These equations were not intended to be a complete analysis as with FEA, but
were intended for quick evaluations to get a feel for differences in materials
and construction. I made a decision to evaluate everything in the plane of the
circuit and parallel to the traces. Generally that makes each composite
element's area in the x direction much less than in the y or z. At one point in
the derivation of the bending moments the poisson ratio terms include an Area x
/ Area y or Area x / Area z factor that allows you to relegate them to
insignificance. Additionally, during the derivation of the equilibrium thermal
strain the poisson ration terms cancel each other out as part of the force
balance assumption. Large deflections, plastic deformation of any of the
elements, layer creep, or gross disruption of the composite structure itself
will obviously invalidate the equations.

Andy Magee
Flex Guru - Consulting
[log in to unmask]
(937) 435-3629

"Andrew J. Scholand" wrote:

> Hi Andy,
>
> Andy Magee [mailto:[log in to unmask]] wrote on Sunday, January 10, 1999 5:53
> PM:
> > By the way, who exactly is your "group'?
>
> The long answer can be found be poking around
> http://eislab.gatech.edu
>
> Basically, we study the use of computer aided analysis and how to do it
> better.  We have a project (ProAM) applying our core expertise to electronic
> packaging, hence my interest in your warpage equation.  (Although our case
> study for warpage is just a big board, not a flex circuit)
>
> One newbie type question- I am curious as to why you do not include
> Poisson's ratio in your equation- is it because of a plain strain
> assumption?  Or is it discontinuities in the traces means loading is
> essentially only ever uniaxial?   Probably you answer this in your paper- i
> will try and get it from the folks at Rogers.
>
> Thanks for the information!
>                 Cheers,
>                         Andy

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