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

• Published in: Mechanics of time-dependent materials Vol. 10; no. 3; pp. 215 - 228
• Main Author: SULLIVAN, R. W
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.09.2006; Springer Nature B.V
• Subjects: Condensed matter: structure, mechanical and thermal properties; Creep; Creep (materials); Exact sciences and technology; Exact solutions; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Integral equations; Laplace transforms; Material properties; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Modulus of elasticity; Physics; Poisson's ratio; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Tensile tests; Time dependence; Viscoelastic materials; Viscoelasticity; Elastic constant; Constitutive equation; Viscoelasticity; Creep; Deformation modulus; Epoxy resin; Polymer; Constitutive model; Elastic-Viscoelastic Correspondence Principle; Potential function; Correspondence principle; Experimental study; Modeling; Tension test; Exact solution; Poisson ratio; Integral equation; Laplace transformation; Volterra integral equation; Spectrum function; Volterra equation; Epoxy polymer
• ISSN: 1385-2000; 1573-2738
• DOI: 10.1007/s11043-006-9019-9

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.