Some results in the theory of non-Newtonian transversely isotropic fluids

Spencer, A. J. M.

doi:10.1016/j.jnnfm.2002.12.001

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…As in the previous section, bearing in mind the results by Edelen [24–26] and assuming that dissipative effects are negligible, the part of the stress tensor that accounts for material dispersion must satisfy a relation formally identical to (2.14), but with the energy density eD depending somehow on the preferred direction. To determine constitutive models for the stress tensor and the specific energy density in dispersive transversely isotropic materials, we take TD of the same form as the Cauchy stress tensor for a transversely isotropic second-grade fluid [29]: right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtruebold-italicTD =ρ1.623em1.623em[ϕ0m⊗m+ϕ1bold-italicA1+ϕ2bold-italicA2+ϕ3bold-italicA12+ϕ4(bold-italicA1m⊗m+m⊗bold-italicA1m) +ϕ5(bold-italicA2m⊗m+m⊗bold-italicA2m)+ϕ6(bold-italicA12m⊗m+m⊗bold-italicA12m)1.623em1.623em],with …”

Section: Materials Dispersion In Transversely Isotropic Materialsmentioning

confidence: 99%

“…As in the previous section, bearing in mind the results by Edelen [24][25][26] and assuming that dissipative effects are negligible, the part of the stress tensor that accounts for material dispersion must satisfy a relation formally identical to (2. somehow on the preferred direction. To determine constitutive models for the stress tensor and the specific energy density in dispersive transversely isotropic materials, we take T D of the same form as the Cauchy stress tensor for a transversely isotropic second-grade fluid [29]:…”

Section: Materials Dispersion In Transversely Isotropic Materialsmentioning

confidence: 99%

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A constitutive model for transversely isotropic dispersive materials

Amendola,

de Castro Motta,

Saccomandi

et al. 2024

Proc. R. Soc. A.

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Due to their intrinsic complexity, it is not easy to model the mechanical behaviour of biomaterials. Despite the challenges they faced, some researchers have presented mathematical models to describe some aspects of the mechanical response of soft tissues. Since most of the materials of biological interest are composites made of different constituents reinforced by collagen and/or elastin fibres, material dispersion and anisotropy are non-negligible. Within the theory of elasticity, several models for anisotropic materials have been developed. The same cannot be said for anisotropic dispersive materials. The models available in the literature that account for material dispersion are valid only for isotropic materials. This paper aims at introducing a very general model for anisotropic dispersion in transversely isotropic bodies within the theory of simple materials of differential type. Our model has the potential to represent a first step towards a better understanding of the mechanical response of fibre-reinforced soft materials.

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Section: Materials Dispersion In Transversely Isotropic Materialsmentioning

confidence: 99%

Section: Materials Dispersion In Transversely Isotropic Materialsmentioning

confidence: 99%

A constitutive model for transversely isotropic dispersive materials

Amendola,

de Castro Motta,

Saccomandi

et al. 2024

Proc. R. Soc. A.

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show abstract

“…We remind that the Navier–Stokes theory is obtained requiring “the most general linear isotropic function T of a symmetric second-order tensor D “ [11]. This requirement in the incompressible case gives the celebrated constitutive equation T = − p I + η D , but the most general transversely isotropic function T linear with respect to the symmetric second-order tensor D is given by Spencer [12]:…”

Section: Introductionmentioning

confidence: 99%

On the Kelvin–Voigt model in anisotropic viscoelasticity

Coco

Saccomandi

2023

Mathematics and Mechanics of Solids

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We propose an anisotropic and nonlinear generalization of the Kelvin–Voigt viscoelastic model obtained considering the additive splitting of the Cauchy stress tensor in an elastic and a dissipative part. The former one corresponds to a fiber-reinforced hyperelastic material while the dissipative effect is described by the most general linear transverse-isotropic tensorial function of symmetric part of the velocity gradient. In a such a way we characterize the dissipative contribution via three viscoelastic moduli. We then show, by a detailed analysis of the simple shear quasistatic motion and the corresponding creep phenomena, that this motion may be used to determine experimentally the viscoelastic parameters.

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Universality of the angled shear wave identity in soft viscous solids

Berjamin,

Gower

2024

Extreme Mechanics Letters

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Some results in the theory of non-Newtonian transversely isotropic fluids

Cited by 5 publications

References 8 publications

A constitutive model for transversely isotropic dispersive materials

A constitutive model for transversely isotropic dispersive materials

On the Kelvin–Voigt model in anisotropic viscoelasticity

Universality of the angled shear wave identity in soft viscous solids

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