  Biological springs can be used in nature for energy conservation and
ultra-fast motion. The loading and unloading rates of elastic materials can
play an important role in determining how the properties of these springs
affect movements. We investigate the mechanical energy efficiency of biological
springs (American bullfrog plantaris tendons and guinea fowl lateral
gastrocnemius tendons) and synthetic elastomers. We measure these materials
under symmetric rates (equal loading and unloading durations) and asymmetric
rates (unequal loading and unloading durations) using novel dynamic mechanical
analysis measurements. We find that mechanical efficiency is highest at
symmetric rates and significantly decreases with a larger degree of asymmetry.
A generalized 1D Maxwell model with no fitting parameters captures the
experimental results based on the independently-characterized linear
viscoelastic properties of the materials. The model further shows that a
broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry
on efficiency. Overall, our study provides valuable insights into the interplay
between material properties and unloading dynamics in both biological and
synthetic elastic systems.
