On the inelastic constitutive equations of plates and shells made of foams

Within the framework of the shear deformable linear theory of plates and shells we discuss the viscoelastic models of two-dimensional (2D) constitutive equations for the stress resultants (forces and moments). The main goal of the paper focuses on the analysis of the influence of the viscoelastic bulk material behaviour, the through-thethickness structure of the plate and surface effects on the resultant governing equations. The two-dimensional constitutive equations are represented using the relaxation functions. As an example 2D constitutive equations for plates and shells made of viscoelastic foams are considered. In addition, the functionally graded structures are presented. Finally, we consider the scaling effect in the case of nano-sized foams using the theory of surface stresses