Adaptive hierarchical multiscale modeling for concrete trans-scale damage evolution

This work presents an adaptive hierarchical multiscale approach for modeling the trans-scale damage evolution in concrete. The problem domain represented by an adaptive hierarchical multiscale finite element (FE) model is decomposed into two regions, namely the macroscopic elastic region and the multiscale critical region prone to damage. The former is simulated only by macroscopic elements, while the latter is modeled by both macroscopic elements and the coupled-volume mesoscopic FE samples assigned to the integration points belonging to these macroscopic elements. A model update criterion is proposed to adaptively identify the multiscale critical region during the loading process. Innovatively, the coupled-volume meso-samples are randomly generated on the fly when the macroscopic integration points are first identified to be included in the multiscale critical region. Concrete damage at the macroscale is quantitatively characterized based on its mesoscopic counterpart thanks to the proposed partition-based averaging scheme. The numerical simulations demonstrate that the presented approach can track and quantify concrete trans-scale damage evolution. Importantly, in the simulation of a 480 mm-length dog-bone-shaped specimen, the number of degrees of freedom and computational time are only 8.35 and 17.57% of those of the direct mesoscale simulation, respectively.