Multiscale stochastic modeling of cement materials using UMT and lattice frameworks

A stochastic UMT-based framework is developed to predict the macroscale mechanical behaviour of C–S–H, bridging nanoscale and microscale heterogeneities. The macroscale RVE is modelled as a 3D stochastic lattice of C–S–H agglomerates, with the elastic modulus and fracture strain represented as Gaussian-like stochastic fields generated through the stochastic harmonic function (SHF) spectral method, ensuring spatially correlated variability that captures microscale heterogeneity. Damage evolution is modelled using an entropy-based index that correlates local energy dissipation with stiffness degradation. The framework incorporates effects across nano-, micro-, and mesoscale levels to simulate compression, tension, and shear. Compressive responses include nonlinear pre-peak behaviour, peak stresses within experimental ranges, and localised post-peak shear-like damage. Tensile predictions show linear-elastic behaviour followed by brittle failure, with strengths ranging from 1/8 to 1/12 of compressive strength. Shear predictions show nonlinear pre-peak behaviour and post-peak plastic-like strain accumulation. The stress- and energy-based damage metrics effectively monitor damage progression, with the latter providing a physically consistent, unidirectional measure. The framework can generate realistic digital microstructures without full XCT reconstruction, visualize failure localization, and replicate key stochastic features observed in cementitious materials. Parametric studies facilitate model calibration, and validation against cement mortar test data demonstrates close agreement in average values, variability, and probabilistic behaviour, with error metrics and probabilistic measures confirming minimal bias and statistically consistent uncertainty. This hierarchical approach links entropy-driven nanoscale bond rupture to macroscale behaviour, offering a physically based, computationally efficient, and statistically robust method for modelling degradation in cement-based materials.