Institute for Regenerative Medicine, Sechenov University, 8 Trubetskaya St., Moscow, 119991, Russia.
N.N. Semenov Institute of Chemical Physics, 4 Kosygin St., Moscow, 119991, Russia.
Sci Rep. 2020 Aug 6;10(1):13302. doi: 10.1038/s41598-020-70361-y.
Instrumented indentation has become an indispensable tool for quantitative analysis of the mechanical properties of soft polymers and biological samples at different length scales. These types of samples are known for their prominent viscoelastic behavior, and attempts to calculate such properties from the indentation data are constantly made. The simplest indentation experiment presents a cycle of approach (deepening into the sample) and retraction of the indenter, with the output of the force and indentation depth as functions of time and a force versus indentation dependency (force curve). The linear viscoelastic theory based on the elastic-viscoelastic correspondence principle might predict the shape of force curves based on the experimental conditions and underlying relaxation function of the sample. Here, we conducted a computational analysis based on this theory and studied how the force curves were affected by the indenter geometry, type of indentation (triangular or sinusoidal ramp), and the relaxation functions. The relaxation functions of both traditional and fractional viscoelastic models were considered. The curves obtained from the analytical solutions, numerical algorithm and finite element simulations matched each other well. Common trends for the curve-related parameters (apparent Young's modulus, normalized hysteresis area, and curve exponent) were revealed. Importantly, the apparent Young's modulus, obtained by fitting the approach curve to the elastic model, demonstrated a direct relation to the relaxation function for all the tested cases. The study will help researchers to verify which model is more appropriate for the sample description without extensive calculations from the basic curve parameters and their dependency on the indentation rate.
仪器压痕已成为定量分析软聚合物和生物样本不同长度尺度机械性能的不可或缺的工具。这些类型的样本以其显著的粘弹性行为而闻名，并且不断尝试从压痕数据计算这些性质。最简单的压痕实验呈现出压头的逼近（深入样本）和缩回的循环，输出力和压痕深度作为时间的函数以及力与压痕依赖性（力曲线）。基于弹性-粘弹性对应原理的线性粘弹性理论可能会根据实验条件和样本的基础松弛函数预测力曲线的形状。在这里，我们基于该理论进行了计算分析，并研究了压头几何形状、压痕类型（三角形或正弦斜坡）以及松弛函数如何影响力曲线。考虑了传统和分数粘弹性模型的松弛函数。从分析解、数值算法和有限元模拟获得的曲线彼此匹配良好。揭示了与曲线相关的参数（表观杨氏模量、归一化滞后面积和曲线指数）的常见趋势。重要的是，通过将逼近曲线拟合到弹性模型来获得的表观杨氏模量，对于所有测试情况都显示出与松弛函数的直接关系。该研究将帮助研究人员在无需从基本曲线参数及其对压痕速率的依赖性进行广泛计算的情况下，验证哪个模型更适合样本描述。
