On the Normal Stresses in Simple Shearing of Fiber-Reinforced Nonlinearly Elastic Materials

Horgan, Cornelius O.; Murphy, Jeremiah G.

doi:10.1007/s10659-011-9310-0

Cited by 21 publications

(3 citation statements)

References 31 publications

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“…What is the functional dependence of the normal stress on the shear stress? Nonlinear elasticity theory can predict the anisotropic normal stress due to shear stress [53,55,[58][59][60][61]. The magnitude of the normal stress response depends on the mechanical properties of the gel and of the crosslinking filaments.…”

Section: Active Forcesmentioning

confidence: 99%

Vascular adaptation model from force balance:Physarum polycephalumas a case study

Marbach

Ziethen

Alim

2023

Preprint

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Understanding vascular adaptation, namely what drives veins to shrink or grow, is key for the self-organization of flow networks and their optimization. From the top-down principle of minimizing flow dissipation at a fixed metabolic cost within flow networks, flow shear rate resulting from the flows pervading veins is hypothesized to drive vein adaptation. Yet, there is no bottom-up derivation of how flow forces impact vein dynamics. From the physical principle of force balance, shear rate acts parallel to vein walls, and hence, naively shear rate could only stretch veins and not dilate or shrink them. We, here, resolve this paradox by theoretically investigating force balance on a vein wall in the context of the vascular network of the model organismP. polycephalum. We propose, based on previous mechanical studies of cross-linked gels, that shear induces a nonlinear, anisotropic response of the actomyosin gel, making up vein walls that can indeed drive vein dilatation. Furthermore, our force balance approach allows us to identify that shear feedback occurs with a typical timescale and with a typical target shear rate that are not universal properties of the material but instead depend smoothly on the location of the vein within the network. In particular, the target shear rate is related to the vein’s hydrostatic pressure, which highlights the role of pressure in vascular adaptation. Finally, since our derivation is based on force balance and fluid mechanics, we believe our approach can be extended to vascular adaptation in other organisms.

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Section: Active Forcesmentioning

confidence: 99%

Vascular adaptation model from force balance:Physarum polycephalumas a case study

Marbach

Ziethen

Alim

2023

Preprint

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“…First, following [32], if the normal component of the surface traction on the inclined faces of the deformed cube is assumed to be zero, then…”

Section: Simple Shearmentioning

confidence: 99%

Computational method for excluding fibers under compression in modeling soft fibrous solids

Ogden

Holzapfel

2016

European Journal of Mechanics - A/Solids

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Abstract. Soft fibrous solids often consist of a matrix reinforced by fibers that render the material anisotropic. Recently a fiber dispersion model was proposed on the basis of a weighted strain-energy function using an angular integration approach for both planar and three-dimensional fiber dispersions (G.A. Holzapfel and R.W. Ogden: Eur. J. Mech. A/Solids, 49 (2015) 561-569). This model allows the exclusion of fibers under compression. In the present study computational aspects of the model are documented. In particular, we provide expressions for the elasticity tensor and the integration boundary that admits only fibers which are extended. In addition, we give a brief description of the finite element implementation for both 2D and 3D models which make use of the von Mises distribution to describe the dispersion of the fibers.The performance and the finite element implementations of the 2D and 3D fiber dispersion models are illustrated by means of uniaxial extension in the mean fiber direction and more general directions, and simple shear with different mean fiber directions. The finite element results are in perfect agreement with the solutions computed from analytical formulas.

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“…Nonlinear elasticity theory can predict the normal stress response due to shear stress [74,[76][77][78][79][80]. The magnitude of the normal stress response depends on the mechanical properties of the gel and the crosslinking filaments.…”

Section: What Is the Functional Dependence Of The Normal Stress On Th...mentioning

confidence: 99%

Vascular adaptation model from force balance: Physarum polycephalum as a case study

Marbach,

Ziethen,

Alim

2023

New J. Phys.

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Understanding vascular adaptation, namely what drives veins to shrink or grow, is key for the self-organization of flow networks and their optimization. From the top–down principle of minimizing flow dissipation at a fixed metabolic cost within flow networks, flow shear rate resulting from the flows pervading veins is hypothesized to drive vein adaptation. Yet, there is no proposed mechanism of how flow forces impact vein dynamics. From the physical principle of force balance, shear rate acts parallel to vein walls, and hence, naively shear rate could only stretch veins and not dilate or shrink them. We, here, resolve this paradox by theoretically investigating force balance on a vein wall in the context of the vascular network of the model organism Physarum polycephalum. We propose, based on previous mechanical studies of cross-linked gels, that shear induces a nonlinear, orthogonal response of the actomyosin gel making up vein walls, that can indeed drive vein dilatation. Furthermore, our force balance approach allows us to identify that shear feedback occurs with a typical timescale and with a typical target shear rate that are not universal properties of the material but instead depend smoothly on the vein’s location within the network. In particular, the target shear rate is related to the vein’s hydrostatic pressure, which highlights the role of pressure in vascular adaptation in this context. Finally, since our derivation is based on force balance and fluid mechanics, we believe our approach can be extended, giving attention to specific differences, to describe vascular adaptation in other organisms.

show abstract

On the Normal Stresses in Simple Shearing of Fiber-Reinforced Nonlinearly Elastic Materials

Cited by 21 publications

References 31 publications

Vascular adaptation model from force balance:Physarum polycephalumas a case study

Vascular adaptation model from force balance:Physarum polycephalumas a case study

Computational method for excluding fibers under compression in modeling soft fibrous solids

Vascular adaptation model from force balance: Physarum polycephalum as a case study

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