The Interrelated Mechanics of Poroelastic Gels in Time- and Frequency-Domain Detected by Indentation

Abstract

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.