Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Abstract In this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from Cosserat material. The dimensional reduction procedure extends methods of classical shell theory case shells. Starting three-dimensional parent model, perform integration over thickness and obtain consistent model order $$ O(h^5) O ( h 5 ) with respect h . We form strain energy density (Cosserat) shells, in which coefficients are expressed terms elasticity constants depend on initial curvature shell. obtained is compared other previous variants literature, advantages our discussed.