NUMERICAL INTERCONVERSION OF LINEAR VISCOELASTIC MATERIAL FUNCTIONS

Calculation of the relaxation modulus in a manner which addresses the ill-posed nature of the problem specifically in the terminal and plate au regions is essential in order to subsequently determine a molecular weight distribution. A novel method to effect this result is demonstr ated. The relaxation modulus is modeled as a discrete N element Maxwel l (N much greater than 1) line spectrum. The method incorporates addit ional independent theological data into a constrained linear regressio n with regularization. Specifically, the zero shear viscosity and the steady-state recoverable compliance are used to impose integral moment equality constraints on the calculated relaxation modulus. Moment con straints necessarily generate a self-consistent conversion. All moduli are further constrained to be positive. The numerical method is robus t and capable of extracting meaningful relaxation spectra from severel y error infected and/or incomplete data sets. Imposing moment constrai nts dramatically reduces the error and dispersion of the calculated re laxation and retardation spectra in the terminal and plateau regions. Analytic conversion of the relaxation modulus to the compliance functi on is demonstrated through knowledge of the root sequence for a discre te Maxwell model.