Limiting Fiber Extensibility as Parameter for Damage in Venous Wall

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—Constitutive model, damage, fiber reinforced composite, limiting fiber extensibility, preconditioning, vena cava inferior. L. Horny is with Department of Mechanics, Biomechanics and Mechatronics Faculty of Mechanical Engineering Czech Technical University in Prague, Prague, 166 07 CZE. (corresponding author to provide phone: 00420-224352690; fax: 00420-233322482; e-mail: Lukas.Horny@ fs.cvut.cz). R. Zitny is with the Department of Process Engineering Faculty of Mechanical Engineering Czech Technical University in Prague, Prague, 166 07 CZE (e-mail: Rudolf.Zitny@ fs.cvut.cz). H. Chlup is with Department of Mechanics, Biomechanics and Mechatronics Faculty of Mechanical Engineering Czech Technical University in Prague, Prague, 166 07 CZE (e-mail: Hynek.Chlup@ fs.cvut.cz). T. Adamek is with Department of Forensic Medicine of Third Faculty of Medicine Charles University in Prague and Faculty Hospital Kralovske Vinohrady, Srobarova 50, Prague, 100 34 CZE (e-mail: adamek@ fnkv.cz). M. Sara was with Department of Mechanics, Biomechanics and Mechatronics Faculty of Mechanical Engineering Czech Technical University in Prague, Prague, 166 07 CZE. He is now with Department of Cardiology Institute for Clinical and Experimental Medicine, Prague, CZE (e-mail: [email protected]). This research has been supported by Czech Ministry of Education, Youth and Sport MSM 68 40 77 00 12 and Czech Science Foundation GACR 106/08/0557.