A Unified Temperature-Dependent Elastoplastic Damage Framework for Concrete from Sub-Zero to Elevated Temperatures

Abstract

Abstract

Concrete exposed to sub-zero and elevated temperatures exhibits strongly non-monotonic mechanical behavior governed by different physical mechanisms. Existing thermo-mechanical constitutive models commonly account for temperature-dependent degradation, but many are formulated for a specific temperature regime, and explicit treatment of reversible freezing-induced strengthening and irreversible high-temperature damage within a single constitutive structure remains limited. This study develops a unified thermo-elastoplastic damage model for concrete over the temperature range from −40 to 800 °C within the framework of irreversible thermodynamics. Plasticity is formulated in the effective-stress space, while compressive damage is driven by the damage energy release rate. Temperature effects are incorporated through evolution laws for compressive strength, elastic modulus, peak strain, and the shape parameters of the ascending and descending branches. Ice-induced strengthening is represented through reversible modifications of stiffness and strength thresholds, whereas high-temperature dehydration and microcracking are represented through irreversible thermal damage. The model was calibrated using published low-temperature compression data for C30–C50 concrete and complete high-temperature stress–strain curves for normal-strength concrete. The normalized curve-shape laws were subsequently assessed using high-strength concrete curves after normalization by their measured peak stress and peak strain, while selected components of the three-dimensional extension were assessed using residual HSC60 true-triaxial data. The calibrated model represented the freezing-point strength valley, sub-zero strengthening and embrittlement, non-monotonic strength evolution at intermediate temperatures, and progressive high-temperature ductilization. Complete high-temperature normal-strength concrete curves were reproduced with R2 values of 0.94–0.99, while the normalized multiaxial strength assessment yielded an average relative error of approximately 8%. These results support the internal consistency of the formulation and the limited cross-strength-grade applicability of the normalized curve-shape laws, rather than unrestricted predictive capability. Further independent experiments are required before application beyond the material, moisture, thermal-history, and loading conditions represented by the available datasets.