Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling

Alastrué, V.; Martı́nez, Miguel Ángel; Doblaré, M.; Menzel, Andreas

doi:10.1016/j.jmps.2008.09.005

Cited by 116 publications

(134 citation statements)

References 65 publications

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“…The unit vectors can be expressed in terms of the spherical coordinates θ ∈ [0, π) and φ ∈ [0, 2π) as r = sin(θ)cos(φ)e x +sin(θ)sin(φ)e y +cos(φ)e z with {e x , e y , e z } the reference Cartesian system. Previous works (Bažant and Oh, 1986;Alastrué et al, 2009a;Ehret et al, 2010) have used used different schemes and compared different number of integration directions for isotropic and anisotropic functions and, in view of the results therein, 368 directions (Heo and Xu, 2001) will be used in all the problems simulated in this work. This has been demonstrated to provide sufficiently accurate results for relatively highly anisotropic materials (see Alastrué et al (2009a)).…”

Section: Microsphere Based Modelmentioning

confidence: 99%

“…Note that a could be oriented in any direction of the space leading to a mismatch angle θ = arccos(r · a). A π-periodic von Mises orientation density function (ODF) (18) has been adopted in this work to take into account the fibrils dispersion (Alastrué et al, 2009a) where the concentration parameter b ∈ R + is a measure of the anisotropy. b → 0 represents an isotropic material, and b → ∞ a transversally isotropic one.…”

Section: Materials Behaviormentioning

confidence: 99%

“…In Alastrué et al (2009a) a comparison between this phenomenological function and the worm-like chain model in the microsphere framework is discussed. Note that, although the integration directions are mathematically identified with the numerical integration scheme, they can also be physically associated to the contribution of the fibrils around each integration direction along its related area.…”

Section: Materials Behaviormentioning

confidence: 99%

“…3a, b and c were obtained using 368 integration directions. Moreover, we present Online Resource 1, 2 and 3 (reduction factor, stress without damage and with damage respectively) to show the evolution of the micro-structure along the load in the stereographic projection (see Miehe et al (2004); Alastrué et al (2009a)), for the parameters of Set 1. Variation of parameter a.…”

Section: Micro Mechanics Of the Tissuementioning

confidence: 99%

“…Caner and Carol (2006) were the first to apply this approach to soft biological tissues. Later Alastrué et al (2009a) focused on the anisotropy of the material.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Microsphere Based Modelmentioning

confidence: 99%

Section: Materials Behaviormentioning

confidence: 99%

Section: Materials Behaviormentioning

confidence: 99%

Section: Micro Mechanics Of the Tissuementioning

confidence: 99%

“…Caner and Carol (2006) were the first to apply this approach to soft biological tissues. Later Alastrué et al (2009a) focused on the anisotropy of the material.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Anisotropic microsphere-based approach to damage in soft fibered tissue

Saéz

Alastrué²,

Peña

et al. 2011

Biomech Model Mechanobiol

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Implementing cell contractility in filament‐based cytoskeletal models

Fallqvist

2016

Cytoskeleton

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Cells are known to respond over time to mechanical stimuli, even actively generating force at longer times. In this paper, a microstructural filament-based cytoskeletal network model is extended to incorporate this active response, and a computational study to assess the influence on relaxation behaviour was performed. The incorporation of an active response was achieved by including a strain energy function of contractile activity from the cross-linked actin filaments. A four-state chemical model and strain energy function was adopted, and generalisation to three dimensions and the macroscopic deformation field was performed by integration over the unit sphere. Computational results in MATLAB and ABAQUS/Explicit indicated an active cellular response over various time-scales, dependent on contractile parameters. Important features such as force generation and increasing cell stiffness due to prestress are qualitatively predicted. The work in this paper can easily be extended to encompass other filament-based cytoskeletal models as well.

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Computational Continuum Biomechanics with Application to Swelling Media and Growth Phenomena

2009

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Biological tissues, no matter if soft or hard tissues are concerned, basically consist of a solid matrix saturated by an interstitial fluid, which is composed of a liquid solvent and various dissolved solutes. In case of vascular tissues, the blood system including the arteries, the capillary system and the veins has to be added. Based on the complex geometric and biophysical nature ofbiological systems, a biomechanical description is based on a macroscopic, continuum‐mechanical approach proceeding from homogenised microstructures rather than on a full microscopic investigation. Consequently, the present article provides a continuum‐biomechanical approach for the description of biological tissues. This includes the well‐founded framework of the Theory of Porous Media (TPM), which can be seen as an extension of the classical Theory of Mixtures (TM) towards immiscible materials. Based on this approach, which easily can be extended by electro‐chemical information, swelling tissues like the intervertebral disc and growth phenomena like avascular tumour growth and muscle stimulation as the basis of any motion of biological systems can be described. However, as a result of page limitations, the article excludes the incorporation of the blood system into the present modelling and simulation examples as well as the description of any muscle stimulation (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling

Cited by 116 publications

References 65 publications

Anisotropic microsphere-based approach to damage in soft fibered tissue

Anisotropic microsphere-based approach to damage in soft fibered tissue

Implementing cell contractility in filament‐based cytoskeletal models

Computational Continuum Biomechanics with Application to Swelling Media and Growth Phenomena

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