Nonlinear indentation of second-order hyperelastic materials
Nonlinear indentation of second-order hyperelastic materials
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DOI：
10.1016/j.jmps.2022.105139
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发表时间：
2022-09
影响因子：
5.3
通讯作者：
Yangkun Du;P. Stewart;N. Hill;Huabing Yin;R. Penta;J. Köry;Xiaoyu Luo;R. Ogden
中科院分区：
文献类型：
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作者：
Yangkun Du;P. Stewart;N. Hill;Huabing Yin;R. Penta;J. Köry;Xiaoyu Luo;R. Ogden
弹性基底上压痕的经典问题在原子力显微镜领域找到了新的应用。然而，线弹性压痕模型不足以准确地预测大压痕深度下的力-位移关系。对于超弹性材料，例如软聚合物和生物材料，需要非线性压痕模型。在本文中，我们使用二阶弹性理论来捕获更大幅度的变形和材料非线性。我们为任意压头轮廓的压痕幅度二阶变形的接触问题提供了通用解决方案。此外，我们通过使用抛物线或四次曲面来模拟球形压头来得出解析解。四次曲面的分析预测与使用球形压头进行的有限元模拟非常吻合，压痕深度约为压头半径。特别是，对于等于压头半径的压痕深度，两种方法之间的相对误差小于 1%，比使用压痕幅度一阶模型或压痕幅度二阶模型但具有抛物线压头轮廓的模型观察到的结果小一个数量级。
The classical problem of indentation on an elastic substrate has found new applications in the field of the Atomic Force Microscopy. However, linearly elastic indentation models are not sufficiently accurate to predict the force–displacement relationship at large indentation depths. For hyperelastic materials, such as soft polymers and biomaterials, a nonlinear indentation model is needed. In this paper, we use second-order elasticity theory to capture larger amplitude deformations and material nonlinearity. We provide a general solution for the contact problem for deformations that are second-order in indentation amplitude with arbitrary indenter profiles. Moreover, we derive analytical solutions by using either parabolic or quartic surfaces to mimic a spherical indenter. The analytical prediction for a quartic surface agrees well with finite element simulations using a spherical indenter for indentation depths on the order of the indenter radius. In particular, the relative error between the two approaches is less than 1% for an indentation depth equal to the indenter radius, an order of magnitude less than that observed with models which are either first-order in indentation amplitude or those which are second-order in indentation amplitude but with a parabolic indenter profile.