On the use of a spectrum-based model for linear viscoelastic materials

A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.     

Time–stress correspondence in viscoelastic materials: an equation for the stress and temperature shift factor

Stress–time correspondence principle discovered experimentally by O’Shaughnessy already in 1948 [1] is considered. Using the Doolittle formula for the viscosity as a function of free volume [2], an equation for the generalized temperature–stress shift factor a_T,σ is obtained. An equation for the stress-dependent shift factor a_σ follows as a special case. The equation for the temperature shift factor a_T already derived in 1985 [3] and successfully used since also follows from the a_T,σ formula. Received: 26 April 2000 / Reviewed and accepted: 17 May 2000