Multi-objective optimization on mechanical properties of nanomaterial-reinforced cementitious composites using response surface methodology (RSM)

In recent years, nanomaterial have garnered significant interest for enhancing engineered cementitious composites (ECC). This study employs response surface methodology (RSM) to conduct multi-objective optimization of the mechanical properties of nanomaterial-reinforced ECC (NR-ECC), aiming to determine the optimal dosages of silica nanoparticles (NS) and carbon nanotubes (CNTs). A central composite design (CCD) was utilized to formulate 13 mixtures with varying NS (1–3%) and CNTs (0.1–0.2%) contents. Three quadratic response surface models were developed and validated to predict uniaxial compressive strength, uniaxial tensile strength, and peak tensile strain, demonstrating high accuracy (R² = 0.94–0.98) and statistical significance (p < 0.05). Multi-objective optimization identified the optimal contents as 1.698% NS and 0.155% CNTs, which were experimentally validated with errors below 5%. The results indicate that NS enhances matrix density and interfacial properties, while CNTs facilitate multi-scale crack bridging. The optimal mixture improved compressive strength, tensile strength, and tensile strain by 9.89%, 27.75%, and 32.45%, respectively, compared to the baseline. This study provides a reliable modeling and optimization framework that supports the efficient design of high-performance NR-ECC for practical engineering applications.