Characterization of isotropic viscoelastic moduli and compliances from 1-D tension experiments

The objective is to formulate numerical implementations of analytical and experimental protocols to determine linear viscoelastic material properties without using Poisson's ratios, as devised in [1 - 4]. The presented analysis is in terms of 3-D generalized viscoelastic constitutive relations with hereditary integrals and relaxation moduli or creep compliances. The numerical procedures are based on experimental data from photogrammetric and tensile testing instrumentations, which provide stress data in the 1-D loaded direction and strains in both longitudinal and transverse directions. Measurements and data analyses include the entire time range of starting transient and steady-state loading conditions. Experimental data conclusively demonstrates that the loading build up on several versions of INSTRON™ testing machines is sufficiently slow to render unrealistic any analyses based on instantaneous loading models. Consistency relations among the various sets of relaxation times are derived and it is shown that in an isotropic medium the only independent ones are those belonging to shear and bulk moduli. Some relaxation moduli are obtainable directly from the shear and bulk ones in the time space while other moduli and compliances can only be determined through Fourier or Laplace transforms of the former.