Multi‑scale homogenization model investigation on the effective elastic modulus of ultra‑high performance concrete considering interfacial transition zone degradation

Abstract Freeze‑thaw (F‑T) damage at the fiber‑matrix interface progressively reduces the stiffness of ultra‑high performance concrete (UHPC) in cold climates, yet a quantitative relationship from nanoscale interfacial degradation to macroscopic modulus loss is missing. Building on previous grid nanoindentation study that quantified the cycle‑dependent evolution of the interfacial transition zone (ITZ)-thickness from 20 μm to 65 μm, modulus from 32 to 12 GPa over 0 ~ 1500 F‑T cycles-a Cylindrical Thin‑Layer Model (CTM) was derived. This model provides a closed‑form analytical homogenization solution for a cylindrical core‑shell inclusion at arbitrary local fiber volume fractions, overcoming the dilute‑assumption limitations of classical Mori‑Tanaka schemes. The CTM requires no iterative solving, reduces computational time compared to the generalized self‑consistent method, and converges reliably for all experimentally relevant ITZ module (≥ 8 GPa). Integrating the CTM into a multi‑scale framework yields macroscopic modulus predictions with a maximum relative error of 11.5% at 0 and 2.1at 1500 cycles (predicted 28.4 GPa vs. experimental 27.8 GPa), a mean absolute percentage error less than 5.8% across all cycles, whereas a Mori‑Tanaka model neglecting the ITZ errs by 19.1%. Parametric analysis identifies ITZ modulus and thickness as the dominant controls on stiffness, with diminishing returns from increased fiber content when the ITZ is compromised. The validated framework offers an efficient, experimentally grounded design tool for fiber‑reinforced composites under F‑T conditions, demonstrating that engineering a dense, thin ITZ is paramount for frost durability.