Fracture via a sequence of events: A saw-tooth softening model

The sequentially linear analysis is a robust alternative to non-linear finite element analysis of structures when bifurcation, snap-back or divergence problems arise. The load-displacement response is captured by a series of linear analyses as a sequence of ‘events’. Every ‘event’ is a scaled critical states corresponding to the reaching of some peak of some saw-tooth for some softening element. In the present paper, the approach is extended with a rippled saw-tooth curve which applies to any stress-strain diagram, included compression nonlinearity and yielding of reinforcement. Several RC structural examples demonstrate that both sharp snap-backs as well as ductile failures can be handled correctly.