Viscoelastic interpretation of AFM nanoindentation for predicting nanoscale stiffness in soft biomaterials

Precise characterization of biomechanical properties at the micro- and nanoscale is essential for developing biomaterials for tissue engineering, regenerative medicine, and drug delivery. Traditional bulk techniques fail to capture the local mechanical heterogeneities of soft materials such as hydrogels, polymers, and biological tissues. Atomic force microscopy (AFM) nanoindentation enables high-resolution stiffness mapping under near- physiological conditions; however, the standard Hertz model assumes purely elastic behavior, overlooking the viscoelastic nature of most biological systems. This study relies on established viscoelastic models to better interpret rate-dependent mechanical responses in AFM nanoindentation experiments. Force-displacement curves were analyzed to separate elastic and viscous contributions and account for the effect of indentation speed. Experiments on four hydrogels (alginate, Cellink-RGD, GelMA, GelMA A) revealed nonlinear stiffening trends with increasing indentation rate, associated with polymer network dynamics and crosslinking density. Additional analyses on erythrocytes and zona pellucida confirmed their complex viscoelastic responses, highlighting physiological and pathological differences in cells and species-specific behavior in reproductive structures. Our approach provides a simple and effective method to predict nanoscale stiffness as a function of indentation rate, improving accuracy in nanomechanical characterization and supporting the design of advanced bioengineered constructs.