The atomic force microscopy (AFM) nanoindentation regarding biological samples is a challenging procedure. Biological samples at the nanoscale can be considered as purely elastic materials under the condition that the indentation depth is very small and the indenter is smooth. However, the indenters that are commonly used are pyramidal and in several cases the indentation depths are big comparing to the dimensions of the tip apex. Hence, pyramidal indenters usually cause a permanent damage to the sample. In this case, the best model that can be applied for the data processing is the Oliver-Pharr model which takes into account the elastic-plastic behavior of the sample. The Oliver-Pharr model is based on the fitting of the unloading load-indentation data to a power law equation. In this paper a simplified procedure which ensures the accurate fitting of the unloading load-indentation data to the Oliver-Pharr model is presented and validated on experimental data obtained from a human glioma cell line. It should be noted that the proposed method can be also applied for the data fitting in the case of purely elastic response.

中文翻译：

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确定生物样品的Oliver-Pharr方法拟合常数的简化方法。

有关生物样品的原子力显微镜（AFM）纳米压痕是一个具有挑战性的过程。在压痕深度非常小且压头光滑的条件下，可以将纳米尺度的生物样品视为纯弹性材料。然而，通常使用的压头是锥形的，并且在某些情况下，压痕深度与尖端的尺寸相比较大。因此，棱锥压头通常会对样品造成永久性损坏。在这种情况下，可以应用于数据处理的最佳模型是Oliver-Pharr模型，该模型考虑了样品的弹塑性行为。Oliver-Pharr模型基于卸载负荷压痕数据与幂律方程的拟合。在本文中，提出了一种简化的程序，该程序可确保将卸载载荷压痕数据准确地拟合到Oliver-Pharr模型，并在从人神经胶质瘤细胞系获得的实验数据中进行验证。应当注意，在纯弹性响应的情况下，所提出的方法也可以应用于数据拟合。