A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues

Lanir, Yoram

doi:10.1016/0021-9290(79)90027-7

Cited by 369 publications

(226 citation statements)

References 19 publications

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“…However, so far no study has investigated the anisotropic mechanical properties of the rat and mice skin tissues at different anatomical locations of their body, i.e., abdomen and back, using histostructural and uniaxial extension data. There have been some studies which used Ogden, 18 Neo-Hookean, 17 Mooney-Rivlin, 26 and Fung-type 29,30 material model to address the nonlinear mechanical behavior of the skin tissue. However, none of those studies implemented the role of fiber orientations into a constitutive equation to capture the anisotropic nonlinear mechanical properties of the skin tissue.…”

Section: Discussionmentioning

confidence: 99%

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

2015

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The skin tissue has been shown to behave like a nonlinear anisotropic material. This study was aimed to employ a constitutive fiber family equation to characterize the nonlinear anisotropic mechanical behavior of the rat and mice skin tissues in different anatomical locations, including the abdomen and back, using histostructural and uniaxial data. The rat and mice skin tissues were excised from the animals' body and then the histological analyses were performed on each skin type to determine the mean fiber orientation angle. Afterward, the preconditioned skin tissues were subjected to a series of quasi-static axial and circumferential loads until the incidence of failure. The crucial role of fiber orientation was explicitly added into a proposed strain energy density function. The material coefficients were determined using the constrained nonlinear optimization method based on the axial and circumferential extension data of the rat and mice samples at different anatomical locations. The material coefficients of the skins were given with R 2 0.998. The results revealed a significant load-bearing capacity and stiffness of the rat abdomen compared to the rat back tissues. In addition, the mice abdomen showed a higher stiffness in the axial direction in comparison with circumferential one, while the mice back displayed its highest stiffness in the circumferential direction. The material coefficients of the rat and mice skin tissues were determined and well compared to the experimental data. The optimized fiber angles were also compared to the experimental histological data, and in all cases less than 11.85% differences were observed in both the skin tissues.

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Section: Discussionmentioning

confidence: 99%

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

2015

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“…The present model is not based on structural considerations as some other studies (e.g. Lanir, 1979). An extension of the model described here could therefore be to determine a correlation between the geometrical structure of the specimens and the three parameters of the constitutive law.…”

Section: Discussionmentioning

confidence: 99%

Viscoelastic constitutive law in large deformations

Pioletti

Rakotomanana

Benvenuti

et al. 1998

Journal of Biomechanics

237

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Traction tests on soft tissues show that the shape of the stress-strain curves depends on the strain rate at which the tests are performed. Many of the constitutive models that have been proposed fail to properly consider the effect of the strain rate when large deformations are encountered. In the present study, a framework based on elastic and viscous potentials is developed. The resulting constitutive law is valid for large deformations and satisfies the principles of thermodynamics. Three parameters -two for the elasticity and one for the viscosity -were enough to precisely fit the non-linear stress-strain curves obtained at different strain rates with human cruciate ligaments and patellar tendons. The identification results then in a realistic, three-dimensional viscoelastic constitutive law. The developed constitutive law can be used regardless of the strain or rotation values. It can be incorporated into a finite element program to model the viscoelastic behavior of ligaments and tendons under dynamic situations.

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“…Most importantly, structural SEFs allocate macroscopic stress to different micro-structural components, and are able to link the macroscopic loading to potential cellular responses. Structural SEFs for the vessel wall are based on fiber-reinforced composite concepts, which assume straight and parallel-aligned [16,33,40], straight and orientation-dispersed [1,13], undulated and parallelaligned [39,40], or undulated and orientation-dispersed [19,23] (families of) fibers. Despite the fact that considerable work has been dedicated to develop and numerically implement structural SEFs, only very few studies consistently validated structural SEFs, i.e.…”

Section: Introductionmentioning

confidence: 99%

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

et al. 2016

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Background Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall’s anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example. Method Porcine common carotid arteries (n = 10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF. Results Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (¿1,2,3=[13.5,0.0,25.2] and ¿1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data. Conclusions The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.Peer ReviewedPostprint (author's final draft

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A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues

Cited by 369 publications

References 19 publications

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

Viscoelastic constitutive law in large deformations

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

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