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.
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.