Micropolar shells with thickness inflation and independent micro‐rotations

Abstract

Starting from constrained three‐dimensional Cosserat elasticity and in a total Lagrangian framework, we derive and discuss a hierarchy of static non‐linear micropolar shell models in which the thickness can stretch, and the independence of the micro‐rotation on the macro‐rotation is not limited to the drilling degree of freedom as in the classical six‐parameter theory. If the thickness stretch is considered, unconstrained quaternions allow a singularity‐free, non redundant and rational parametrization of the strain measures. Emphasis is placed in the discussion of the differences between curvatures, wryness and director deformation strains.