A rotating smeared crack approach in Sequentially Linear Analysis using the Elastic-brittle fraction model

Sequentially Linear Analysis (SLA), an event-by-event solution strategy in which a sequence of scaled linear analyses with decreasing secant stiffness is performed, representing local damage increments; is a robust alternative to nonlinear finite element analysis of quasi-brittle structures. Since it is based on a fixed smeared crack...

Simulation of Brittle Collapse Mechanisms in Historical Masonry Using Sequentially Linear Analysis (SLA)

Sequentially Linear Analysis (SLA) is known for robust and reliable finite element simulations of masonry constructions, often considered challenging because of the brittle behaviour of the masonry material. Herein a sequence of scaled linear analyses is performed with decreasing secant stiffness of one integration point per analysis,...

A multi-surface interface model for sequentially linear methods to analyse masonry structures

In the finite element modelling of masonry structures, the micro-modelling technique of differentiating the continuum into a linear elastic bulk, and interfaces representing non-linear joints is common. However, this approach of simulating cracking-crushing-shearing failure possibilities in interfaces, typical of damage in masonry, also poses...

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)...

Non-proportional loading in sequentially linear solution procedures for quasi-brittle fracture: A comparison and perspective on the mechanism of stress redistribution

Sequentially linear solution procedures provide a robust alternative to their traditional incremental-iterative counterparts for finite element simulation of quasi-brittle materials. Sequentially linear analysis (SLA), one such non-incremental (total) approach, has been extended to non-proportional loading situations in the past few years....

From sequentially linear analysis to incremental sequentially linear analysis: Robust algorithms for solving the non-linear equations of structures of quasi-brittle materials

It is difficult to accurately predict the strength of masonry and concrete structures. The most widely used method for simulating their behaviour is finite element analysis with the Newton-Raphson method and arch length control. However, the Newton-Raphson method can diverge and not produce a result, for example in bifurcations or during snap...

Non-proportional loading in sequentially linear analysis for 3D stress states

Sequentially linear analysis (SLA), a non-incremental-iterative approach towards finite element simulation of quasi-brittle materials, is based on sequentially identifying a critical integration point in the model, to reduce its strength and stiffness, and the associated critical load multiplier (λ _crit ), to scale the linear...

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 non-proportional loading with a large prestress. In this paper a...