Generalization of non-iterative numerical methods for damage-plastic behaviour modeling

Modelling fracture in concrete or masonry is known to be problematic regarding the robustness of iterative solution procedures and, the use of non-iterative methods (or that minimize the use of iterations) in quasi-brittle materials is now under strong development, due to the necessity to obtain effective results in finite element analysis [1, 2] where strong non-linearities emerge that are otherwise unwieldy to model. In the proposed lecture, two new methods designated as Non-Iterative Energy based Method (NIEM) and Automatic presented in [1, 3] are applied with extension to modelling damage-plastic behaviour. The new methods combine an incremental-total procedure with the preferential use of incremental steps, switching to the total approach only at critical bifurcation points. The development of the load-unloading abilities is allowed by these incremental/total methods, which take advantage of keeping the material’s stress/strain memory due to the preferential use of an incremental procedure. A new approach to the unload-load cycles is used in the scope of a noniterative procedure, which will mitigate the numerical difficulties inherent to cyclic loading. The formulation for both methods for structures with both softening and hardening behaviour is presented and a structural example where the numerical results are compared with experimental results.Structural EngineeringCivil Engineering and Geoscience