A Composite Micromechanical Model for Connective Tissues: Part I—Theory

Ault, Holly K.; Hoffman, Allen H.

doi:10.1115/1.2895437

Cited by 46 publications

(32 citation statements)

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“…In this formulation, tendon is modelled by embedding straight or wavy collagen fibrils/fibres in a surrounding non-fibrillar matrix, mainly composed of PGs [91][92][93]. The strain energy function for the composite tendon can then be simply decomposed into the elastic strain energy stored within reinforcing fibres and the isochoric energy of the deformation in the matrix [80,94].…”

Section: Contribution Of Proteoglycans To Tendon Mechanics and Their mentioning

confidence: 99%

“…The global load-sharing model hypothesizes a perfect, no-slip bond of the fibre/ matrix interface and negligible contact among fibres. In this formulation, the loading modules are unbranched fibres and non-fibrillar matrix with a uniform strain [102,103], and the representative volume of material is developed to guarantee transverse homogeneity [92]. Different mechanical parameters (e.g.…”

Section: Contribution Of Proteoglycans To Tendon Mechanics and Their mentioning

confidence: 99%

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Modelling approaches for evaluating multiscale tendon mechanics

Fang

Lake

2016

Interface Focus.

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Tendon exhibits anisotropic, inhomogeneous and viscoelastic mechanical properties that are determined by its complicated hierarchical structure and varying amounts/organization of different tissue constituents. Although extensive research has been conducted to use modelling approaches to interpret tendon structure–function relationships in combination with experimental data, many issues remain unclear (i.e. the role of minor components such as decorin, aggrecan and elastin), and the integration of mechanical analysis across different length scales has not been well applied to explore stress or strain transfer from macro- to microscale. This review outlines mathematical and computational models that have been used to understand tendon mechanics at different scales of the hierarchical organization. Model representations at the molecular, fibril and tissue levels are discussed, including formulations that follow phenomenological and microstructural approaches (which include evaluations of crimp, helical structure and the interaction between collagen fibrils and proteoglycans). Multiscale modelling approaches incorporating tendon features are suggested to be an advantageous methodology to understand further the physiological mechanical response of tendon and corresponding adaptation of properties owing to unique in vivo loading environments.

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Section: Contribution Of Proteoglycans To Tendon Mechanics and Their mentioning

confidence: 99%

Section: Contribution Of Proteoglycans To Tendon Mechanics and Their mentioning

confidence: 99%

Modelling approaches for evaluating multiscale tendon mechanics

Fang

Lake

2016

Interface Focus.

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“…Glycosaminoglycans are also rod like and are linked at one end to the proteoglycan core protein (Muir, 1977;Heinegard and Paulsson, 1984;Quinn, et al 2001). Here we apply the composite cylinder model (Ault et al, 1992;Schwartz et al, 1994;Lei and Szeri, 2006) to describe the orientation of the equivalent cartilage network.…”

Section: Diffusivity Tensor-letmentioning

confidence: 99%

Transport of neutral solute in articular cartilage: Effect of microstructure anisotropy

Zhang

Szeri

2008

Journal of Biomechanics

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Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What's more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date.We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain.Our results indicate that in cartilage the degree of diffusion anisotropy is site specific but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.

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“…The fibril orientations for the three different zones are described by equations (24)(25)(26). The boundary conditions are that the stretch 1 is known, and t 2 = t 3 = 0 ; therefore, we need to solve equations (22)(23) to get the other two stretches 2 , 3 , and to calculate stress t 1 using equation (21).…”

Section: Equilibrium Strain-dependent Behavior: Single Tissue Layermentioning

confidence: 99%

“…In contrast, microstructural models consider the solid phase to be a composite whose properties depend on the structure and the properties of its components [10,[14][15][16][17]. There also exist micromechanical models for fiber composites [18][19][20][21], and microstructural models for the drained elastic properties of soft tissues [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Predicting Articular Cartilage Behavior with a Non-Linear Microstructural Model

Lei¹,

Szeri²

2007

TOMECHJ

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Abstract:We report here on a non-linear poroelastic model for the mechanical response of collagenous soft tissues such as articular cartilage. The tissue consists of a porous, fibril-reinforced, hyperelastic solid, saturated with an incompressible fluid, and Darcy's law governs solid-fluid interaction. The solid matrix is characterized by the isotropic hyperfoam strain energy function and its permeability is made to depend on local strain. The fibrils are non-linear, provide tensile stiffness only, exhibit viscoelasticity and have arbitrary, three-dimensional, statistical distributions. The stress tensor in the fibril network is calculated from the constitutive law for a single fibril with the aid of the fibril distribution functions. With a specific viscoelastic fibril constitutive relationship and a three-layered cartilage construction, the model is shown to predict well strain-dependent and time-dependent behavior in unconfined compression and tension and in unconfined compression and indentation, using identical sets of material parameters.

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A Composite Micromechanical Model for Connective Tissues: Part I—Theory

Cited by 46 publications

References 0 publications

Modelling approaches for evaluating multiscale tendon mechanics

Modelling approaches for evaluating multiscale tendon mechanics

Transport of neutral solute in articular cartilage: Effect of microstructure anisotropy

Predicting Articular Cartilage Behavior with a Non-Linear Microstructural Model

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