Inferring mechanical relaxation spectra as an ill-posed problem

Inferring a relaxation spectrum from mechanical test data was approached as a mathematically ill-posed or incorrectly formulated problem in the Tikhonov sense. A compound technique presented previously by the authors, which incorporates Tikhonov’s regularization ideas into quadratic programming, was successfully applied to the inversion of the Fredholm integral equations of the first kind encountered in the theory of linear viscoelasticity. Very good results were obtained when computer-simulated data from initially assumed unimodal and symmetrical bimodal distributions were used.