A new load-controlled testing method for viscoelastic characterisation through stress-rate measurements

This paper introduces a new load-controlled viscoelastic characterization approach termed the sigma-dot method (σ̇M), based on unconfined compression tests performed at multiple constant stress-rates and global fitting of the resulting strain-time curves to a Generalised Voigt model. The method uses physically implementable ramp stress inputs (rather than idealized step inputs), and allows viscoelastic parameters (instantaneous modulus, equilibrium modulus, characteristic retardation time) to be derived without requiring a priori definition of the linear viscoelastic region. The σ̇M was demonstrated on PDMS elastomers (10:1 and 30:1 ratios) and hydroxyapatite/gelatin (HA/Gel) composite hydrogels using both a universal testing machine and the CellScale MechanoCulture TR (MCTR) bioreactor; derived parameters were not significantly different between devices, indicating instrument-independence. The authors also compared σ̇M against traditional creep testing performed on the MCTR and found broadly comparable elastic moduli but method-dependent retardation time estimates, highlighting practical differences between ramp- and step-based approaches for time-dependent materials.