Extension and Verification of Sequentially Linear Analysis to Solid Elements

When analyzing three-dimensional problems with nonlinear finite element analysis (NLFEA) often problems are encountered such as bifurcation and divergence of the solution. In particular, cases subjected to tension softening tend to encourage the emergence of multiple equilibrium paths. In order to overcome these problems the Sequentially Linear Analysis (SLA) method has been developed for three-dimensional solid elements. SLA is an alternative for incremental-iterative solution schemes to model the nonlinear fracture behavior of quasi-brittle materials. It is an attractive method since it avoids the well known convergence and bifurcation problems that are often encountered when using incremental-iterative schemes such as Newton-Raphson. SLA uses a series of linear analyses to model the nonlinear behavior of the structure. By directly specifying a damage increment in each linear analysis, extensive iterations within the load or displacement increment can be avoided. The main objective of this research was to see how the Sequentially Linear Analysis approach could be extended to solid elements, so that it could be used for three-dimensional fracture problems as well. Although three-dimensional geometries such as masonry structures have been analyzed before using SLA, it was always restricted to two-dimensional finite elements only (shell elements). Therefore, first a theoretical constitutive model for three-dimensional stress-strain states has been developed that served as the starting point. Implementation in DIANA was the major second step from which the third and last step could be started: the verification on various fictive and real cases. A single element pull test was used to solve programming errors, whereas the notched beam offered the possibility to check how the newly developed SLA-code would perform for larger models. Both cases showed excellent agreement with the experiment. However, most attention was dedicated to the verification and physical interpretation of a real reinforced concrete slab. The results were critically evaluated, interpreted and compared to results from the experiment and the incremental-iterative Newton-Raphson method. It was concluded that the Sequentially Linear Analysis is able to properly capture the quasi-brittle behavior of the reinforced concrete slab. Especially in comparison to the three-dimensional Newton-Raphson results, SLA turned out to be more robust and accurate.Structural EngineeringCivil Engineering and Geoscience