The characterization of the constitutive behavior of embedded particles is crucial for the mechanical analysis of functional particulate composites. However, current methods for identifying the elastic parameters through instrumented indentation tests lack robust theoretical foundations. In this study, a series-connection analytical model was proposed to determine the Young's modulus of the embedded particles based on the Oliver-Pharr (O-P) model. Additionally, a simplified regression function was derived from the complete analytical model.

To validate the accuracy of these methods in estimating the Young's modulus, 2D indentation simulations were conducted. Furthermore, in order to facilitate practical engineering applications, a data processing strategy was developed and implemented to determine the statistical value of the Young's modulus for LiNi_xMn_yCo_zO₂ (NMC) particles in the cathode of a Lithium-ion battery (LIB). Moreover, data obtained from continuous stiffness measurement (CSM) of a single embedded NMC particle were utilized to verify the reliability of the simplified regression function. The simplified regression function was found to possess significant engineering potential in related studies, as it enables a quick and reliable approximation of the Young's modulus of embedded particles without requiring detailed experimental information.

嵌入颗粒本构行为的表征对于功能颗粒复合材料的力学分析至关重要。然而，目前通过仪器压痕试验识别弹性参数的方法缺乏可靠的理论基础。在本研究中，提出了一种串联分析模型，用于确定基于 Oliver-Pharr (OP) 模型的嵌入颗粒的杨氏模量。此外，从完整的分析模型中得出了简化的回归函数。

为了验证这些方法在估算杨氏模量方面的准确性，进行了二维压痕模拟。_{此外，为了便于实际工程应用，开发并实施了数据处理策略来确定LiNi x} Mn _y Co _z O ₂杨氏模量的统计值锂离子电池 (LIB) 阴极中的 (NMC) 颗粒。此外，利用单个嵌入 NMC 颗粒的连续刚度测量 (CSM) 获得的数据来验证简化回归函数的可靠性。人们发现简化的回归函数在相关研究中具有显着的工程潜力，因为它能够快速可靠地近似嵌入粒子的杨氏模量，而不需要详细的实验信息。