A Direct Finite Element Square–Sobol’ Framework for Global Sensitivity Analysis of Porous Piezoelectric Ceramics

• DFE 2 –Sobol’ pipeline cuts cost by 96% with negligible loss of GSA accuracy. • Saltelli–Sobol’ indices show clear parameter dominance. • Validated on porous piezoelectric plates; readily extendable to 3D RVEs. Piezoelectric ceramics are widely used for sensing, energy harvesting, and smart structures; their electromechanical response is strongly influenced by material heterogeneity and pore morphology. However, high-dimensional parameter studies remain computationally expensive using direct numerical simulations (DNS). To overcome this limitation, a Direct Finite Element Square (DFE 2 )–Sobol’ hybrid framework is proposed to efficiently analyze the influence of eight key parameters, including material constants and pore size, on the electromechanical responses of porous piezoelectric ceramics. The method maintains DNS-level accuracy while significantly reducing computational cost, enabling thousands of parametric simulations. Based on 3600 DFE 2 evaluations, Sobol’ indices reveal that elastic modulus and dielectric constants dominate stress and electric potential, whereas the pore-size factor and Poisson’s ratio mainly affect displacement. The proposed DFE 2 –Sobol’ framework provides an efficient and interpretable tool for global sensitivity analysis and optimization of advanced porous piezoelectric ceramics.