Reduced‐Order Modeling of the Lattice Discrete Particle Model via Proper Orthogonal Decomposition

ABSTRACT The Lattice Discrete Particle Model (LDPM) provides a robust computational framework for modeling the behavior of quasi‐brittle cementitious composites, excelling at simulating fracture processes, crack initiation and propagation, and material failure mechanisms at the mesoscopic scale of concrete, which schematizes the material at the level of coarse aggregate and mortar paste. However, LDPM remains computationally expensive, particularly when modeling large‐scale structural elements under complex dynamic conditions. This study utilizes Proper Orthogonal Decomposition (POD) to develop a reduced‐order model (ROM) for the LDPM integration solver employing the central difference scheme. A novel two‐stage projection strategy is introduced, enabling direct and consistent enforcement of boundary conditions in the reduced subspace, while maintaining compatibility with the original solver. The objective is to balance accuracy and computational efficiency. In constructing the ROM, both offline and online modes are presented and discussed in detail, including the demonstration of offline ROM for mesoscale parameter calibration to enhance predictive capabilities. The proposed methodology is validated through various independent tests involving highly nonlinear behavior. The results demonstrate significant computational savings without compromising the accuracy of the numerical predictions, highlighting the potential to apply ROM techniques to the LDPM framework.