Tomas Adamek

Publications

2 Limiting Fiber Extensibility as Parameter for Damage in Venous Wall

Authors: Lukas Horny, Rudolf Zitny, Hynek Chlup, Tomas Adamek, Michal Sara

Abstract:

An inflation–extension test with human vena cava inferior was performed with the aim to fit a material model. The vein was modeled as a thick–walled tube loaded by internal pressure and axial force. The material was assumed to be an incompressible hyperelastic fiber reinforced continuum. Fibers are supposed to be arranged in two families of anti–symmetric helices. Considered anisotropy corresponds to local orthotropy. Used strain energy density function was based on a concept of limiting strain extensibility. The pressurization was comprised by four pre–cycles under physiological venous loading (0 – 4kPa) and four cycles under nonphysiological loading (0 – 21kPa). Each overloading cycle was performed with different value of axial weight. Overloading data were used in regression analysis to fit material model. Considered model did not fit experimental data so good. Especially predictions of axial force failed. It was hypothesized that due to nonphysiological values of loading pressure and different values of axial weight the material was not preconditioned enough and some damage occurred inside the wall. A limiting fiber extensibility parameter Jm was assumed to be in relation to supposed damage. Each of overloading cycles was fitted separately with different values of Jm. Other parameters were held the same. This approach turned out to be successful. Variable value of Jm can describe changes in the axial force – axial stretch response and satisfy pressure – radius dependence simultaneously.

Keywords: Damage, constitutive model, preconditioning, fiber reinforcedcomposite, limiting fiber extensibility, vena cavainferior

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1 Constitutive Equations for Human Saphenous Vein Coronary Artery Bypass Graft

Authors: Hynek Chlup, Lukas Horny, Rudolf Zitny, Svatava Konvickova, Tomas Adamek

Abstract:

Coronary artery bypass grafts (CABG) are widely studied with respect to hemodynamic conditions which play important role in presence of a restenosis. However, papers which concern with constitutive modeling of CABG are lacking in the literature. The purpose of this study is to find a constitutive model for CABG tissue. A sample of the CABG obtained within an autopsy underwent an inflation–extension test. Displacements were recoredered by CCD cameras and subsequently evaluated by digital image correlation. Pressure – radius and axial force – elongation data were used to fit material model. The tissue was modeled as onelayered composite reinforced by two families of helical fibers. The material is assumed to be locally orthotropic, nonlinear, incompressible and hyperelastic. Material parameters are estimated for two strain energy functions (SEF). The first is classical exponential. The second SEF is logarithmic which allows interpretation by means of limiting (finite) strain extensibility. Presented material parameters are estimated by optimization based on radial and axial equilibrium equation in a thick-walled tube. Both material models fit experimental data successfully. The exponential model fits significantly better relationship between axial force and axial strain than logarithmic one.

Keywords: digital image correlation, constitutive model, coronary artery bypass graft, fiber reinforced composite, inflation test, saphenous vein

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