Simulating quasi-brittle failure in structures using Sequentially Linear Methods: Studies on non-proportional loading, constitutive modelling, and computational efficiency

Sequentially Linear Analysis (SLA) is a proven robust alternative to incremental-iterative solution methods in nonlinear finite element analysis (NLFEA) of quasi-brittle specimen. The core of the method is in its departure from a load, displacement or arc-length driven incremental approach (aided by internal iterations to establish equilibrium) to a damage driven event-by-event approach that approximates the nonlinear response by a sequence of scaled linear analyses. The constitutive relations are discretised into secant-stiffness based saw-tooth laws, with successively reducing strengths and stiffnesses. In each linear analysis, the global load is scaled such that the critical integration point, with the largest stress, jumps to its next saw-tooth representing locally applied damage increments. The use of an event-by-event approach and the secant-stiffness based constitutive model enables SLA to avoid problems such as pushing multiple integration points simultaneously into softening, snap-backs, jumps, bifurcation points, and divergence, that are typically encountered in NLFEA. Despite the advantages of simplicity and numerical robustness in comparison to NLFEA, SLA as a solution procedure needed significant developments to be used in engineering practice as a numerical tool for structural applications, such as the pushover analysis of a masonry structure or the capacity assessment of a shear-critical reinforced concrete slab. To this end, this dissertation contributes to extending SLA and similar methods, together referred to as a class of Sequentially Linear Methods (SLM), to 3D applications in both the continuum and discrete damage frameworks under non-proportional loading conditions, and additionally improving on its computational efficiency.