# Stress due to the mismatch of thermal expansion coefficients of two different attached materials

I'm simulating the thermo-electro-mechanical behavior of a copper wire which is surrounded by silicon dioxide. In other words, the wire segments is under mechanical and thermal loads and at the same time an electrical current is flowing in it.

In order to perform the simulation accurately, I think that I should consider an initial stress due to the mismatch of thermal expansion coefficients between copper and oxide. I am using COMSOL to do my simulation. The options that COMSOL provides me with are "body load" and "boundary load". Can anyone advise me which one I should choose? Which one is a more realistic assumption. Thanks.

• I think you'll get better answers if you post this question on SciComp.SE . Aug 27, 2013 at 8:32
• The initial stress is caused by the fact that the current temperature is different than the temperature at which the SiO2 was bonded to the copper. Unless you know the conditions under which that happened you will have a hard time getting your simulation right. And if you do know - then I would use that as the initial condition (no stress, temperature $T_1$) and then solve for the new condition (ambient temperature $T$, current through wire $I$, resistance per unit length $R$, thermal conductities, h factor of surface, medium beyond wire...). Don't take a shortcut. Jul 3, 2014 at 22:19

It differs depending on how you formulate it. However, based on your experiments, "Body load" is more descriptive and realistic. Essentially you may want to add a diagonal body load (i.e. $xx,yy$ and $zz$).

I'm not a COMSOL user, but it seems to be a boundary load since the mismatch in thermal expansion creates a force that acts only along the interface between the two solids.

Multiphysics simulations can of course model thermal expansion which is typically a body property (some codes will even call it a "body load"). However, if you are trying to get around modeling the expansion itself and just want to apply the mismatch directly, it will be a boundary condition applied at the interface between the two materials, since that is the only location at which they can act on each other. That boundary condition will be a built in interface strain. How that strain is shared between the two solids will depend on their relative stiffnesses. It may actually be best to let COMSOL figure that one out by having run through the thermal expansion model at least once.

• I think so, but how do you justify that? Aug 28, 2013 at 3:23