Non-ideal effects in indentation testing of soft tissues

Abstract

Indentation has several advantages as a loading mode for determining constitutive behavior of soft, biological tissues. However, indentation induces a complex, spatially heterogeneous deformation field that creates analytical challenges for the calculation of constitutive parameters. As a result, investigators commonly assume small indentation depths and large sample thicknesses to simplify analysis and then restrict indentation depth and sample geometry to satisfy these assumptions. These restrictions limit experimental resolution in some fields, such as brain biomechanics. However, recent experimental evidence suggests that conventionally applied limits are in fact excessively conservative. We conducted a parametric study of indentation loading with various indenter geometries, surface interface conditions, sample compressibility, sample geometry and indentation depth to quantitatively describe the deviation from previous treatments that results from violation of the assumptions of small indentation depth and large sample thickness. We found that the classical solution was surprisingly robust to violation of the assumption of small strain but highly sensitive to violation of the assumption of large sample thickness, particularly if the indenter was cylindrical. The ramifications of these findings for design of indentation experiments are discussed and correction factors are presented to allow future investigators to account for these effects without recreating our finite element models.

Brain stiffens post mortem

“…In agreement with the literature, our loss modulus increases for increasing frequencies and exceeds the magnitude of the storage modulus (Samadi-Dooki et al, 2017). Several studies suggest to correct these moduli by a correction factor (Hayes et al, 1972; Finan et al, 2014), in our case ~1.2, to account for our large probe-radius-to-sample-thickness ratio of 0.75 mm/5 mm. This correction factor can be determined via finite element simulations (Samadi-Dooki etal., 2018) and depends on the contact condition between the brain slice and the petri dish.…”

Mechanical Characterization by Mesoscale Indentation: Advantages and Pitfalls for Tissue and Scaffolds

“…2A, normalized mean square error [NMSE] = 0.9959) as seen in other studies. 38,39 Regressions in the form of F d ð Þ ¼ C Á d b for force-displacement curves during the loading phase of indentations experiments, where both C and b are free coefficients, show that b ¼ 1:5 for indentations of 10% or less of the sample thickness (Fig. 2C).…”

Nanoindentation of Soft Biological Materials

“…Sometimes, the above equations may need to be modified owing to the non-ideal effects while mechanical characterization [31,75], such as the correction factor of size effect [76,77] and the compensating factor for the tip [78,79]. When it comes to micro/nano-scale (such as cell indentation), the above effect may be much more significant considering that the indentation depth is comparable to the cell dimension.…”