Explicit Nonlocal Space-Time Multiscale (EN^STM) Model

We present a reduced order multiscale explicit nonlocal (ROMEN) model, which consists of the following features: a). Systematic upscaling: derivation of coupled coarse-scale (macro) equations from fine-scale (micro) equations using mathematical homogenization theory. The upscaling procedure incorporates dynamic effects into a unit cell model. b). Model reduction with explicit nonlocality of micro-phases: reducing the complexity of solving a fine-scale problem to a manageable size. Size effect has been incorporated into the fine-scale model by defining nonlocal micro-phase fields by averaging eigenstrains over characteristic length in the physical problem domain. c). Model characterization: solving an inverse problem for constitutive parameters (fiber-reinforcement, cement) by minimizing the error between experimental data at coupon level and multiscale simulation results. d). Material optimization: optimizing microstructure (geometry, volume fraction of fibers, interface properties) based on user-defined design criteria, such as energy absorption. This module allows designing optimal Very High Strength Concrete (VHSC), Fiber Reinforced Concrete (FRC), and other types of special concrete materials. The ROMEN model has been verified to be mesh size independent and validated against experimental data for the three-point bending problem.