Enhanced transverse shear strain shell formulation applied to large elasto-plastic deformation problems

In this work, a previously proposed Enhanced Assumed Strain (EAS) finite element formulation for thin shells is revised and extended to account for isotropic and anisotropic material non-linearities. Transverse shear and membrane-locking patterns are successfully removed from the displacement-based formulation. The resultant EAS shell finite element does not rely on any other mixed formulation, since the enhanced strain field is designed to fulfil the null transverse shear strain subspace coming from the classical degenerated formulation. At the same time, a minimum number of enhanced variables is achieved, when compared with previous works in the field. Non-linear effects are treated within a local reference frame affected by the rigid-body part of the total deformation. Additive and multiplicative update procedures for the finite rotation degrees-of-freedom are implemented to correctly reproduce mid-point configurations along the incremental deformation path, improving the overall convergence rate. The stress and strain tensors update in the local frame, together with an additive treatment of the EAS terms, lead to a straightforward implementation of non-linear geometric and material relations. Accuracy of the implemented algorithms is shown in isotropic and anisotropic elasto-plastic problems