A novel approach for the fractional SLS material model experimental identification

A multi-step, iterative technique for the local non-parametric identification of the standard linear solid (SLS) material model employing fractional order time differential operators is presented. Test input data consists of a set of identified material complex modulus values estimated at different frequency values, obtained from input–output experimental measurements made on a material specimen by means of forced harmonic excitation and from experimental measurements made on the same specimen in quasi-static relaxation conditions. The proposed technique is mainly based on an algebraic procedure leading to the solution of an overdetermined system of linear equations, in order to get the optimal value of the model unknown parameters. The procedure is non-parametric, since the SLS model order is initially unknown. The optimal model size can be found by evaluating the stability properties of the solution associated to any model size and by automatically discarding computational, non-physical contributions. The identification procedure is first validated by means of numerically simulated test data from within known model examples, and then it is applied to some experimentally obtained test data associated to different materials.