VI. An application of the theory of quasi-properties to the treatment of anomalous strain-stress relations

Blair, G. W. Scott; Caffyn, J. E.

doi:10.1080/14786444908561213

Cited by 114 publications

(32 citation statements)

References 8 publications

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“…He noted that, from the best fitting of experimental curves, the relationship between deformation and time could be described by a power law, i.e. u / t n F m : In 1949, Blair & Caffyn [49] justified analytically this experimental law through fractional derivatives, introducing a new analytical model in viscoelasticity: the spring-pot model. Successively, a number of scientific papers have been produced for approaching viscoelastic problems in several classical as well as pioneering engineering and physical fields (e.g.…”

Section: Cells Behaving As a Quasi-standard Maxwell Modelmentioning

confidence: 99%

“…For this purpose, the spring-pot model is substantially that firstly introduced by Blair & Caffyn [49], but it is here generalized to take into account the virtual friction and the added mass by means of the suitable introduction of additional contributions. In particular, the response spring-pot force f SP is defined as follows:…”

Section: Cells Behaving As a Quasi-standard Maxwell Modelmentioning

confidence: 99%

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A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells

Fraldi¹,

Cugno

Deseri

et al. 2015

J. R. Soc. Interface.

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Experimental studies recently performed on single cancer and healthy cells have demonstrated that the former are about 70% softer than the latter, regardless of the cell lines and the measurement technique used for determining the mechanical properties. At least in principle, the difference in cell stiffness might thus be exploited to create mechanical-based targeting strategies for discriminating neoplastic transformations within human cell populations and for designing innovative complementary tools to cell-specific molecular tumour markers, leading to possible applications in the diagnosis and treatment of cancer diseases. With the aim of characterizing and gaining insight into the overall frequency response of single-cell systems to mechanical stimuli (typically low-intensity therapeutic ultrasound), a generalized viscoelastic paradigm, combining classical and spring-pot-based models, is introduced for modelling this problem by neglecting the cascade of mechanobiological events involving the cell nucleus, cytoskeleton, elastic membrane and cytosol. Theoretical results show that differences in stiffness, experimentally observed ex vivo and in vitro, allow healthy and cancer cells to be discriminated, by highlighting frequencies (from tens to hundreds of kilohertz) associated with resonance-like phenomena-prevailing on thermal fluctuations-that could be helpful in targeting and selectively attacking tumour cells.

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Section: Cells Behaving As a Quasi-standard Maxwell Modelmentioning

confidence: 99%

Section: Cells Behaving As a Quasi-standard Maxwell Modelmentioning

confidence: 99%

A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells

Fraldi¹,

Cugno

Deseri

et al. 2015

J. R. Soc. Interface.

View full text Add to dashboard Cite

show abstract

“…(5) shows the stress-strain relation of a new mathematical model of viscoelasticity that is known as spring-pot [29], [30]; the involved β order of fractional operator is defined in the range ]0, 1[ (β = 0 corresponds to pure elastic behavior of Eq. (1), while β = 1 represents the pure viscous behavior of Eq.…”

Section: γ(T) σ(T) ηmentioning

confidence: 99%

Viscoelasticity: An electrical point of view

Ala

Paola

Francomano

et al. 2014

ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014

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Abstract-Time dependent hereditary properties of complex materials are well described by power-laws with real order exponent. This experimental observation and analogous electrical experiments, yield a description of these properties by using fractional-order operators. In this paper, elasto-viscous and viscoelastic behaviors of fractional order hereditary materials are firstly described by using fractional mathematical operators, based on recent work of some of the authors. Then, electrical analogous models are introduced. Viscoelastic models have elastic and viscous components which can be obtained by combining springs and dashpots: these models can be equivalently viewed as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials.

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“…(6) shows the stress-strain relation of a new mathematical model of viscoelasticity that is known as spring-pot [42][43][44][45]; the involved b order of fractional operator is defined in the range 0; 1 ½(b ¼ 0 corresponds to pure elastic behavior of Eq. (1), while b ¼ 1 represents the pure viscous behavior of Eq.…”

Section: Mechanical Models Of Fractional Viscoelasticitymentioning

confidence: 99%

Electrical analogous in viscoelasticity

Ala

Paola

Francomano

et al. 2014

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tIn this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical experiments based on finite difference time domain method shows that, for long time simulations, the correct time behavior can be obtained only with modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials.

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VI. An application of the theory of quasi-properties to the treatment of anomalous strain-stress relations

Cited by 114 publications

References 8 publications

A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells

A frequency-based hypothesis for mechanically targeting and selectively attacking cancer cells

Viscoelasticity: An electrical point of view

Electrical analogous in viscoelasticity

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