# Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Depth-Sensing Indentation: Conventional Approaches

#### 2.1. DSI by Sharp Indenters: The BASh Formula and the Oliver–Pharr Approach

#### 2.2. Adhesion in Depth-Sensing Indentation, and the Conventional Use of Spherical Indenters

## 3. The BG Method

## 4. The Extended BG (eBG) Method

^{2}. In the simulation, the Tabor–Muller parameter was calculated after setting all the parameters. Hence, the validity of the JKR theory in this scenario was confirmed a priori, and no further checks were done. The theoretical force-displacement curve is depicted if Figure 4 as the solid line. The compressive part of it was used to generate noisy data emulating a DSI experiment. The noisy data is denoted by points in Figure 4 (shifted).

^{2}in the high noise scenario, ${E}^{*}=0.9987$ MPa and $w=101.2$ mJ/m

^{2}in the low noise scenario.

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Preliminary fitting the experimental data with an auxiliary curve $\mathsf{\Psi}\left(\delta \right)$.

**Figure 3.**The workflow of the numerical simulation demonstrating the accuracy and robustness of the extended Borodich–Galanov (eBG) method.

**Figure 4.**Numerical simulation. The theoretical force-displacement curve (solid line) and an example data sets simulating DSI readings (dots, shifted). (

**a**) High noise scenario. (

**b**) Low noise scenario.

**Figure 5.**Numerical simulation. The results of identification of material properties from 20 data sets containing noise and random coordinate origin shift. (

**a**) High noise scenario. (

**b**) Low noise scenario.

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**MDPI and ACS Style**

Perepelkin, N.V.; Borodich, F.M.; Kovalev, A.E.; Gorb, S.N.
Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials. *Nanomaterials* **2020**, *10*, 15.
https://doi.org/10.3390/nano10010015

**AMA Style**

Perepelkin NV, Borodich FM, Kovalev AE, Gorb SN.
Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials. *Nanomaterials*. 2020; 10(1):15.
https://doi.org/10.3390/nano10010015

**Chicago/Turabian Style**

Perepelkin, Nikolay V., Feodor M. Borodich, Alexander E. Kovalev, and Stanislav N. Gorb.
2020. "Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials" *Nanomaterials* 10, no. 1: 15.
https://doi.org/10.3390/nano10010015