Sequentially linear analysis for simulating brittle failure

The numerical simulation of brittle failure at structural level with nonlinear finite
element analysis (NLFEA) remains a challenge due to robustness issues. We attribute these problems to the dimensions of real-world structures combined with softening behavior and negative tangent stiffness at local level which may lead to non-convergence, i.e. the applied external loads are not in equilibrium with the internal forces. Also multiple cracks that compete to “survive” and the possibility of bifurcations, i.e. the existence of multiple equilibrium paths, contribute to these problems. However, in engineering practice robust numerical methods become increasingly important. For example, NLFEA may be used to determine the actual load bearing capacity of existing concrete bridges in order to assess whether these meet the current regulations. Also for the prediction of building damage due to underground construction or seismic action NLFEA may be employed.