Abstract:
Instrumented indentation testing has been widely adopted for rapid and non-destructive evaluation of mechanical properties, especially in micro-scale and structurally complex materials, due to its small testing scale, high spatial resolution, and ease of implementation. However, because of the highly nonlinear and coupled nature of elasto-plastic constitutive behavior, conventional inversion approaches typically rely on finite element simulations and trial-and-error optimization procedures. These methods are often computationally expensive, lack physical interpretability, and are difficult to apply efficiently in practical engineering scenarios. To address these challenges, this study proposes an inverse analysis method based on the Deep Symbolic Optimization (DSO) algorithm. By learning the nonlinear mapping relationship between indentation load–displacement curve features and elasto-plastic material parameters, the DSO model generates symbolic expressions with explicit physical meaning. DSO-based inversion models are constructed under various hardening indices and two representative indenter types (conical and spherical). Furthermore, the proposed method is systematically compared with three commonly used machine learning approaches—multilayer perceptron, Gaussian process regression, and random forest—using evaluation metrics including the coefficient of determination (R2), root mean squared error, and mean absolute error. The results indicate that the DSO model achieves superior prediction accuracy and robustness in most cases, particularly in fitting highly nonlinear parameters such as yield strength. In addition, the generated symbolic expressions improve the physical interpretability compared to black-box models. The method also demonstrates strong generalization performance under different loading conditions and material types, with R2 values reaching 0.8–0.96. Overall, this work provides an efficient, accurate, and interpretable solution for inverse analysis in indentation-based characterization of elasto-plastic materials