Numerical simulations of four-point beam bending test using a macroscopic probabilistic model

Resumo

This article aims to present the numerical simulations of a four-point bending test of a large plain con-
crete beam, performed by using a three-dimensional macroscopic probabilistic model. The model is developed

in the context of the finite element method and considers that each finite element represents a volume of hetero-
geneous material, with the mechanical properties of tensile strength and local cracking energy being randomly

distributed over the mesh. In this way, that means the cracks are created within the concrete with different energy
dissipation depending on the spatial distribution of material constituents and initial defects. Once the model is
based on a probabilistic approach, a Monte Carlo procedure is used to give coherent statistical results. In order
to verify the efficiency of the developed model related to different levels of refinement, analyzes for two mesh
refinements are presented. The results show agreement with the expected physical behavior for this type of beam
in terms of global response and macrocrack propagation. Regarding the mesh refinements, the results are quite
similar indicating that the model provides a suitable global response in both cases and, therefore, it can be stated
that the utilization of the model with the set of adopted parameters furnishes a consistent outcome for the analyzed
cases.