Ivan D. Breslavsky

Viscoelastic Characterization of Woven Dacron for Aortic Grafts by using Direction-Dependent Quasi-Linear Viscoelasticity

In case of direction-dependent viscoelasticity, a simplified formulation of the three-dimensional quasi-linear viscoelasticity has been obtained manipulating the original Fung equation. The experimental characterization of the static hyperelastic behaviour, the relaxation, the dynamic modulus and the loss factor of woven Dacron from a commercial aortic prosthesis has been performed. An 11% difference of the reduced relaxation (after infinite time) between axial and circumferential directions has been observed for the woven Dacron. A very large increase in stiffness is obtained in case of harmonic loading with respect to the static loading. These findings are particularly relevant for dynamic modelling of currently used aortic grafts.

Static and Dynamic Behavior of Circular Cylindrical Shell Made of Hyperelastic Arterial Material

Static and dynamic responses of a circular cylindrical shell made of hyperelastic arterial material are investigated. The material is modeled as a combination of Neo-Hookean and Fung hyperelastic materials. Two pressure loads are implemented: distributed radial force and deformation-dependent pressure. The static responses of the shell under these two different loads differ essentially at moderate strains, while the behavior is similar for small loads. The main difference is in the axial displacements that are much larger under distributed radial forces. Free and forced vibrations around pre-loaded configurations are analyzed. In both cases the nonlinearity of the single-mode (driven mode) response of the pre-loaded shell is quite weak but a resonant regime with co-existing driven and companion modes is found with more complicated nonlinear dynamics.

Nonlinear model of human descending thoracic aortic segments with residual stresses

The nonlinear static deformation of human descending thoracic aortic segments is investigated. The aorta segments are modeled as straight axisymmetric circular cylindrical shells with three hyperelastic anisotropic layers and residual stresses by using an advanced nonlinear shell theory with higher-order thickness deformation not available in commercial finite element codes. The residual stresses are evaluated in the closed configuration in an original way making use of the multiplicative decomposition. The model was initially validated through comparison with published numerical and experimental data for artery and aorta segments. Then, two different cases of healthy thoracic descending aorta segments were numerically simulated. Material data and residual stresses used in the models came from published layer-specific experiments for human aortas. The material model adopted in the study is the mechanically based Gasser–Ogden–Holzapfel, which takes into account collagen fiber dispersion. Numerical results present a difference between systolic and diastolic inner radii close to the data available in literature from in vivo measurements for the corresponding age groups. Constant length of the aortic segment between systolic and diastolic pressures was obtained for the material model that takes the dispersion of the fiber orientations into account.

Large Amplitude Vibrations of Thin Hyperelastic Plates: Neo-Hookean Model

Static deflection and large amplitude vibrations of a rubber plate are analyzed. Both the geometrical and physical (material) nonlinearities are taken into account. The properties of the plate hyperelastic material are described by the Neo-Hookean law. A method for building a local model, which approximates the plate behavior around a deformed configuration, is proposed. This local model takes the form of a system of ordinary differential equations with quadratic and cubic nonlinearities. The results obtained with the help of this local model are compared to the solution of the exact model, and are found to be accurate. The difference between the model retaining both physical and geometrical non-inearities and a model with only geometrical nonlinearities is also analyzed. It is found that influence of physically induced nonlinearities at moderate strains is significant.Copyright