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…
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 non- iterative 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.