On the experimental identification of equilibrium relations and the separation of inelastic effects in soft biological tissues

The mechanical characterization of vascular tissues has been mainly focused on the measurement of elastic properties, while the investigation of inelastic effects has received comparatively little attention. Even the relatively simple, purely elastic description of the material behavior requires an appropriate set of experimental data that cannot be easily isolated using standard testing procedures. The presence of viscous and damage-related phenomena poses some challenges in the definition of appropriate testing protocols capable of identifying an equilibrium response, which in general does not solely represent the elastic material behavior. The primary goal of the present study is therefore to devise an experimental procedure that can distinguish and evaluate the different constitutive phenomena separately. To this end, we apply methodologies widely used in the mechanical testing of rubber-like materials and transfer them to the field of biomechanics. We performed two types of experiments in equibiaxial extension on porcine thoracic aorta: a continuous cyclic test followed by a single-step relaxation test and a cyclic multi-step relaxation test, each at varying stretch rates. We demonstrate that the approximation of quasi-stationarity through continuous testing at slow rates is inadequate for the identification of an equilibrium relation. Alternatively, a step-wise protocol allows for the separation of equilibrium and viscous effects. This motivates a thermodynamic discussion of the experimental results in terms of energy dissipation and a closer look at the interplay of inelastic phenomena.