# Characterization of Shear Strain on PDMS: Numerical and Experimental Approaches

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Constitutive Models

^{T}is the transposed deformation gradient and p is a multiple of Lagrange obtained according to the state of tension T.

_{3}, is 1 and Equation (5) is defined as:

_{1}).

_{1}, C

_{2}and C

_{3}are constants of the material that are determined from the experimental tests.

_{1}and I

_{2}are the constant strain and C

_{10}and C

_{01}are the material constants.

_{i}and α

_{i}are material constants that can be positive, negative, integer or not.

_{1}and I

_{2}, of the left Cauchy-Green deformation tensor, with Cij denoting material constants. The strain energy is given by [34]:

_{1}− 3.

## 3. Materials and Methods

#### 3.1. Experimental Tests

^{®}by enterprise Dow Corning from Wiesbaden, Germany, To obtain the PDMS resin, it was necessary to mix the curing agent with the prepolymer; for each 10 g of prepolymer, 1 g of the curing agent was added (10: 1).

^{3}) was determined which is very similar to other references [40].

#### 3.1.1. Tensile Testing

#### 3.1.2. Shear Testing

^{3}dimensions were used. The bars’ surfaces were sanded and degreased with acetone to improve the adhesion of the PDMS to the steel. After the cleaning, the PDMS bonding was done using a cyanoacrylate structural adhesive Locttice Super Glue 3 (Germany), presenting the following configuration Figure 3.

^{®}DIC system made it Dutchman Blvd. Irmo, SC, USA was used to measure the strain field in-plane and out-plane of the PDMS surface.

#### 3.2. Numerical Simulation

^{®}R18.1 academic research mechanical license.

## 4. Results and Discussion

#### 4.1. Experimental

#### 4.2. Numerical

^{−3}.

#### 4.3. Comparison

## 5. Conclusions

- From experimental tests, the hyperelastic behavior of PDMS was verified using a simple shear test. The DIC tests showed that the most significant shear strain occurred in the centre of the PDMS plate. These experimental tests also verified that the PDMS rupture occurred at the bonding interface between the steel and PDMS plates. The rupture happened for different PDMS thicknesses. For 4 mm of PDMS, the specimen broke up at a 154 N of shear force. The specimen with 2 mm of PDMS suffered rupture at a shear force of 80 N. For an equal value of shear force, a higher value of displacement happened for the higher PDMS thickness.
- The numerical simulations were done using four hyperelastic constitutive models (Mooney–Rivlin, Yeoh, Gent and polynomial). All the hyperelastic constitutive models presented similar results despite some critical differences. The main reason to obtain similar results in shear stress was due to the appliance of low displacement values and the constitutive models, for this displacement level, have identical behavior. The values that show a greater difference in shear strain occurred for the Mooney–Rivlin constitutive model when compared with the other constitutive models (see Table 2). The numerical model with 2 mm of PDMS results in higher values of shear strain than with 4 mm. So, for low displacement levels it is possible to use any of the hyperelastic constitutive to simulate the shear test.
- Qualitatively, in the central region of the specimen, the numerical and experimental results have similar behavior, and the values of shear strain are close. Nevertheless, the maximum relative error between the numerical and experimental results is very different for the two thickness values. It is possible to conclude that, for higher values of displacement and thicknesses, the numerical simulation results move further away from experimental values.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 8.**Image of 2 mm polydimethylsiloxane (PDMS) thickness: (

**a**) before deformation; (

**b**) beginning of rupture; (

**c**) after rupture.

**Figure 9.**Image of 4 mm PDMS thickness: (

**a**) before deformation; (

**b**) beginning of rupture; (

**c**) after rupture.

**Figure 10.**(

**a**) Shear strain field for a 2 mm thickness PDMS plate; (

**b**) Shear strain field for a 4 mm thickness PDMS plate.

**Figure 11.**Shear strain field obtained by numerical simulation using the Mooney–Rivlin constitutive model. (

**a**) 2 mm and (

**b**) 4 mm of PDMS thickness.

**Figure 12.**Shear strain obtained numerically and experimentally along the y-direction for 2 mm of PDMS.

**Figure 13.**Shear strain obtained numerically and experimentally along the y-direction for 4 mm of PDMS.

Numerical Simulation | Displacement [mm] |
---|---|

1 | 0.5 |

2 | 0.2 |

Constitutive Model | Average | Minimum | Maximum | |
---|---|---|---|---|

Mooney-Rivlin 3 parameter | −0.09684 | −0.04678 | −0.10238 | PDMS Thickness 2 mm |

Yeoh 3rd Order | −0.09680 | −0.04722 | −0.10237 | |

Polynomial 3rd Order | −0.09680 | −0.04362 | −0.10514 | |

Gent | −0.09680 | −0.04709 | −0.10240 | |

Mooney-Rivlin 3 parameter | −0.02056 | −0.00585 | −0.02128 | PDMS Thickness 4 mm |

Yeoh 3rd Order | −0.02060 | −0.00585 | −0.02128 | |

Polynomial 3rd Order | −.02060 | −0.00585 | −0.02128 | |

Gent | −0.02060 | −0.00585 | −0.02128 |

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**MDPI and ACS Style**

Souza, A.; Marques, E.; Balsa, C.; Ribeiro, J. Characterization of Shear Strain on PDMS: Numerical and Experimental Approaches. *Appl. Sci.* **2020**, *10*, 3322.
https://doi.org/10.3390/app10093322

**AMA Style**

Souza A, Marques E, Balsa C, Ribeiro J. Characterization of Shear Strain on PDMS: Numerical and Experimental Approaches. *Applied Sciences*. 2020; 10(9):3322.
https://doi.org/10.3390/app10093322

**Chicago/Turabian Style**

Souza, Andrews, Eduardo Marques, Carlos Balsa, and João Ribeiro. 2020. "Characterization of Shear Strain on PDMS: Numerical and Experimental Approaches" *Applied Sciences* 10, no. 9: 3322.
https://doi.org/10.3390/app10093322