Abstract A new model of the interaction of AFM sharp probe with a soft incompressible elastic material is proposed. The model takes into account the finite deformations of the material. The novelty is the consideration of bending and increasing of the material-air interface during the process of indentation. The work performed by the probe is spent both on the elastic deformation of the sample and on changing the geometry of the material-air interface. The paper proposes an explanation of possibility to simulate the phase boundary by a thin elastic layer under the condition of its large shrinkage. The obtained approximation dependences allow quick computer calculations. The presented arguments justify the possibility of neglecting the probe jump to the sample surface. It is established that the Deryagin-Muller-Toporov model is a special case of the proposed model.

中文翻译：

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界面现象对原子力显微镜探头与软材料相互作用特性的影响

摘要 提出了一种新的原子力显微镜尖探针与不可压缩的软弹性材料相互作用的模型。该模型考虑了材料的有限变形。新颖之处在于在压痕过程中考虑了材料-空气界面的弯曲和增加。探头所做的工作既用于样品的弹性变形，也用于改变材料-空气界面的几何形状。论文提出了在大收缩条件下用薄弹性层模拟相界的可能性的解释。获得的近似依赖性允许快速的计算机计算。所提出的论点证明忽略探针跳跃到样品表面的可能性是合理的。