MEASURES OF DEFORMATION AND CONVECTED DERIVATIVES

Fixed spectrum quasilinear viscoelastic models are reviewed and relationships between them discussed. Measures of deformation in simple shear are obtained both from network theories (Johnson and Segalman; Phan-Thien and Tanner; Doi and Edwards) and phenomenological theories (Chang, Bloch and Tschoegl; Kaye-BKZ models modified by various authors). The effect of vorticity in the non-affine network models is considered, and preference expressed for the phenomenological nonlinear strain model for which a notional non-affine network is suggested and found to be less affected by the vorticity. The undesirable predictions of the non-affine theory, notably that for a suddenly applied shear strain of appropriate magnitude it predicts a negative shear stress, should serve as a warning against indiscriminate use of the theory and of related theories with co-rotational and similar convected derivatives. © 1979.