Nonlinear system identification of soft materials based on Hilbert transform

Abstract

Characterization of broadband nonlinear properties of soft materials is time consuming and costly. This work demonstrates that transient excitation of a tester-sample system, and subsequent nonlinear dynamics-based inverse identification could provide quick and accurate estimation of nonlinear constitutive properties of soft materials. In particular, free vibration response of a system where a rigid plate shears a hyperporoviscoelastic sample is simulated to deliver time series. Then, Hilbert-Transform-based nonlinear system identification (HT-based ID) is applied to the simulated time series to retrieve constitutive properties of the sample such as linear and nonlinear shear moduli, and viscosity. In addition, bulk modulus of the sample can be uniquely identified once shear and viscosity terms are found. The technique is robust even under large viscoelastic damping. To illustrate broad applicability, the technique is successfully applied to various soft materials from cheese to gels, liver to human skin. Extension of the model to more sophisticated nonlinearities (both elastic and dissipative); desired tester configurations for reliable identification, and practical challenges before its implementation are also discussed in the paper.