Augmented Hooke's law based on alternative stress relaxation models
The author presents a unified model (augmented Hooke's law, AHL) of material damping in the presence of linear vibrations. It is based on constitutive modelling of simple solid materials at the macroscopic level, on an internal anelastic strain variable, and on specific assumptions concerning the Helmholtz free energy. The existing discrete AHL model (by the same author) is extended to apply to materials with continuously distributed relaxation frequency spectra under isothermal conditions. Using experimentally estimated data, it is demonstrated that linear material damping may be simulated by using the enhanced AHL relaxation models. It is also shown that there exists a correspondence between each admissible linear damping model and a continuously distributed relaxation spectrum, where the latter can be computed using the Stieltjes-Perron inversion formula. Traditional relaxation time spectra are shown to be directly related to AHL relaxation amplitude distributions derived in the paper.
continuously distributed relaxation frequency spectrum
scientific article; zbMATH DE number 1506967