Crack propagation in concrete at meso scale using topology optimization

The current research seeks to present a novel method for numerical modeling of concrete behavior at meso-scale. In this method, as the stress distribution at the macro scale can be a suitable indicator for critical areas (crack propagate and growth), the areas under stress (critical areas) are identified through numerical modeling at the macro scale (coarse mesh) and using the extended finite element method and topology optimization. Macro-scale critical regions are considered cumulatively using topology optimization. Therefore, critical regions are modeled at the meso-scale, and the rest are modeled on the macro scale. At the meso-scale, the three phases including aggregate, mortar matrix, and ITZ were considered. The aggregate phase was distributed in the mortar matrix using a random algorithm and a Fuller curve. The accuracy of modeling concrete at the meso-scale using topology optimization was investigated by two examples, the results of which show the appropriate accuracy of the method. Furthermore, the method can reduce the computational cost and analysis time compared to modeling the whole sample at the meso-scale. In this research, the piecewise meshing method was used for numerical modeling. Using this method, traction-separation crack growth and expansion are modeled with appropriate accuracy.