# Transformation of Test Data for the Specification of a Viscoelastic Marlow Model

## Abstract

**:**

## 1. Introduction

#### 1.1. Hyperelasticity and Marlow Model

#### 1.2. Combination of Hyperelasticity and Viscoelasticity

#### 1.3. Instantaneous Response

#### 1.4. Aim

## 2. Results

#### 2.1. Stress Transformation and Compressibility

#### 2.2. Viscoelasticity in Uniaxial Tension

#### 2.3. Consideration of Constant Strain Rate

#### 2.4. Discretization of Stress Function

#### 2.5. Implementation and Convergence

## 3. Discussion

- The model describes strain-rate dependence of the mechanical behavior.
- The model can be defined so that it fits exactly to the result of one experiment, e.g., a tensile test. In contrast, hyperelastic models based on a small set of parameters like polynomial models or Ogden’s model exhibit significant deviations from experimental data for some materials.
- The parameter identification is direct in the sense that it requires no optimization procedure. Consequently, the result does not depend on parameters of an optimization like the choice of an absolute or relative error measure, the optimization algorithm, or the initial values.

## 4. Materials and Methods

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Example stress–strain curves showing tensile test data, transformed data, and verification.

${\mathit{g}}_{1}$ | ${\mathit{\tau}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{\tau}}_{2}$ | ${\mathit{g}}_{3}$ | ${\mathit{\tau}}_{3}$ | ${\mathit{g}}_{4}$ | ${\mathit{\tau}}_{4}$ | ${\mathit{g}}_{5}$ | ${\mathit{\tau}}_{5}$ | K |
---|---|---|---|---|---|---|---|---|---|---|

in s | in s | in s | in s | in s | in GPa | |||||

0.3539 | 0.08124 | 0.07458 | 1.692 | 0.05052 | 35.23 | 0.04117 | 733.5 | 0.04575 | 15275 | 2.5 |

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**MDPI and ACS Style**

Hesebeck, O.
Transformation of Test Data for the Specification of a Viscoelastic Marlow Model. *Solids* **2020**, *1*, 2-15.
https://doi.org/10.3390/solids1010002

**AMA Style**

Hesebeck O.
Transformation of Test Data for the Specification of a Viscoelastic Marlow Model. *Solids*. 2020; 1(1):2-15.
https://doi.org/10.3390/solids1010002

**Chicago/Turabian Style**

Hesebeck, Olaf.
2020. "Transformation of Test Data for the Specification of a Viscoelastic Marlow Model" *Solids* 1, no. 1: 2-15.
https://doi.org/10.3390/solids1010002