The Effects of Viscoelasticity on Residual Strain in Soft Biological Tissues

Residual stress is thought to play an critical role in modulating stress distributions in soft biological tissues and in maintaining the mechanobiological stress environment of cells. Residual stresses in arteries and other tissues are classically assessed through opening angle experiments, which demonstrate the continuous release of residual stresses over hours. These results are then assessed through nonlinear biomechanical models to provide estimates of the residual stresses in vivo. Although well studied, these analyses typically focus on hyperelastic material models despite significant evidence of viscoelastic phenomena over both short and long timescales. In this work, we extended the state-of-the-art Holzapfel-Ogden-Gasser model for arterial tissues using fractional viscoelasticity. Models were tuned to capture consistent levels of hysteresis observed in biaxial experiments, while also minimizing the fractional viscoelastic weighting and opening angles to correctly capture opening angle dynamics. Results suggest that a substantial portion of the human abdominal aorta is viscoelastic, but exhibits a low fractional order (i.e.more elasticly). Additionally, a significantly larger opening angle in the fully unloaded state is necessary to produce comparable hysteresis in biaxial testing. As a consequence, conventional estimates of residual stress using hyperelastic approaches over-estimate their viscoelastic counterparts by a factor of 2. Thus, a viscoelastic approach, such as illustrated in this study, in combination with an additional source of rate-controlled viscoelastic data is necessary to accurately analyze the residual stress distribution in soft biological tissues.