Analytical and experimental probabilistic constitutive relation characterizations, part I: linear viscoelastic media

Abstract

Analytical and experimental deterministic and statistical protocols are formulated for the constitutive linear relations that characterize viscoelastic media. These proceedings are achieved in the real time space in terms of moduli and/or compliances without any inclusion of viscoelastic Poisson's ratios.
Independent experimental determinations of linear viscoelastic material properties of three distinct polymers include single conditions of creep, relaxation, and constant strain and extensometer time rates - except for starting transients.

Statistical dynamic data for the instantaneous modulus and quasi-static data for relaxation moduli are analytically and numerically merged to produce relaxation modulus and creep compliance expressions containing properly evaluated parameters. The combined actual starting load and displacement transient and subsequent time histories are tracked, recorded and incorporated into the analyses to produce moduli and compliances based on actual continuous loading-time sequences. Prony series and generalized continuous relaxation time spectral modulus and compliance functions are derived and discussed.
Four distinct probability models of material properties and temperature are postulated and evaluated for two sets of real viscoelastic materials (polymers). Statistical sufficiency considerations are included in the analyses.