Planar Biaxial Extension Research Articles

A constitutive description of the anisotropic response of the fascia lata

In this paper we propose a constitutive model to analyze in-plane extension of goat fascia lata. We first perform a histological analysis of the fascia that shows a well-organized bi-layered arrangement of undulated collagen fascicles oriented along two well defined directions. To develop a model consistent with the tissue structure we identify the absolute and relative thickness of each layer and the orientation of the preferred directions. New data are presented showing the mechanical response in uniaxial and planar biaxial extension. The paper proposes a constitutive relation to describe the mechanical response. We provide a summary of the main ingredients of the nonlinear theory of elasticity and introduce a suitable strain-energy function to describe the anisotropic response of the fascia. We validate the model by showing good fit of the numerical results and the experimental data. Comments are included about differences and analogies between goat fascia lata and the human iliotibial band.

An Experimentally Derived Stress Resultant Shell Model for Heart Valve Dynamic Simulations

In order to achieve a more realistic and accurate computational simulation of native and bioprosthetic heart valve dynamics, a finite shell element model was developed. Experimentally derived and uncoupled in-plane and bending behaviors were implemented into a fully nonlinear stress resultant shell element. Validation studies compared the planar biaxial extension and three-point bending simulations to the experimental data and demonstrated excellent fidelity. Dynamic simulations of a pericardial bioprosthetic heart valve with the developed shell element model showed significant differences in the deformation characteristics compared to the simulation with an assumed isotropic bending model. The new finite shell element model developed in the present study can also incorporate various types of constitutive models and is expected to help us to understand the complex dynamics of native and bioprosthetic heart valve function in physiological and pathological conditions.

Biaxial Deformation of a Polymer Network Measured via Deuteron Quadrupolar Interactions

Deuterium quadrupolar interactions have been used to measure chain ordering for poly(dimethylsiloxane) elastomers under planar biaxial extension. The NMR spectral splittings obtained from two different deuterium-labeled probe molecules diffusing within the network were measured as a function of extension ratio λ and the orientation of the principal axis of deformation with respect to the magnetic field. Theoretical predictions based on a phantom Gaussian chain model are compared with the data and good agreement is found. The implications of axial asymmetry at various levels of the probe molecule motional hierarchy are discussed. For rapidly diffusing probe molecules, only the highest level in the hierarchy influences the observed quadrupole interaction symmetry, and the true distribution of chain segment directors is measured.