ANISOTROPIC STRESS-STRAIN RELATIONS AND COMPLEX MODULI OF A VISCOELASTIC COMPOSITE WITH ALIGNED SPHEROIDAL INCLUSIONS

By means of a micromechanical theory this study seeks to uncover the i nfluence of the inclusion shape on the stress-strain behavior and comp lex moduli of a class of composites containing aligned spheroidal incl usions. Before we set out the analysis it is shown first that, by comb ining two Maxwell or two Voigt constituents, the composite as whole is generally not of the Maxwell or the Voigt type; however, under the co nditions that the Poisson's ratio of both phases remains constant and the ratios of their shear modulus to shear viscosity are equal, a tran sversely isotropic Maxwell or Voigt composite can be constructed. The strain-rate sensitivity of the stress-strain behavior is then examined for a system containing elastic inclusions and a viscoelastic matrix, at various inclusion shapes. It is found that the stress-strain curve s are strongly dependent upon the applied strain rate in most cases, a nd that the precise increase of flow stress with increasing strain rat e is intimately related to the inclusion shape and loading mode. Excep t for the axial tension with continuous fibers and the transverse tens ion, shear, and biaxial plane-strain with aligned discs, most stress-s train curves exhibit a saturation stress under a constant strain-rate loading. The real and imaginary parts of the five complex moduli are s ubsequently examined for their dependence upon the inclusion shape and concentration, and loading frequency. It is observed that the real pa rts of the moduli tend to increase with increasing frequency, and even tually approach their corresponding elastic moduli. The imaginary part s of the moduli may actually increase with increasing amount of elasti c inclusions, albeit droping to zero again as the entire composite tur ns into inclusions. Their dependence on the frequency starts out at ze ro initially and again returns to zero as the frequency approaches inf inity, but in the intermediate range multiple maxima are experienced w ith all inclusion shapes.