A simple assumed-strain quadrilateral shell element for finite strains and fracture

Abstract

This work recovers an established technique for improving quadrilateral shell element performance in both out-of-plane and in-plane bending cases using a mixed formulation. A four-field variational principle is established and we relate, at the discrete level, the Lagrange multipliers and secondary right Cauchy---Green field with the displacement and rotation fields. This is the main contribution of this work. High coarse-mesh accuracy is observed for distorted meshes and the robustness is shown to be adequate for crack propagation simulations. A consistent director normalization is performed, as an alternative to our recent spherical interpolation. Covariant metric components are deduced and exact linearization of the shell element is performed. Full assessment of the element is accomplished, showing similar performance to more costly approaches such as enhanced assumed strain. Patch test is satisfied ab-initio and benchmarks present very accurate results. Numerical experimentation for geometrically and material nonlinear problems is presented, as well as one fracture example using our recently proposed cracked edge technique.