Incremental sequentially linear analysis to control failure for quasi-brittle materials and structures including non-proportional loading

Quasi brittle materials, such as un-reinforced masonry or concrete are difficult to analyse because often the traditional Newton-Raphson (N-R) procedure fails to converge. Many solutions have been proposed such as Sequentially Linear Analysis (SLA), but these may fail in case of nonproportional loading with a large prestress. In this paper a new method is proposed that is based on a combination of the Newton-Raphson method and Sequentially Linear Analysis. The method is incremental; each increment starts and ends with an equilibrium state. The solution search path follows damage cycles sequentially with secant stiffness. The proposed method is demonstrated to be robust and accurate. It has been tested on prestressed concrete beams. It can be naturally extended to other types of analyses (e.g. geometrically non-linear analysis and transient analysis) due to the incremental procedure. In addition, it is shown that high prestress values can transform the behaviour of a concrete beam from softening to hardening.