A New Method for Analysing Large Elasto-Plastic Deformations of a Thin Cosserat Shell

Abstract

One of the best approaches for modelling the large deformation of shells is the Cosserat surface; however, the finite-element implementation of this model suffers from membrane and shear locking, especially for very thin shells. If the director vector is constrained to remain perpendicular to the mid-surface, during deformation, locking will be prevented. This constraint is in fact a limiting analysis of the Cosserat theory in which Kirchhoff's hypothesis is enforced. This has been considered for the first time. Simo's plastic approach is modified to implement the constrained director. This model includes both kinematic and isotropic hardening behaviours. A consistent elasto-plastic tangent modular matrix is extracted. Numerical solution is performed by interpolation of displacement on the whole domain, and a hierarchical finite-element scheme is developed. The principle of virtual work is used to obtain the weak form of the governing differential equations and the material and geometric stiffness matrices are derived through a linearization process. The validity and the accuracy of the method are illustrated by numerical examples.