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)...

Two solution strategies to improve the computational performance of Sequentially Linear Analysis for quasi-brittle structures

Sequentially linear analysis (SLA), an event-by-event procedure for finite element (FE) simulation of quasi-brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λ _crit), to scale the linear analysis...

Exploiting BiCGstab(?) strategies to induce dimension reduction

IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...