A multi-scale model from microscopic cracks to macroscopic damage of concrete at elevated temperatures.

The article focuses on the development of a multi-scale model that links microscopic crack behaviors to macroscopic damage evolution in concrete subjected to elevated temperatures. This model establishes an evolution equation for the number density of microscopic cracks, incorporating parameters that characterize crack nucleation and growth, to predict both microscopic crack density and macroscopic damage. Validated through numerical simulation and experimental data on concrete blocks heated from 100°C to 800°C, the model demonstrates a near-linear relationship between temperature rise and macroscopic damage, as well as an inverse relationship between crack length and microscopic crack density. The multi-scale model addresses limitations of traditional macroscopic models, which lack physical mechanism considerations, and microscopic models, which are difficult to apply at structural scales, thereby providing a tool for fire damage assessment and physical mechanism explanation in concrete structures under high temperatures. However, the model is currently limited to thermal damage due to temperature rise and does not account for coupled thermal-mechanical effects.