Two-dimensional linear viscoelasticity of paper

Summary Linear viscoelastic properties of laboratory handsheets have been investigated from the two dimensional aspect. According to the linear theory of viscoelasticity, the behavior of transverse isotropic materials such as handsheets subjected to plane stresses is fully described by the two in-plane relaxation functions G₁₁ (t) and G₁₂ (t). In the present paper, some viscoelastic characteristic functions describing responses to in-plane deformation histories are derived from G₁₁ (t) and G₁₂ (t) determined by strip biaxial stress relaxation testing. The predicted uniaxial relaxation function curve was in good agreement with the experimental one, and the viscoelastic Poisson's ratios in uniaxial stress relaxation and in uniaxial constant strain rate extension were decrease functions of time. Effects of beating on the areal dilatation and shear relaxation functions are discussed by introducing the classical concept of relaxation spectrum.