Optimal experimental design for repeatable hyperelastic material characterization

Reliable identification of hyperelastic material parameters is essential for precisely modeling the mechanical behavior of various materials including biological tissues, which in turn has significant medical applications. However, experimental configurations often lack quantitative design guidelines, leading to high variance in reported parameters and sometimes irreproducible results. To address the sensitivity of material parameter identification, this study introduces a novel "stress-material Jacobian" framework to determine optimal experimental configurations, i.e., loading mode, loading level, and number of experiments, for hyperelastic material characterization. By analyzing the determinant and condition number of the Jacobian relating the stress parameter space and the material parameter space, we propose a novel approach to determine optimal experimental configurations across different deformation ranges, modes, and hyperelastic models, providing quantitative measures for experimental design. Our method identifies configurations that minimize sensitivity to noise, ensure robustness, and reduce the number of required tests. We verify the approach on three classical hyperelastic models, namely, Neo-Hookean, Mooney-Rivlin and Ogden models, under various loading conditions. Results show significant improvement in parameter identification reproducibility and robustness to measurement uncertainties. The analysis also briefly addresses heterogeneous material characterization, paving the way for its broader application in biomechanics and engineering.