Structural Analysis of Articular Cartilage Using Multiphoton Microscopy: Input for Biomechanical Modeling

Mathematics and Mechanics of Solids

2017

constitutive model excluding fibers under compression: application to extension-inflation of a residually stressed carotid artery. Mathematics and Mechanics of Solids, (doi:10.1177/1081286517712077) This is the author's final accepted version.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.http://eprints.gla.ac.uk/142898/ Abstract. Detailed information on the three-dimensional dispersion of collagen fibers within layers of healthy and diseased soft biological tissues has been reported recently. Previously we have proposed a constitutive model for soft fibrous solids based on the angular integration approach which allows the exclusion of any compressed collagen fiber within the dispersion.In addition, a computational implementation of that model in a general purpose finite element program has been investigated and verified with the standard fiber-reinforcing model for fiber contributions. In this study, we develop the proposed fiber dispersion model further using an exponential form of the strain-energy function for the fiber contributions. The finite element implementation of this model with a rotationally symmetrical dispersion of fibers is also pre-

Section: Introductionmentioning

confidence: 62%

An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery

Mathematics and Mechanics of Solids

2017

“…Specifically, in human arterial walls the collagen fibers are not perfectly aligned but are dispersed around a mean direction. Such a fiber dispersion has been observed in, for example, human arterial walls [1][2][3][4][5], the myocardium [6,7], corneas [8,9] and articular cartilage [10]. In particular, recent extensive experimental results [4] have shown that the collagen fiber dispersion in each of the layers of (healthy) human thoracic and abdominal aortas and iliac arteries is non-symmetric, in contrast to the rotationally symmetric fiber dispersion assumed in previous studies; see, for example, [11].…”

Section: Introductionmentioning

confidence: 78%

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

European Journal of Mechanics - A/Solids

2016

Self Cite

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.

“…Recent work [7] has revealed that, while helical fibre structures are present in human elastic arteries, in more muscular arteries (as for the murine basilar artery) and veins (such as the porcine jugular vein) a transition from the helical arrangement to two nearly orthogonal fibre families aligned in the circumferential and axial directions can be observed, and it is suggested that this is to ensure optimal efficiency of the vasculature. Observations of dispersion for other tissues, including the myocardium, corneas and articular cartilage, can be found in [8,9], [10,11] and [12], respectively.…”

Section: Introductionmentioning

confidence: 99%

Modelling non-symmetric collagen fibre dispersion in arterial walls

Niestrawska

et al. 2015

J. R. Soc. Interface.

Self Cite

222

233

New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new nonsymmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15 -35. (doi:10.1098/ rsif.2005). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues.