Is there a way to find out the theoretical stretch of an elastic band?

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SUMMARY

The discussion focuses on calculating the theoretical heat dissipation through hysteresis in elastic bands, particularly under non-linear stretching conditions where Hooke's Law is not applicable. The user seeks methods to graph the theoretical lengths during loading and unloading phases. They consider using Poisson's ratio for rubber but express uncertainty about the appropriate formula. The conversation highlights the complexity of the problem and the need for advanced understanding of material properties.

PREREQUISITES
  • Understanding of hysteresis in materials
  • Familiarity with non-linear elasticity
  • Knowledge of Poisson's ratio and its application in rubber
  • Basic principles of thermodynamics related to heat dissipation
NEXT STEPS
  • Research non-linear elasticity models for rubber materials
  • Study the application of Poisson's ratio in calculating stress and strain
  • Explore methods for graphing hysteresis loops in elastic materials
  • Investigate advanced thermodynamic principles related to heat dissipation in materials
USEFUL FOR

Researchers in material science, students conducting experiments on elastic materials, and engineers focused on the thermal properties of rubber under stress.

kodadra
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I'm in the middle of doing an experiment where I find the heat dissipation by hysteresis through the stretching of an elastic band. I have experimentally found out how much heat is dissipated, but I was wondering if there is a way to theoretically find out the dissipated heat, most likely by creating a graph of the theoretical lengths of loading and unloading. The elastic bands are stretched with great forces, so they have non-linear extensions thus Hooke's Law doesn't work. Are there any other possible solutions?
 
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I thought I could possibly use Poisson's ratio for rubber to calculate it, but I'm not sure what formula I could use. This might even just be too complicated for my level right now.
 

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