Discrete multi-scale modeling of ultra-high-performance concrete with an energy-based coarse-graining approach

Reinforced ultra-high-performance concrete (R-UHPC) beams exhibit shear and flexural failure modes influenced by the interplay of continuous longitudinal reinforcements (rebars) and discrete fiber content. Accurate characterization of these failure modes requires understanding the stress redistribution between fibers and rebars after matrix cracking. Mesoscale discrete numerical models effectively capture this material-level behavior. Among various models, the lattice discrete particle model (LDPM) with fibers (LDPM-F) has proven successful in elucidating the failure behavior of R-UHPC. However, these models pose computational challenges in scenarios where the simulated structural scale is significantly larger than the smallest represented scale of heterogeneity and a high volume of fiber inclusions is considered within the simulated domain. These computational challenges lead to an increased number of degrees of freedom and heightened computational costs at the element level to account for interactions between fibers and matrix. Recently, a multi-scaling method, employing an energy-based coarse-graining (CG) approach, was introduced for LDPM. This approach aims to simulate the accurate damage behavior of concrete with a coarser mesostructure, resulting in a reduction of degrees of freedom. In the present study, this coarse-graining framework is integrated with the LDPM-F model to establish the Coarse-Grained LDPM-F (CG-LDPM-F) framework. In CG-LDPM-F, the coarser mesostructure leads to a reduction in nodal degrees of freedom and fiber–matrix intersections, while the number of fibers generated within the domain remains constant. CG-LDPM-F was initially validated against experimental data from material-level uniaxial compression, notched three-point bending, and notched direct tension tests, considering various coarse-graining factors up to 12. Subsequently, laboratory-scale R-UHPC beams, exhibiting gradual strain hardening and crack-localization-driven flexural failures, were simulated and validated. Additionally, a new UHPC material model, calibrated from the literature, was employed to simulate shear and flexural failure in a structural-scale R-UHPC I beam. Overall, the results demonstrate that the CG-LDPM-F framework can reliably simulate UHPC class materials without modifying fiber geometric and micromechanical properties.