Phenomenological Theory of Non-Linear Viscoelasticity

Abstract

Two three-dimensional models are introduced in order to describe the non-linear behavior and the three-dimensional cross effects occurring in the stress-deformation relations of viscoelastic materials. These models are the analogues of the so-called Maxwell and Voigt models in the classical one­ dimensional case. Non-linearities in the stress-deformation relations are classified into three categories: Elastic, viscous and geometrical ones, which are connected with the energy stored and dissipative mechanisms and the three-dimensional character of the materials, respectively. It is pointed out that we can actually separate these three non-linearities by observing the structural viscosity and the Weissenberg effect. The viscoelasticity of the so-called weakly coupled network model is briefly discussed as an example of the three-dimensional Maxwell model.