Implementation of a 3D macroscopic probabilistic model for semi-explicit concrete cracking

Abstract

This work implements a three-dimensional macroscopic probabilistic model for semi-explicit concrete cracking, taking into account crack propagation in mode I. The model is developed in the finite element method framework. Each element represents a volume of heterogeneous material with the mechanical properties of tensile strength and fracture energy randomly distributed over the mesh. Thus, the cracks are created with different energy dissipation depending on the spatial distribution of material constituents and initial defects. The dissipative process follows an isotropic damage law. The model is probabilistic regarding these properties’ random distribution. Therefore, a strategy to determine the statistical parameters that describe the material behavior is proposed, based on an inverse analysis procedure related to the fracture energy, through a large-scale double cantilever beam test simulation. For this aim, an iterative numerical procedure is used to estimate the parameters associated with tensile strength, using empirical scale laws as input data. A Monte Carlo procedure is used to provide coherent statistical results. A parallelization strategy is employed in the procedure implementation through the use of OpenMP, aiming to perform 3D simulations in a viable computational time. The model applicability associated with the set of estimated parameters is verified by modeling two case studies: the four-point bending test for two types of beams and the uniaxial tensile test for different specimens. Finally, the Monte Carlo parallelization performance indicates a considerable computational time reduction