Various kinds of two-dimensional rheological models

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Abstract
Two-dimensional rheological models consisting of two-dimensional elastic, viscous, and plastic elements are introduced in order to represent more closely the real rheological behavior of various isotropic and orthotropic viscoelastic, elastoplastic, viscoplastic, and elastoviscoplastic bodies in the plane-stress or plane-strain state, respectively. These models represent schematically the unit area of a body and consist of plane elastic, viscous, and plastic regions with rectangular straight boundaries lying in the principal direction of orthotropy. The two-dimensional rheological models may be considered either from the phenomenological or from the structural point of view. They may also represent rheological structures with variously oriented multiphase systems having elastic, viscous, and plastic properties. The configuration of such models may correspond to the rheological nonhomogeneity of bodies and to both kinds of orthotropy arising either from the orthotropic properties of elastic, plastic, and viscous phases or from various configurations of phases. These models may also represent nonsymmetrical shear effects which are analogous to those arising in elastic Cosserat media. The main differences between the presented two-dimensional models and the usual rheological models, which are one-dimensional, consist of the possibilities of representing directly two-dimensional rheological behavior, the anisotropy of rheological processes, and nonsymmetrical shear effects in rheological bodies.

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