The force response of poroelastic materials including poroelastic gels to indentation is known to be time- and space-dependent (i.e., a function of indenter shape and size). Despite the complexity of the poroelastic response and in contrast to viscoelastic mechanics, poroelastic mechanics can be captured in terms of several intrinsic mechanical properties, such as elasticity, permeability, and Poisson ratio. While these intrinsic properties can be found from time-domain or frequency-domain master curves, indentation is usually conducted and analyzed only in the time domain using stress-relaxation or creep experiments. This paper advocates using frequency-domain analysis of poroelastic gels by reviewing and analyzing the relevant works of the literature. The analysis and methods, proposed here, enable researchers to characterize dynamic moduli of poroelastic gels in frequency domain using only a few experimental defining parameters. The authors have intentionally provided extensive details and background, to make this work useful for researchers who consider using frequency-domain analysis for the first time. This work reviews and explains the instantaneous elastic modulus, depicted over normalized time as a unifying and understandable set of master curves for time-domain stress relaxation tests on poroelastic gels for cylindrical, conical, and spherical indenters. The dynamic elastic modulus, depicted over normalized frequency, are derived symbolically and numerically and explained for the first time as master curves with simple transfer function in the frequency domain for presenting poroelastic mechanics of gels.

中文翻译：

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压痕检测时域和频域中多孔弹性凝胶的相关力学

众所周知，包括多孔弹性凝胶在内的多孔弹性材料对压痕的力响应与时间和空间有关（即，是压头形状和尺寸的函数）。尽管多孔弹性响应很复杂，并且与粘弹性力学相比，多孔弹性力学可以根据弹性、渗透性和泊松比等几种内在机械特性来捕捉。虽然这些内在特性可以从时域或频域主曲线中找到，但通常仅使用应力松弛或蠕变实验在时域中进行和分析压痕。本文通过对相关文献的回顾和分析，提倡对多孔弹性凝胶进行频域分析。这里提出的分析和方法，使研究人员能够仅使用几个实验定义参数来表征频域中多孔弹性凝胶的动态模量。作者有意提供了广泛的细节和背景，以使这项工作对首次考虑使用频域分析的研究人员有用。这项工作回顾并解释了瞬时弹性模量，在归一化时间内描绘为一组统一且易于理解的主曲线，用于对圆柱形、锥形和球形压头的多孔弹性凝胶进行时域应力松弛测试。在归一化频率上描绘的动态弹性模量以符号和数字方式导出，并首次作为在频域中具有简单传递函数的主曲线解释，用于呈现凝胶的多孔弹性力学。