This paper introduces a three-dimensional (3D) semi-explicit probabilistic numerical model for simulating crack propagation within the framework of the finite element method. The model specifically addresses macrocrack propagation using linear volume elements. The criteria governing the macrocrack propagation is based on the softening behavior observed in concrete under uniaxial tension. This softening behavior corresponds to a dissipated cracking energy that is equal to the mode I critical fracture energy $\left(G_{IC}\right)$ used in the Linear Elastic Fracture Mechanics theory (LEFM). The probabilistic nature of this model revolves around the random distribution of two mechanical properties: tensile strength $\left(f_t\right)$ and fracture energy, which varies based on the volume of finite elements. The scattering of the fracture energy increases as the volume of finite elements decreases in order to consider the strong heterogeneity of the material. This work primarily aims to estimate the relationship between the standard deviation of $G_{IC}$ and the volume of finite elements through the development of the numerical model. For this purpose, an inverse analysis is conducted based on a fracture mechanical test simulation. This test involves macrocrack propagation in a large Double Cantilever Beam (DCB) specimen with a crack length exceeding two meters. The proposed inverse analysis procedure yields highly significant results, indicating that the numerical model effectively evaluates both crack length and crack opening during propagation.

In this paper, the development of a 3D adaptive probabilistic explicit cracking model for concrete is reported. The contribution offered herein consists in a new adaptive mesh strategy designed to optimize the use of interface elements in probabilistic explicit cracking models. The proposed adaptive mesh procedure is markedly different from other strategies found in the literature, since it takes into account possible influences on the redistribution of stresses after cracking and can also be applied to purely deterministic cracking models. The process of obtaining the most appropriate adaptive mesh procedure involved the development and evaluation of three different adaptivity strategies. Two of these adaptivity strategies were shown to be inappropriate due to issues related to stress redistribution after cracking. The validation results demonstrate that the developed adaptive probabilistic model is capable of predicting the scale effect at a level similar to that experimentally observed, considering the tensile failure of plain concrete specimens. The results also show that different softening levels can be obtained. The proposed adaptive mesh strategy proved to be advantageous, being able to promote significant reductions in the simulation time in comparison with the classical strategy commonly used in probabilistic explicit cracking models.

This work presents the application of a finite element model utilizing a three-dimensional (3D) probabilistic semi-explicit cracking model to analyze the rupture process of a large concrete wall beam. The numerical analysis predicts both the global behavior of the structure and its primary rupture mechanisms, utilizing three different finite element mesh refinements to ensure robustness. A Monte Carlo (MC) procedure is integrated into the modeling approach to account for probabilistic variations of the material properties. The statistical analysis derived from this probabilistic model may sometimes result in overly conservative safety coefficients, particularly when using a coarse mesh. Additionally, the detailed understanding of the structure’s cracking process, regardless of its rupture mechanism, may experience some reduction in precision. Due to the necessity of numerous simulations to achieve statistically significant results, the MC procedure can become computationally expensive. To address this, a straightforward parallelization of the Monte Carlo procedure was implemented, allowing multiple finite element analyses to be conducted concurrently. This strategy significantly reduced computational time, thereby enhancing the efficiency of the numerical model in performing numerical simulations of structural engineering.

The civil construction industry has shown increasing interest in 3D printing technology due to its ability to produce highly complex structures with different internal wall geometries using concrete as the raw material. With the advancement of technology, the use of numerical modeling software has become necessary to simulate heat transfer and the thermal performance of objects developed through 3D printing. The objective of this work is to simulate heat transfer in a wall geometry obtained by 3D printing, featuring triangular cavities filled with air, and to compare the results using two different approaches. Initially, computational simulation with air voids in a wall as solid elements will be presented using DIANA FEA software, and subsequently, the air voids will be treated as a fluid using OpenFOAM software. The comparison between the two simulations will be presented, highlighting the influence of modeling air voids on the thermal properties of 3D-printed structures.