A structural constitutive model for chemically treated planar tissues under biaxial loading

Sacks, Michael S.

doi:10.1007/s004660000175

Cited by 32 publications

(39 citation statements)

References 17 publications

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“…In a previous work, a structural approach was used that incorporated experimentally measured angular distribution of collagen fibres and an assumed isotropic form for the EXL matrix [28]. Good agreement with the experimental data was observed, supporting the basic approach.…”

Section: Introductionsupporting

confidence: 53%

A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues

2016

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Exogenous cross-linking of soft collagenous tissues is a common method for biomaterial development and medical therapies. To enable improved applications through computational methods, physically realistic constitutive models are required. Yet, despite decades of research, development and clinical use, no such model exists. In this study, we develop the first rigorous full structural model (i.e. explicitly incorporating various features of the collagen fibre architecture) for exogenously cross-linked soft tissues. This was made possible, in-part, with the use of native to cross-linked matched experimental datasets and an extension to the collagenous structural constitutive model so that the uncross-linked collagen fibre responses could be mapped to the cross-linked configuration. This allowed us to separate the effects of cross-linking from kinematic changes induced in the cross-linking process, which in turn allowed the non-fibrous tissue matrix component and the interaction effects to be identified. It was determined that the matrix could be modelled as an isotropic material using a modified Yeoh model. The most novel findings of this study were that: (i) the effective collagen fibre modulus was unaffected by cross-linking and (ii) fibre-ensemble interactions played a large role in stress development, often dominating the total tissue response (depending on the stress component and loading path considered). An important utility of the present model is its ability to separate the effects of exogenous cross-linking on the fibres from changes due to the matrix. Applications of this approach include the utilization in the design of novel chemical treatments to produce specific mechanical responses and the study of fatigue damage in bioprosthetic heart valve biomaterials.

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Section: Introductionsupporting

confidence: 53%

A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues

2016

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“…Physical mechanisms underlying stress-softening in biological membranes is more complex and actually poorly understood ( cf. [2,7,8]). Nevertheless, phenomenological modelling using twodimensional constitutive equations is possible and often very successful.…”

Section: Figmentioning

confidence: 99%

“…Its general form is only restricted by the inequality (9). However, there are experimental evidence that many biological membranes may be modelled as orthotropic ones (see [2,7,8]). This kind of an anisotropy may be characterised at each point of the membrane by a unit vector a along the preferred direction, usually called the fibre direction.…”

Section: Anisotropic Membranesmentioning

confidence: 99%

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Damage-Induced Stress-Softening Effects in Elastomeric and Biological Membranes

Kazakevičiūtė-Makovska

2002

Journal of Civil Engineering and Management

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Abstract. The two-dimensional finite strain constitutive model for membranes is presented; it incorporates stress-softening behaviour typically observed in elastomeric and natural or biologically-derived soft membranes subjected to severe deformations. It is assumed that the experimentally observed progressive degradation of a membrane stiffness under monotonous and cycling loading can macroscopically be modelled by a scalar damage variable. The evolution of this variable during the deformation process is specified by the kinetic law of damage growth, which together with the constitutive equation for the surface stress tensor and the damage criteria completely determines the presented constitutive model. It is shown that the general constitutive model can be specified for particular classes of problems under certain additional assumptions. In particular, a remarkable simplification of the model is achieved assuming that the state of strain at membrane points can be characterised by a single scalar variable, the so-called effective (equivalent) strain. This assumption is combined with the hypothesis of maximum strain according to which the stress softening in the membrane depends only on the maximum previous strain experienced during deformation history. Within these two hypotheses the progressive degradation of membrane stiffness is completely described by a softening function which determines the current value of damage variable in terms of maximum equivalent strain. Various specific forms of such a softening function as well as different definitions of the effective strain are considered.

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“…Based on incompressibility J ¼ det(F) ¼ 1, the first and second Piola-Kirchhoff stress tensors, P and S, can be determined from t as [1,[20][21][22][23] under the framework of hyperelasticity was used for FE simulation to describe the underlying mechanisms of soft biological tissues, with the commercial FE simulation software ABAQUS (6.12, Simulia, RI). The full structural model corresponding to Eq.…”

Section: Final Stress Analysismentioning

confidence: 99%

A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations

Zhang

Feng

Lee

et al. 2015

Journal of Biomechanical Engineering

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Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress-strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.

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A structural constitutive model for chemically treated planar tissues under biaxial loading

Cited by 32 publications

References 17 publications

A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues

A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues

Damage-Induced Stress-Softening Effects in Elastomeric and Biological Membranes

A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations

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