On material representation and constitutive branching in finite compressible elasticity

Storåkers, Bertil

doi:10.1016/0022-5096(86)90033-5

Cited by 150 publications

(76 citation statements)

References 10 publications

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“…We also make use of the hyperfoam strain energy function (Hill 1978, Lei andSzeri, 2007b). (Hill, 1978;Storakers, 1986) is (12) where λ 1 , λ 2 , λ 3 are the principal stretches, J = detF is the ratio of deformed to original volume at a point, while the constants μ, α and β relate to the initial aggregate modulus and Poisson's ratio through (13) The constants α and β define the nonlinearity of the material.…”

Section: Constitutive Equationsmentioning

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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Section: Constitutive Equationsmentioning

confidence: 99%

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

Zhang

Szeri

2008

Journal of Biomechanics

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“…MooneyRivlin model and Van der Waals model). The Ogden model [24,25] is a more general energetic model which is supposed to be composed of multiple Green Lagrange generalized models. These energetic models confirm the nonlinear elastic behaviour of foam undergoing large deformation.…”

Section: Symbolsmentioning

confidence: 99%

Quasi-static behavior identification of polyurethane foam using a memory integer model and the difference-forces method

Jmal

Dupuis

Aubry

2011

Journal of Cellular Plastics

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. Quasi-static behavior identification of polyurethane foam using a memory integer model and the difference-forces method. Journal of Cellular Plastics, SAGE Publications, 2011, pp.447-465 ABSTRACT: Flexible polyurethane (PU) foam is widely used in numerous comfort applications such as automotive seat cushions and mattresses. It would be interesting to design a mechanical model which describes the behaviour of this material in a series of test conditions. The present study is devoted to the modelling of the quasi-static behaviour of polyurethane foam using a memory integer model. Polyurethane foam undergoing large compressive deformation exhibits highly nonlinear elasticity and a viscoelastic behaviour. The memory integer model describes the nonlinearity in a polynomial function and the viscoelasticity through a convolution function. Uni-axial compression tests help to identify the mechanical parameters of the model. The difference between the force responses of foam in load and unload phases constitute the base element of the method used in this paper. Numerous precautions are taken into account to obtain accurate results which verify the thermodynamic conditions. Finally, the reliability as well as the limits of the memory integer model are discussed.

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“…Truly, rubber-like materials are also almost incompressible, having a very high bulk modulus or, equivalently, a value for Poisson's ratio of approximately 0)5 but hyperelastic theory has been extended to admit compressibility, giving what is known as a hyperfoam. Storakers (1986) thus developed the strain-energy functional ; as…”

Section: Hyperelasticitymentioning

confidence: 99%

AP—Animal Production Technology

Tierney¹,

Thomson

2001

Journal of Agricultural Engineering Research

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On material representation and constitutive branching in finite compressible elasticity

Cited by 150 publications

References 10 publications

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

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

Quasi-static behavior identification of polyurethane foam using a memory integer model and the difference-forces method

AP—Animal Production Technology

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