Assumed Natural Strain NURBS-based solid-shell element for the analysis of large deformation elasto-plastic thin-shell structures

• The Assumed Natural Strain method for Isogeometric Analysis is proposed.
• The formulation proves effective in alleviating locking in shell structures.
• The extension to nonlinear problems is straightforward and detailed in the paper.

In this work, a recently proposed quadratic NURBS-based solid-shell element based on the Assumed Natural Strain (ANS) method is applied in the analysis of shell-like structures in the geometrical nonlinear regime, together with small strain plasticity. The proposed formulation is based on the additive split of the Green–Lagrange strain tensor, leading to a straightforward implementation of the nonlinear kinematics and to the introduction of a corotational coordinate system, used to integrate the constitutive law, ensuring incremental objectivity. Since the proposed approach is based on Updated Lagrangian formulation combined with a corotational coordinate system, the extension of the ANS methodology is straightforward. Well-known benchmark tests are employed to assess the performance of the proposed formulation and to establish a detailed comparison with the formulations available in the literature. The results indicate that the proposed solid-shell approach based on the NURBS ANS methodology presents good predictability characteristics in the analysis of elasto-plastic thin-shell structures subjected to large deformations.