A time-shift correction for extraction of viscoelastic parameters from ramp-hold AFM experiments

Abstract

The stress relaxation and creep measurements are commonly implemented in AFM indentation experiments to analyze the viscoelastic properties of a sample in the time domain. The assumption of an instantaneous step load is often applied which can lead to erroneous estimation of viscoelastic parameters from the experimental data. A viscoelastic solution for the ramp-hold indentation profile might be used but requires higher computational costs. Here, we employed simulations for the ramp-hold indentations for the power-law rheology (PLR) and standard linear solid models. The error coming from the instantaneous load assumption was analyzed and a simple empirical correction for the finite ramp time was employed as a time shift of the hold region. The correction was tested in experiments on cells, in which the data from stress relaxation, creep, and force volume experiments were compared. The correction showed good applicability for the extraction of the PLR viscoelastic parameters.

Measuring biological materials mechanics with atomic force microscopy ‐ Determination of viscoelastic cell properties from stress relaxation experiments

“…The SLS has one associated relaxation time, while the Maxwell model has two. Relaxation times of cells and cytoskeletal structures have been reported to be in the range of a few seconds (Efremov et al, 2021 ; Hiratsuka et al, 2009 ; Moreno‐Flores et al, 2010b ). Importantly, the measured relaxation times scale with the experimental time.…”

Grading cartilage damage with diffuse reflectance spectroscopy: Optical markers and mechanical properties

“…In addition, the experimental curves were processed by the standard Hertz's model (also with the finite-thickness correction), which considers the sample as purely elastic. Numerical processing was performed in MATLAB (MathWorks, Natick, MA) using previously developed algorithms [31,32].…”

Study on the Testing Method of Relaxation Modulus under Spherical Indenter Loading

“…A large number of scholars have studied and analyzed this, hoping to reduce the influence of the strain application process on the relaxation modulus test process through a reasonable method. Some scholars used the step strain history method of the indentation instrument to measure the relaxation modulus by correcting the data in the relaxation stage [6][7][8][9][10]. e correction method of Zapas and Phillips [6] is the simplest, which is calculated by moving the relaxation area forward for a certain time range.…”

“…e correction method of Zapas and Phillips [6] is the simplest, which is calculated by moving the relaxation area forward for a certain time range. Of course, some scholars calculate the relaxation modulus by adding correction factors [8][9][10]. Among them, the best method is to calculate the relaxation modulus by using the measured data with the minimum error between the relaxation data after 5t 0 -10t 0 and the ideal step loading in a recursive manner [6,7].…”