I want to do a very simplified model to try to modelize the change of temperature in ultrasonic welding of polimers.
As a starting point, I only want to simulate the change of temperature of a 1D homogeneous polymer (viscoelastic solid) when I apply a constant pressure and ultrasounds on it.
I considered two types of models:
-an energetic one using the energy of the ultrasonic wave, the impedances for the transmited-reflected energy and de absorption coeficient of the materials
-a mechanical one, considering the strain induced by the sonotrode and the resulting stress using the Voigth model. Then the work done by the material is obtained and, from this, the quantity of heat generated.
My question/problem is: how can I introduce in these models the heat generated due to the applied pressure in the solid ?
If anyone can help me, i would be pleased.