Hyper-reduced arc-length algorithm for stability analysis in elastoplasticity

In this article an “hyper-reduced” scheme for the Crisfield’s algorithm (Crisfield, 1981) applied to buckling simulations and plastic instabilities is presented. The two linear systems ellipse equation entering are projected on a reduced space solved in integration domain, resulting system of equations. Use made Gappy proper orthogonal decomposition recover stresses outside domain. Various methods proposed construct bases, making use simulation data obtained with standard finite element method stress-based error criterion hyper calculations proposed. A “greedy” coupled used generate intelligently full enrich base, demonstrating adequacy criterion. Finally, numerical results pertaining elastoplastic structures undergoing strains, emphasis limit load predictions parametric study geometry structure carried out order determine domain validity hyper-reduced modeling approach.