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利用有限元数值分析方法，对球形刚性压头压入由金属膜与硅基体组成的膜-基体系的加载过程进行了模拟计算．建立了薄膜硬化指数同载荷-位移曲线的特征值，屈服强度、硬化指数及杨氏模量同最大压入载荷间的关系．据此，可由纳米压入仪实测所得载荷-位移曲线的特征值与最大压入载荷，确定金属薄膜材料的应变硬化指数和屈服强度．
Using finite element method, the loading process of the ball-shaped rigid indenter into the membrane-based system composed of metal film and silicon substrate was simulated. The relationship between the characteristic value, yield strength, hardening index and Young ’s modulus of the film’ s hardening exponent with the load - displacement curve was established. Accordingly, the characteristic value of the load-displacement curve measured by the nanoindenter and the maximum press-in load can be used to determine the strain hardening index and the yield strength of the metal thin film material.