Estimation of material functions using system identification techniques

Material properties of an elastic material are characterized by the elastic modulus, which is real-valued and constant. For viscoelastic materials, such as plastics and polymers, the relationship between stress and strain is instead dynamic, and characterized by the complex-valued and frequency-dependent complex modulus. It is in this paper described how system identification techniques can be used to determine the complex modulus using strain data from wave propagation experiments on a test specimen. Modeling, derivation of estimators, and analysis of their numerical and statistical properties are included. Identifiability and experimental design are examined in some detail. Several practical examples are presented using real-world data, and a number of extensions are outlined.