Nonlinear micropolar shells: theory and applications

The general static and dynamic theory of micropolar shells undergoing finite deformations is presented. The micropolar shell, or the Cosserat shell, is the material surface each point of which has six degrees of freedom of the rigid body. The shell kinematics is determined by the displacement vector and the rotation tensor as two independent field variables describing the shell deformation. Some formulations of boundary value problems of the nonlinear statics of elastic micropolar shells are given and their variational statements are formulated. A new definition of the local symmetry group of the micropolar elastic shell is proposed. An analogue of the Noll rule is established. Special subgroups and corresponding constitutive equations are given. Applications of the micropolar shell theory to mechanical modelling of biological or lipidic membranes and other nanostructures, such as nanofilms, nanotubes and nanocrystal arrays grown on substrate, are briefly outlined.