A new analysis of stresses in arteries based on an Eulerian formulation of growth in tissues

Safadi, M.M.; Rubin, M. B.

doi:10.1016/j.ijengsci.2017.05.004

Cited by 10 publications

(3 citation statements)

References 32 publications

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“…where ρ 0 is the constant mass density of the tissue in any stress-free state. Moreover, to simplify the numerical integration algorithm, the rate r m was specified in [39] by…”

Section: (B) Eulerian Formulation Of Growthmentioning

confidence: 99%

“…This means that the constitutive equations for the homeostatic values (J h , H ) can be used to model experimental observations about the stresses in biological materials in their homeostatic states (e.g. [39]). Also, the constitutive equations for (Γ m , Γ ) control the rates of homeostasis.…”

Section: (B) Eulerian Formulation Of Growthmentioning

confidence: 99%

“…Rubin et al [37] developed a unified theoretical structure for modelling interstitial growth and muscle activation in soft tissues. Safadi & Rubin [38] used this theory to study significant differences in the mechanical modelling of confined growth predicted by Lagrangian and Eulerian formulations and Safadi & Rubin [39] used the theory to analyse stresses in arteries. This section reviews the generalized formulation developed within the context of the purely mechanical theory in [38].…”

Section: (B) Eulerian Formulation Of Growthmentioning

confidence: 99%

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An Eulerian formulation of inelasticity: from metal plasticity to growth of biological tissues

Rubin

2019

Phil. Trans. R. Soc. A.

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The purpose of this paper is to review and contrast the Lagrangian and Eulerian formulations of inelasticity as they apply to metal plasticity and growth of biological tissues. In contrast with the Lagrangian formulation of inelasticity, the Eulerian formulation is unaffected by arbitrary choices of the reference configuration, an intermediate configuration, a total deformation measure and an inelastic deformation measure. Although the Eulerian formulation for growth of biological tissues includes a rate of mass supply and can be used to understand the mechanics of growth, it does not yet model essential mechanobiological processes that control growth. Much research is needed before this theory can help design medical treatments for growth related disease. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

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“…where ρ 0 is the constant mass density of the tissue in any stress-free state. Moreover, to simplify the numerical integration algorithm, the rate r m was specified in [39] by…”

Section: (B) Eulerian Formulation Of Growthmentioning

confidence: 99%

Section: (B) Eulerian Formulation Of Growthmentioning

confidence: 99%