| Planar biaxial loading offers two simultaneous independent measures of deformation, providing insight on the mechanical performance of materials to facilitate the development of suitable response functions. To investigate the response of isotropic and anisotropic biological and engineered materials the first planar biaxial testing device capable of full strain control was perfected. The manuscript begins with an overview of the fundamental concepts of large deformation theory and biaxial experimental methods used to characterize the elastic behavior of materials. This is followed by actual examples in Chapters 2 and 3 of the application of planar biaxial testing to characterize constitutive functions for particle filled and un-filled elastomers using experimental data obtained via dedicated protocols. More precisely, in Chapter 2 using unfilled natural rubber, the Valanis-Landel hypothesis is applied to proof material isotropy was retained by different material samples experiencing very different strain histories from one another. As a consequence, unfilled rubber does not suffer from deformation induced anisotropy and time dependent phenomena. In Chapter 3, change in material symmetry to carbon-filled samples experiencing different strain histories is exploited and the departure from the purely elastic behavior is highlighted through the development of a new constitutive model to characterize this phenomenon. Stress softening associated with the Mullins effect is examined, and the different degrees of stress softening due to the experimental protocols are highlighted. The two latter chapters of this thesis focus on recent experimental and theoretical work concerning the coupling of mechanical and biomedical effects. The behavior of Abdominal Aortic Aneurysm (AAA) and of fascia tissues is examined in detail. The histological analysis of the fascia tissue shows a well-organized bi-layered arrangement of undulated collagen fascicles oriented along two well-defined directions, while that of the AAA reveals large inter- and intra-patient variation and disruption of the normal ultrastructure. New stress-deformation data in uniaxial and planar biaxial tension are presented. The fundamental concepts of the nonlinear theory of elasticity are addressed and suitable strain-energy functions to describe the anisotropic response measured experimentally are formulated. |
