A Coupled Harmonic Mean - Cubic Nonlinear Terms Based Multi Objective Optimization of Compressive and Tensile Strengths of a Concrete

Evaluating the mechanical response of a cylindrical concrete is crucial for structural reliability. This paper develops a multi-objective optimization framework to analyze concrete performance under uniaxial compression and split tensile loading, utilizing the Von Mises stress (S, Mises) and Plastic strain (PE) to model the failure of concrete. The parameter estimation is cast as a cubic programming problem to handle the non-linear nature of concrete degradation. To resolve competing structural objectives, a multi-objective model is established, and the resulting Pareto front is solved via the harmonic mean method—an approach that prevents outlier distortion and balances tensile and compressive capacities. The numerical findings confirm that this methodology significantly enhances predictive accuracy over traditional single-objective and arithmetic mean approaches, providing a stable, computationally efficient solution for optimizing concrete mixes and predicting failure states.