Modular implementation framework of partitioned path-following strategies: Formulation, algorithms and application to the finite element software Cast3M
Résumé
Damaging, cracking, and strain localization mechanisms often lead to unstable structural responses characterized by snap-backs(i.e., the force and the displacement decrease simultaneously). The usual nonlinear Newton-based solution algorithms with displacement/force control cannot capture the complete equilibrium curve in a numerical context. This shortcoming can be circumventedusing path-following formulations. They rely on two hypotheses: (i) the decomposition of loading into two parts, one knownand the other unknown (only its direction is imposed); (ii) the use of path-following equations so that the unknown load (forceor displacement) contribution can be determined indirectly. Collecting the essential concepts and the formalism of path-followingarc-length methods, we design a unique framework into the Cast3M toolbox, capable of receiving existing and new path-followingequations without significant modifications. Three path-following constraints were chosen to demonstrate its applicability: a constrainton the combination of the displacement increment at a given set of nodes, a constraint on the maximum strain incrementover the computational domain, and a constraint on the maximum elastic predictor of the damage/plastic criterion function over thecomputational domain. Two- and three- dimensional strain localization simulations show that the proposed framework behaves ina stable and convergent manner, even in the presence of multiple severe snap-back instabilities. The proposed study proves helpfulbecause the user can focus on developing new path-following equations into the Cast3M toolbox. The developments discussed inthis manuscript will be made available to the users/developers community with Cast3M 2021 (release date: April 2021).
Domaines
Sciences de l'ingénieur [physics]
Origine : Fichiers produits par l'(les) auteur(s)