A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids

Horgan, Cornelius O.; Saccomandi, Giuseppe

doi:10.1016/j.jmps.2005.04.004

Cited by 115 publications

(106 citation statements)

References 28 publications

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“…where the term W iso represents the isotropic matrix and W fib accounts for the directional reinforcements (Qiu and Pence, 1997;Holzapfel et al, 2000;Merodio and Ogden, 2005;Horgan and Saccomandi, 2005;Dorfmann et al, 2007Dorfmann et al, , 2008. Based on the structure of fascia lata outlined in Section 3.1 and following the simplification suggested by Holzapfel et al (2000), we reduce the number of invariants and consider the form…”

Section: Basic Equationsmentioning

confidence: 99%

A constitutive description of the anisotropic response of the fascia lata

Pancheri

Eng

Lieberman

et al. 2014

Journal of the Mechanical Behavior of Biomedical Materials

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In this paper we propose a constitutive model to analyze in-plane extension of the fascia lata in goats. We first perform a histological analysis of the fascia that shows a well-organized bi-layered arrangement of undulated collagen fascicles oriented along two well defined directions. To develop a model consistent with the tissue structure we identify the absolute and relative thickness of each layer and the orientation of the preferred directions. New data are presented showing the mechanical response in uniaxial and planar biaxial extension. The main part of the paper focuses on a constitutive theory to describe the mechanical response. We provide a summary of the main ingredients of the nonlinear theory of elasticity and introduce a suitable strain-energy function to describe the anisotropic response of the fascia. In the final part of the paper we validate the model by showing good agreement of the numerical results and the experimental data.

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Section: Basic Equationsmentioning

confidence: 99%

A constitutive description of the anisotropic response of the fascia lata

Pancheri

Eng

Lieberman

et al. 2014

Journal of the Mechanical Behavior of Biomedical Materials

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“…In this paper, we will only be concerned with the range 0 ≤ q ≤ p/2 so that I 4 ≥ 1 and so the fibres are always in extension. The constitutive law for the Cauchy stress T for incompressible transversely isotropic hyperelastic materials with W = W (I 1 , I 2 , I 4 , I 5 ) is given by, for example, Ogden (2001), Horgan & Saccomandi (2005) and Holzapfel & Ogden (2009a) as…”

Section: Simple Shear Of Fibre-reinforced Elastic Materialsmentioning

confidence: 99%

“…The model (3.3) with quadratic nonlinearity in I 4 was proposed initially by Polignone & Horgan (1993a,b) Horgan & Saccomandi (2005) that reflect the stretch-induced stiffening of collagen fibres as they are loaded. One of the simplest of these models is given by…”

Section: Shear Stress Response For Soft Tissuesmentioning

confidence: 99%

“…In order for the logarithm function in the model (3.4) to be well defined, it is required that the deformation satisfy the constraint (3.6) where the fibre stretch l is defined in equation (2.6). As is discussed by Horgan & Saccomandi (2005), the model (3.4) was motivated by the Gent model (Gent 1996) of rubber elasticity that reflects limiting chain extensibility of the molecular chains; see e.g. Horgan & Saccomandi (2002, 2006 for a review of such models and their applications to strain-stiffening rubber-like and biological tissues.…”

Section: Shear Stress Response For Soft Tissuesmentioning

confidence: 99%

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Simple shearing of soft biological tissues

Horgan

Murphy

2010

Proc. R. Soc. A.

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Shearing is induced in soft tissues in numerous physiological settings. The limited experimental data available suggest that a severe strain-stiffening effect occurs in the shear stress when soft biological tissues are subjected to simple shear in certain directions. This occurs at relatively small amounts of shear (when compared with the simple shear of rubbers). This effect is modelled within the framework of nonlinear elasticity by consideration of a class of incompressible anisotropic materials. Owing to the large stresses generated for relatively small amounts of shear, particular care must be exercised in order to maintain a homogeneous deformation state in the bulk of the specimen. The results obtained are relevant to the development of accurate shear test protocols for the determination of constitutive properties of soft tissues. It is also demonstrated that there is a fundamental ambiguity in determining the normal stresses in simple shear when soft tissues are modelled as incompressible hyperelastic materials owing to the arbitrary nature of the hydrostatic pressure term. Two physically well-motivated approaches to determining the pressure are presented here, and the resulting hydrostatic stresses are compared and contrasted. The possible generation of cavitational damage owing to critical hydrostatic stress levels is briefly discussed.

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“…Hence, two families of fibers have to be considered to give a better comparison with in vivo results for soft tissues. Also, the more realistic models of fiber reinforcements (such as the one proposed by Horgan and Saccomandi (2005) and by ) must be incorporated in the present study, to identify with a greater precision the range of parameters for which strange behaviors may occur.…”

Section: Discussionmentioning

confidence: 99%

Creep, Recovery, and Waves in a Nonlinear Fiber-Reinforced Viscoelastic Solid

Destrade¹,

Saccomandi²

2007

SIAM J. Appl. Math.

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We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the equation governing rectilinear shear motion in the plane of the fiber reinforcement; it is a nonlinear partial differential equation for the shear strain. Specializing the equation to the quasistatic processes of creep and recovery, we find that usual (exponential-like) time growth and decay exist in general, but that for certain ranges of values for the material parameters and for the angle between the shearing direction and the fiber direction, some anomalous behaviors emerge. These include persistence of a non-zero strain in the recovery experiment, strain growth in recovery, strain decay in creep, disappearance of the solution after a finite time, and similar odd comportments. For the full dynamical equation of motion, we find kink (traveling wave) solutions which cannot reach their assigned asymptotic limit.

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A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids

Cited by 115 publications

References 28 publications

A constitutive description of the anisotropic response of the fascia lata

A constitutive description of the anisotropic response of the fascia lata

Simple shearing of soft biological tissues

Creep, Recovery, and Waves in a Nonlinear Fiber-Reinforced Viscoelastic Solid

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