Department of Physics, Arizona State University, Tempe, AZ 85287, USA.
Soft Matter. 2019 Feb 20;15(8):1776-1784. doi: 10.1039/c8sm02121j.
Atomic force microscopy (AFM) is becoming an increasingly popular method for studying cell mechanics, however the existing analysis tools for determining the elastic modulus from indentation experiments are unable to quantitatively account for mechanical heterogeneity commonly found in biological samples. In this work, we numerically calculated force-indentation curves onto two-layered elastic materials using an analytic model. We found that the effect of the underlying substrate can be quantitatively predicted by the mismatch in elastic moduli and the homogeneous-case contact radius relative to the layer height for all tested probe geometries. The effect is analogous to one-dimensional Hookean springs in series and was phenomenologically modeled to obtain an approximate closed-form equation for the indentation force onto a two-layered elastic material which is accurate for up to two orders of magnitude mismatch in Young's modulus when the contact radius is less than the layer height. We performed finite element analysis simulations to verify the model and AFM microindentation experiments and macroindentation experiments to demonstrate its ability to deconvolute the Young's modulus of each layer. The model can be broadly used to quantify and serve as a guideline for designing and interpreting indentation experiments into mechanically heterogeneous samples.
原子力显微镜（AFM）正成为研究细胞力学的一种越来越受欢迎的方法，然而，现有的用于从压痕实验确定弹性模量的分析工具无法定量地解释生物样本中常见的力学异质性。在这项工作中，我们使用解析模型数值计算了双层弹性材料的力-压痕曲线。我们发现，对于所有测试的探针几何形状，基底的影响可以通过弹性模量失配和相对于层高度的均质情况接触半径来定量预测。这种影响类似于串联的一维胡克弹簧，并对其进行了现象学建模，以获得一个近似的封闭形式方程，用于计算双层弹性材料上的压痕力，当接触半径小于层高度时，该方程在杨氏模量失配高达两个数量级时仍然准确。我们进行了有限元分析模拟来验证该模型，并进行了 AFM 微压痕实验和宏观压痕实验来证明其能够解卷积每个层的杨氏模量。该模型可广泛用于量化和指导设计以及解释具有力学异质性的样品的压痕实验。
