Experimental investigation on the rate dependence of the equilibrium relations in aortic tissue

The stress state of a material at the end of a relaxation process is commonly assumed to be independent of the rate of deformation. However, only few experimental investigations have been conducted to directly test this hypothesis. Recently, the authors have shown the difficulty in isolating the equilibrium response of porcine thoracic aorta using continuous cyclic protocols, due to the presence of viscous effects even at low deformation rates. Alternatively, step-wise stress relaxation protocols can be used. Their application at varying transient stretch rates enables the investigation of the uniqueness of the equilibrium relation and, if extended to multiple loading-unloading cycles, it can provide insights into the interaction between dissipative phenomena. The present study aims to investigate further the rate dependence of the equilibrium relation in porcine thoracic aorta under uniaxial tensile loading conditions, applying the methodology of the previous work and addressing its limitations. To this end, we first investigated the spatial homogeneity of the deformation field with 2D-Digital Image Correlation. Cyclic step-wise stress relaxation tests were then carried out at three distinct stretch rates. In order to make proper statements about the material behavior on average, given the large sample variability, we performed each test on ten distinct samples. The collected experimental data provide further evidence of the rate dependence of the equilibrium response in both circumferential and longitudinal directions. Additionally, the mechanical results are substantiated by a thermodynamic discussion of dissipative phenomena, revealing anisotropic inelastic effects and the presence of an interaction between viscosity and damage.