Nonlinear three-dimensional finite-element modelling of reinforced-concrete beams: Computational challenges and experimental validation

Three-dimensional nonlinear finite-element models have been developed to investigate the loading-unloading-reloading behaviour of two reinforced-concrete beams under four-point bending using explicit dynamics in ABAQUS. The damaged-plasticity model proposed by Lubliner and collaborators was employed for the plain concrete, and elastic-perfectly plastic models were employed for the steel reinforcement. A perfect bond was assumed between the steel rebars and concrete, whereby the bond-slip behaviour, as well as damage along crack patterns, were modelled through concrete damage. The influence of the shape of the tension-softening law on the numerical load-deflection response was studied by considering bi-linear, exponential and linear post-failure stress-displacement and stress-strain relationships. The effect of modelling steel rebars with truss or beam elements was also investigated. Structured meshes of linear hexahedral elements either with incompatible modes or with reduced integration, and unstructured meshes of either linear or 'modified' quadratic tetrahedral elements were considered. In terms of load-deflection curves, both the structured and the unstructured meshes gave results in very good agreement with test results. In terms of crack patterns, results predicted by the structured meshes exhibited some mesh bias, which was less pronounced with the unstructured meshes. In the post-yield phase, if a geometrically nonlinear model is used, discrepancies were found when truss elements were used for steel rebars, whereas good agreement was found if the bending stiffness of the rebars is included using beam elements. This is a non-obvious result that may be important to consider when studying the progressive collapse of RC structures.