Indentation analysis of biphasic viscoelastic hydrogels

• The geometry of loading applied to a hydrogel has a dramatic effect on the response of the two phases within the hydrogel. By applying a shear load to a specimen, the solid matrix response can be isolated, since no fluid flow is induced.
• Other types of loading, including indentation, probe a combined response of both phases to varying degrees. A clear consequence of the build-up of interstitial fluid pressure is a higher instantaneous modulus value measured for indentation tests over that of shear tests.
• The instantaneous modulus is therefore not a good measure of material behavior since the values are test dependent. A better quantity to assess the true behavior of hydrogels is the relaxed modulus.
• The relaxed modulus from a load relaxation test is shown to agree within 17% of the relaxed modulus from a shear stress relaxation test. Relaxed modulus measurements from quasistatic indentation tests are found to be consistently higher than those from shear relaxation experiments. The relaxed modulus is only dependent on the elastic behavior of the matrix, not on the rate or geometry of applied load.
• A reliable estimate of relaxed modulus from quasistatic indentation requires the viscoelastic analysis of small indentation depths relative to the radius of the indenter. Beyond approximately 15% of the indenter radius, increasing indentation depths cause a growing bias in the modulus estimate. At the same time, noise in the measured force and uncertainty in contact lead to larger errors in the modulus estimate at small depths.
• Therefore, to avoid significant random errors and minimize the error due to the bias, an appropriate indentation depth must be chosen for analysis. In this study for gelatin hydrogel ranging from 600 Pa to 2400 Pa in stiffness (relaxed modulus) and a load resolution of 0.01 g, the acceptable normalized indentation depth was δ/R = 0.15 – 0.25.

Mechanical properties of soft biological materials are dependent on the responses of the two phases of which they are comprised: the solid matrix and interstitial fluid. Indentation techniques are commonly used to measure properties of such materials, but comparisons between different experimental, and analytical techniques can be difficult. Most models relating load, and time during spherical indentation are based on Hertzian contact theory, but the exact limitation of this theory for soft materials are unclear. Here, we examine the response of gelatin hydrogels to shear and indentation loading to quantify combined effects of the solid, and fluid phases. The instantaneous behavior of the hydrogels is different for each test geometry, and loading rate, but the relaxed response, measured by the relaxed modulus, is the same for all tests, within 17%. Additionally, indentation depths from 15% to 25% of the radius of the spherical indenter are found to minimize error in the estimate of relaxed modulus.