al. 2019

Preprint

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The mechanical response of single cells and tissues exhibits a broad distribution of time scales that gives often rise to a distinctive power-law regime. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times can be derived from the model parameters, and together these explain different qualitative behaviours observed in creep after genetic and chemical treatments. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach for diagnostic methods based on mechanical traits as well as more accurate computational models of tissues mechanics.As part of their physiological function, single cells and tissues are continuously exposed to mechanical stress. For example, leukocytes circulating in the blood must squeeze through small capillaries, and the epidermis must deform in response to movements of our limbs. During development, mechanical forces initiate morphogenetic processes involving epithelial growth, elongation or bending, acting as cues to coordinate morphogenetic events [1]. Epithelial cell sheets are also continuously subjected to deformation as part of normal physiology. For instance, lung epithelial cells are exposed to fast cyclical mechanical stress during respiration [2], while epithelia lining the intestinal wall or those in the skin can experience long lasting strain [3]. Failure to withstand physiological forces results in fracture of monolayers which may lead to severe clinical conditions, such as hemorrhage or pressure ulcers [3]- [6]. Despite significant progress with the experimental characterization of cell and tissue mechanics, understanding the role of mechanical forces in development and pathology is hampered by the lack of a unified quantitative approach to capture, compare and predict the complex mechanical behaviours of tissues, cells, and sub-cellular components across all physiologically relevant time-scales. Such a framework would also enable us to assess the effects of pharmacological treatments on tissue mechanical response without necessitating experimental characterization of the tissue response to all loading conditions, something important for tissue engineering and the design of palliative treatment strategies.In recent years, experimental characterization of the mechanical behaviour o...

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The Subjective Conception of the Firmness of Soft Materials

Cited by 37 publications

References 0 publications

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

A unified rheological model for cells and cellularised materials

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