TWO-DIMENSIONAL RHEOLOGICAL MODELS FOR SIMPLE AND FIBRE-REINFORCED VISCOELASTIC MATERIALS.

Models are introduced for orthotropic simple and fiber-reinforced viscoelastic materials in order to represent more closely the real viscoelastic behavior in the plane-stress and in the plane-strain states. The unit representative area of these models is divided into two-dimensional elastic and viscous regions with perpendicular boundaries lying in the principal directions of orthotropy. Contrary to usual rheological models, which are one-dimensional, the two-dimensional models represent directly the two-dimensional rheological behavior, the orthotropy of rheological processes, effects of internal cohesion as well as those of reinforcement by elastic fibers, the rheological nonhomogeneity with various configurations of elastic and viscous phases and nonsymmetrical shear effects which are analogous to those in elastic Cosserat media. Based on the two-dimensional models, expressions are presented for both kinds of orthotropy arising either from orthotropic properties of elastic and viscous phases, or from various configurations of these phases and of the reinforcement. Two-dimensional rheological models give a rational basis for the realistic union of phenomenological and structural points of view.