Consider a heat shrink film (as used in shrink sleeves that decorate plastic or glass bottles). These materials are produced by blow extrusion. When the film is heated (hot steam, hot air or radiation) the film will retract to a smaller size, typically anisotropic (shrink more in one direction than in the other).

Empirical data is available for unconstrained samples of film. However in real life situations there are constraints to the movement of the film and the system will look for a balance of thermal shrink and elastric stretch forces.

What would be a practical model for the macroscopic mechanics of such film? This model should provide internal forces (shrink and stress forces) for a given temperature, strain and history of an small area of film.

I wonder how related this is to visco-elasticity? VE can be modeled as a system of springs and dampers. Because of the damper(s) the forces also depends on the history. Does it make sense to model heat shrinking as visco-elasticity with temperature-dependent springs and dampers?


1 Answer 1


Yes, a Maxwell–Wiechert model would be appropriate for the modelling of such a plastic, once it is deformed.

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As a first approach I would suggest making all the individual Maxwell-Elements purely linear and only adding temperature dependency to the long term Modulus $K_0$ (usually referred to as $G_\infty$). This should give a good first approximation. Otherwise you might have trouble fitting your individual Parameters to empirical data.

These types of Models are easily integrated (or already present) in modern FEM-packages like ANSYS.

However, for the deformation process itself, making it shrink while heated, you will need to play with the $\Delta \rho \sim \Delta T$ scale. As you have empirical data for this, this should again be no problem. This feature should be readily available in current FEM applications.

Basically you will end up with 2 Models using the above. The interplay between the two would give the desired result of heat shrinking plastic.

  • $\begingroup$ What do you mean with $\Delta\rho$ ? $\endgroup$ Sep 18, 2011 at 20:56
  • $\begingroup$ The change in density in relation to the change in Temperature $\endgroup$
    – Michael
    Sep 19, 2011 at 8:10
  • $\begingroup$ How would the model then link a density change to a shrink force? Wouldn't the damping factors and/or the spring rest lengths need to be temperature dependent? $\endgroup$ Sep 19, 2011 at 21:43
  • $\begingroup$ In pure theory and real life, density change will cause it to shrink. How this is implemented in different FEM-packages can however vary. Also, making your damping factors, etc, temperature dependant can make your Model more accurate. But they will not make your plastic shrink. Imagine a fully relaxed model (without density change this time) with no external forces acting on it. Now heat it up. while the dampners/springs change their factors, nothing actually happens => No shrinking $\endgroup$
    – Michael
    Sep 20, 2011 at 8:55
  • $\begingroup$ Imagine a strip of shrink film at rest, contrained at its current length. Then you raise the temperature. How will your model return the proper shrink force? $\endgroup$ Sep 20, 2011 at 22:03

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