A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour

Peña, Estefanía; Alastrué, V.; Laborda, Alicia; Martı́nez, Miguel Ángel; Doblaré, M.

doi:10.1016/j.jbiomech.2009.10.046

Cited by 63 publications

(41 citation statements)

References 35 publications

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“…For example viscoelasticity has been observed to be important in fracture models of ventricular tissue (Forsell and Gasser, 2011). It would be possible to introduce a viscous effect to modify the permanent deformations by modifying the inelastic stress tensor S IN to incorporate non-equilibrium stresses, similar to viscoelastic models in the literature (Pena et al, 2010;Peña et al, 2008;Simo, 1987). One example of this sort of formulation would be a strain energy density function defined as where the non-equlibrium stress Q i is related to (Eqn.…”

Section: Discussionmentioning

confidence: 99%

“…Another phenomenon that occurs as a result of non-physiological loading is the presence of residual inelastic strains (or permanent set) on unloading. Both stress softening and permanent set have been observed for other soft tissues: such as skin, brain, venous and vaginal tissue (Ehret and Itskov, 2009;Franceschini et al, 2006;Peña, 2011); as well as arterial tissue (Calvo et al, 2007;Pena et al, 2010) and atherosclerotic plaque (Maher et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…At these nonphysiological loads arteries display inelastic behaviour as a result of damage to the tissue, which can be observed as a softening of the stress-strain response between loading cycles (Alastrué et al, 2008;Pena et al, 2010). Such structural changes due to tissue damage need be considered when modelling surgical interventions.…”

Section: Introductionmentioning

confidence: 99%

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An anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue

Maher

Creane

Lally

et al. 2012

Journal of the Mechanical Behavior of Biomedical Materials

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A n anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue A bstractInelastic phenomena such as softening and unrecoverable inelastic strains induced by loading have been observed experimentally in soft tissues such as arteries. These phenomena need to be accounted for in constitutive models of arterial tissue so that computational models can accurately predict the outcomes of interventional procedures such as balloon angioplasty and stenting that involve non-physiological loading of the tissue. In this study, a novel constitutive model is described that accounts for inelastic effects such as Mullins-type softening and permanent set in a fibre reinforced tissue. The evolution of inelasticity is governed by a set of internal variables. Softening is introduced through a typical continuum damage mechanics approach, while the inelastic residual strains are introduced through an additive split in the stress tensor. Numerical simulations of aorta and carotid arterial tissue subjected to uniaxial testing in the longitudinal, circumferential and axial directions reproduce the anisotropic inelastic behaviour of the tissue. Material parameters derived from best-fits to experimental data are provided to describe these inelastic effects for both aortic and carotid tissue.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue

Maher

Creane

Lally

et al. 2012

Journal of the Mechanical Behavior of Biomedical Materials

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“…In the following section the material parameters of the constitutive behavior and the damage model are fitted using experimental data (Peña et al, 2010). Vessel samples were cut comprising longitudinal and a circumferential strips in order to perform uniaxial tests.…”

Section: Parameter Identificationmentioning

confidence: 99%

“…In this approach, incompressible behavior has been considered with a deformation gradient tensor given by F = 1/ √ λe x ⊗ e x + 1/ √ λe y ⊗ e y + λe z ⊗ e z , considering strain in the direction of pulling: e θ for the circumferential sample; or e z in the longitudinal one. Following these assumptions, Table 3 shows the identified parameters for the experimental test performed by Peña et al (2010). Note that α represent the angle of the fibers with respect to the circumferential direction.…”

Section: Parameter Identificationmentioning

confidence: 99%

Anisotropic microsphere-based approach to damage in soft fibered tissue

Saéz

Alastrué²,

Peña

et al. 2011

Biomech Model Mechanobiol

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An anisotropic damage model for soft fibered tissue is presented in this paper, using a multi scale scheme and focusing on the directionally-dependent behavior of these materials. For this purpose, a microstructural or, more precisely, a microsphere-based approach is used to model the contribution of the fibers. The link between micro-structural contribution and macroscopic response is achieved by means of computational homogenization, involving numerical integration over the surface of the unit sphere. In order to deal with the distribution of the fibrils within the fiber, a von Mises probability function is incorporated, and the mechanical (phenomenological) behavior of the fibrils is defined by an exponential-type model. We will restrict ourselves to affine deformations of the network, neglecting any cross-link between fibrils and sliding between fibers and the surrounding ground matrix. Damage in the fiber bundles is introduced through a thermodynamic formulation, which is directly included in the hyperelastic model. When the fibers are stretched far from their natural state, they become damaged. The damage increases gradually due to the progressive failure of the fibrils that make up such a structure. This model has been implemented in a finite element code, and different boundary value problems are solved and

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Finite element analysis of balloon‐expandable coronary stent deployment: Influence of angioplasty balloon configuration

Martín¹,

Boyle²

2013

Numer Methods Biomed Eng

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SUMMARYToday, the majority of coronary stents are balloon-expandable and are deployed using a balloon-tipped catheter. To improve deliverability, the membrane of the angioplasty balloon is typically folded about the catheter in a pleated configuration. As such, the deployment of the angioplasty balloon is governed by the material properties of the balloon membrane, its folded configuration and its attachment to the catheter. Despite this observation, however, an optimum strategy for modelling the configuration of the angioplasty balloon in finite element studies of coronary stent deployment has not been identified, and idealised models of the angioplasty balloon are commonly employed in the literature. These idealised models often neglect complex geometrical features, such as the folded configuration of the balloon membrane and its attachment to the catheter, which may have a significant influence on the deployment of a stent. In this study, three increasingly sophisticated models of a typical semi-compliant angioplasty balloon were employed to determine the influence of angioplasty balloon configuration on the deployment of a stent. The results of this study indicate that angioplasty balloon configuration has a significant influence on both the transient behaviour of the stent and its impact on the mechanical environment of the coronary artery.

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A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour

Cited by 63 publications

References 35 publications

An anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue

An anisotropic inelastic constitutive model to describe stress softening and permanent deformation in arterial tissue

Anisotropic microsphere-based approach to damage in soft fibered tissue

Finite element analysis of balloon‐expandable coronary stent deployment: Influence of angioplasty balloon configuration

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