Mesoscale FEM Model of Concrete: Statistical Assessment of Inherent Stress Concentrations in Dependence on Phase Heterogeneity

Abstract

Concrete heterogeneity originates from its production process, which involves bonding aggregates with a binder matrix. This study presents a mesoscale finite element model (MFEM) that offers detailed insights into the fracture process at the aggregate--cement matrix interface, focusing on one of concrete's key properties: its mechanical response. Unlike discrete models, which often average out critical stress concentrations within the mesostructure, the MFEM approach captures detailed stress distributions, revealing localized effects crucial for understanding damage evolution. Although computationally more demanding, the MFEM leverages modern high-performance computing (HPC) to provide a detailed description of the stress field and material damage across different phases and interfaces. The proposed modeling framework integrates a collision-checked aggregate generation procedure, Voronoi-based mesostructure construction, and adaptive 3D meshing, forming a reusable methodology for stress analysis in heterogeneous composites. This approach offers transparent, physically interpretable parameterization of phase properties in contrast to black-box discrete models. Another methodological contribution is the statistical post-processing of stress data using histogram-based analysis across cross-sectional planes. This enables quantitative evaluation of stress concentration distributions, providing valuable insights into the mesoscale mechanical response and serving as a useful visualization tool for researchers working on heterogeneous material modeling. Various matrix-to-aggregate stiffness ratios are considered to evaluate the influence of material heterogeneity on the stress field.