An updated Lagrangian framework for Isogeometric Kirchhoff–Love thin-shell analysis

Abstract

We propose a comprehensive Isogeometric Kirchhoff–Love shell framework that is capable of undergoing large elasto-plastic deformations. Central to this development, we reformulate the governing thin-shell equations in terms of the mid-surface velocity degrees of freedom, accommodating the material response in the time-rate form while ensuring objectivity. To handle complex multipatch geometries, we propose a consistent penalty coupling technique for enforcing the continuity conditions at patch interfaces. Penalty is also employed to weakly enforce symmetry boundary conditions. A recently proposed non-local penalty contact is adopted as part of the formulation in order to handle complex dynamic crushing simulations. Numerical examples, ranging from static elasto-plastic shell benchmarks to highly dynamic crushing scenarios, validate the accuracy, efficiency and robustness of the proposed framework.