An intermediate model method for obtaining a discrete relaxation spectrum from creep data

• Published in: Rheologica acta Vol. 36; no. 4; pp. 472 - 482
• Main Authors: Dooling, Paul J., Buckley, C. Paul, Hinduja, Srichand
• Format: Journal Article
• Language: English
• Published: Berlin Springer 01.07.1997; Springer Nature B.V
• Subjects: Applied sciences; Exact sciences and technology; Finite element method; Mathematical analysis; Organic polymers; Physicochemistry of polymers; Polymethyl methacrylate; Polynomials; Properties and characterization; Rheology and viscoelasticity; Stress relaxation; Viscoelasticity; Viscoelasticity; Rheological model; Stress relaxation; Creep; Relaxation spectrum; Theoretical study; Polymer; Rheological properties
• ISSN: 0035-4511; 1435-1528
• DOI: 10.1007/BF00396332

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.