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New Mathematical Model for Correlation Between Tensile Elastic Modulus and Shore "A" and "00" Hardness for Flexible
Josip Hoster1, Nikola Šimunić1, Tihana Kostadin1
1Mechanical Engineering Department, Karlovac University of Applied Sciences, Trg J.J. Strossmayera 9, 47000 Karlovac, Croatia.
Polymers
|March 14, 2026
Summary
A new correlation model estimates the initial tensile elastic modulus of flexible polymers using Shore hardness measurements. This practical method, applicable to various rubbers and silicones, offers rapid material characterization.
Area of Science:
- Materials Science
- Polymer Engineering
- Mechanical Engineering
Background:
- Estimating the initial tensile elastic modulus of flexible polymers is crucial for material selection and performance prediction.
- Existing methods may be time-consuming or destructive, limiting rapid assessment.
Purpose of the Study:
- To develop a robust correlation model for predicting the initial tensile elastic modulus of flexible polymers based on Shore hardness.
- To provide a practical, non-destructive method for rapid material characterization.
Main Methods:
- Developed a piecewise exponential function model correlating Shore hardness (OO and A scales) with initial tensile elastic modulus.
- Utilized true stress and logarithmic strain with iterative corrections for large strain analysis.
- Determined model coefficients by minimizing S2 error norm and relative error, ensuring C0 continuity.
Main Results:
- The developed correlation model accurately predicts elastic modulus across OO and A hardness scales.
- Maximum relative errors were 13.4% for the OO scale and 7% for the A scale.
- The model demonstrates monotonic behavior and provides reasonable elastic modulus values at hardness extremes.
Conclusions:
- The correlation model offers a practical and rapid approach for estimating initial tensile elastic modulus from non-destructive hardness measurements.
- This method is valuable for industrial applications and material modeling, including dental surgery simulations.
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