Nonlinear Elasticity for Soft Fibrous Materials

Saccomandi, Giuseppe

doi:10.1007/978-3-7091-1838-2_3

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…When a solid is modelled as a generalised neo-Hookean material, for which W = W (I 1 ) only, the formula (2.2) 2 predicts that σ 22 should be zero. This observation will provide a universal check on the validity of such an assumption [7,8].…”

Section: Analytical Modelling Of Simple Shearmentioning

confidence: 78%

Extreme softness of brain matter in simple shear

Destrade

Gilchrist

Murphy

et al. 2015

International Journal of Non-Linear Mechanics

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We show that porcine brain matter can be modelled accurately as a very soft rubberlike material using the Mooney-Rivlin strain energy function, up to strains as high as 60%. This result followed from simple shear experiments performed on small rectangular fresh samples (2.8 cm 3 and 1.2 cm 3 ) at quasi-static strain rates. They revealed a linear shear stress-shear strain relationship (R 2 > 0.97), characteristic of Mooney-Rivlin materials at large strains. We found that porcine brain matter is about 30 times less resistant to shear forces than a silicone gel. We also verified experimentally that brain matter exhibits the positive Poynting e↵ect of nonlinear elasticity, and numerically that the stress and strain fields remain mostly homogeneous throughout the thickness of the samples in simple shear.

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Section: Analytical Modelling Of Simple Shearmentioning

confidence: 78%

Extreme softness of brain matter in simple shear

Destrade

Gilchrist

Murphy

et al. 2015

International Journal of Non-Linear Mechanics

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“…Mooney, therefore, found one possible form of 𝑊(𝐼 1 , 𝐼 2 ) out of infinite number of functional formssee the general solution of the Mooney problem by Mangan et al (2016). While this model has been a driving force for further developments within the modern theory of nonlinear elasticity, it is not fully compatible with the requirements of the fourth order weak nonlinear elasticity (Saccomandi (2015), Destrade et al (2017)). The reason for this incompatibility is that the Mooney-Rivlin model is a linearly degenerate model 2 , constraining its response in shear deformation to a very special case.…”

Section: Introductionmentioning

confidence: 99%

On the central role of the invariant I2 in nonlinear elasticity

Anssari-Benam

Bucchi

Saccomandi

2021

International Journal of Engineering Science

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“…In biology and in nature, most soft connective tissues in human and animal bodies (e.g., tendons and ligaments, but also cartilage) are built from a collagen fiber network performing structural functions. In biological tissues, the extracellular matrix consists essentially of collagen fibers, and provides structural support for cells [1]; at the lower cell level, the cytoskeleton, which provides the structural resistance of the cell, is a network of F-actin filaments, playing, furthermore, an essential role in the adjustment of the biochemical activity of the cell [2]. Both the practical importance of random fiber networks and their complexity in terms of fibrous organization motivates the need to develop a quantitative understanding of the relationship between the microstructure of random fiber networks and the mechanical behavior of the respective material or system including this random fibrous microstructure at the macroscopic scale.…”

Section: Introductionmentioning

confidence: 99%

Homogenized elastic response of random fiber networks based on strain gradient continuum models

Berkache

Deogekar

Goda

et al. 2019

Mathematics and Mechanics of Solids

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The purpose of this work is to develop anisotropic strain gradient linear elastic continuum models for two-dimensional random fiber networks. The constitutive moduli of the strain gradient equivalent continuum are assessed based on the response of the explicit network representation in so-called windows of analysis, in which each fiber is modeled as a beam and the fibers are connected at crossing points with welded joints. The principle of strain energy equivalence based on the extension to the strain gradient of the Hill–Mandel macro homogeneity condition is employed to identify the classical and strain gradient moduli, based on the application of a sequential set of polynomial displacements on windows of analysis of different sizes. The scaling of the first- and second-order moduli with network parameters, such as network density and the ratio of fiber bending to axial stiffness, is determined. We observe a similar dependency of classical and strain gradient moduli on the same network parameters. The internal length scales associated with the gradient coefficients of the constitutive equation are also defined in terms of the network parameters. The strain gradient moduli prove to be size-independent in the affine regime, and they converge toward a size-independent value in the non-affine deformation regime after a rescaling of physical dimensions by the window size. The obtained results show that the strain gradient moduli scale uniformly with the square of the magnitude of the strain gradients applied to the window of analysis.

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Nonlinear Elasticity for Soft Fibrous Materials

Cited by 4 publications

References 19 publications

Extreme softness of brain matter in simple shear

Extreme softness of brain matter in simple shear

On the central role of the invariant I2 in nonlinear elasticity

Homogenized elastic response of random fiber networks based on strain gradient continuum models

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