The nano-epsilon dot method for strain rate viscoelastic characterisation of soft biomaterials by spherical nano-indentation

Nano-indentation is widely used for probing the micromechanical properties of materials. Based on the indentation of surfaces using probes with a well-defined geometry, the elastic and viscoelastic constants of materials can be determined by relating indenter geometry and measured load and displacement to parameters which represent stress and deformation. Here we describe a method to derive the viscoelastic properties of soft hydrated materials at the micro-scale using constant strain rates and stress-free initial conditions. Using a new self-consistent definition of indentation stress and strain and corresponding unique depth-independent expression for indentation strain rate, the epsilon dot method, which is suitable for bulk compression testing, is transformed to nano-indentation. We demonstrate how two materials can be tested with a displacement controlled commercial nano-indentor using the nano-espilon dot method (nano-ε̇M) to give values of instantaneous and equilibrium elastic moduli and time constants with high precision. As samples are tested in stress-free initial conditions, the nano-ε̇M could be useful for characterising the micro-mechanical behaviour of soft materials such as hydrogels and biological tissues at cell length scales.