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

Abstract

Summary 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 (λcrit), to scale the linear analysis results. In this article, two novel methods are presented to enable SLA simulations for non‐proportional loading situations in a three‐dimensional fixed smeared crack framework. In the first approach, the cubic function in the load multiplier is analytically solved for real roots using trigonometric solutions or the Cardano method. In the second approach, the load multiplier is expressed as a function of the inclination of a potential damage plane and is deduced using a constrained optimization approach. The first method is preferred over the second for the validation studies due to computational efficiency and accuracy reasons. A three‐point bending beam test, with and without prestress, and an RC slab tested in shear, with and without axial loads, are used as benchmarks. The proposed solution method shows good agreement with the experiments in terms of force‐displacement curves and damage evolution.

Implementation of an elastic no-tension material model in a sequentially linear analysis framework

“…The solution of the inherent non-linear problem is tackled herein by resorting to the concept of Sequential Linear Analysis (SLA), instead of implementing the energy-based procedure that were originally proposed to this goal. SLA was developed as a robust alternative to incremental-iterative finite element solutions for brittle materials [20,21], and is herein extended in this study to ENT masonry-like material. In the present version, the approach is limited to 2D bodies, with some generalization to 3D structures.…”