Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates

TL;DR

This study demonstrates that biological and synthetic viscoelastic materials achieve maximum energy efficiency when loaded and unloaded at equal rates, with efficiency decreasing as the rate asymmetry increases, supported by experimental and modeling results.

Contribution

It reveals the importance of loading-unloading symmetry for energy efficiency in viscoelastic materials, combining experimental measurements with a generalized Maxwell model.

Findings

Efficiency peaks at symmetric loading and unloading rates.

Efficiency decreases with increasing rate asymmetry.

A Maxwell model captures the experimental trends.

Abstract

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.