On the constitutive equations of viscoelastic micropolar plates and shells of differential type

Within the framework of the micropolar theory of continuum we discuss the constitutive equations of viscoelastic micropolar thin-walled structures, i.e. viscoelastic micropolar plates and shells. Starting from the linear viscoelastic micropolar continuum and using the correspondence principle of the linear viscoelasticity we extend the procedure of reduction of three-dimensional equilibrium equations of elastic shell-like solids to the case of viscoelastic behavior. We restricted ourselves by constitutive equations of differential type. In other words, we consider both 2D and 3D constitutive equations which are linear dependencies between certain set of time derivatives of stress and strain measures.