Unbiased retrieval of frequency-dependent mechanical properties from noisy time-dependent signals

The mechanical response of materials to dynamic loading is often quantified by the frequency-dependent complex modulus. Probing materials directly in the frequency domain faces technical challenges such as a limited range of frequencies, long measurement times, or small sample sizes. Furthermore, many biological samples, such as cells or tissues, can change their properties upon repetitive probing at different frequencies. Therefore, it is common practice to extract the material properties by fitting predefined mechanical models to measurements performed in the time domain. This practice, however, precludes the probing of unique and yet unexplored material properties. In this report, we demonstrate that the frequency-dependent complex modulus can be robustly retrieved in a model-independent manner directly from time-dependent stress-strain measurements. While applying a rolling average eliminates random noise and leads to a reliable complex modulus in the lower frequency range, a Fourier transform with a complex frequency helps to recover the material properties at high frequencies. Finally, by properly designing the probing procedure, the recovery of reliable mechanical properties can be extended to an even wider frequency range. Our approach can be used with many state-of-the-art experimental methods to interrogate the mechanical properties of biological and other complex materials.