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Nonlinearity in Silicon

Posted 24 juin 2016, 17:07 UTC−4 Version 5.2 1 Reply

Pratyusha Karri
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Hi! I'm trying to study the non-linear frequency response in a Silicon resonator for different crystal orientations. Is it possible to define anisotropy under the non-linear elastic material? Also can COMSOL show a peak bending effect in the frequency versus displacement plot?
1 Reply Last Post 24 juin 2016, 23:21 UTC−4
Daniel Connelly
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Posted: 8 years ago 24 juin 2016, 23:21 UTC−4
How does nonlinearity work with anisotropy?

For a linear response, you have:
σij = Eijkl ϵkl

with implicit summation over repeated indices.

But with nonlinear, you'd have:

σij = Eijkl ϵjk + E'ijklmn ϵmn ϵkl

where E' is the 2nd order contribution

Sure, there's symmetry reduction, but that's a lot of coefficients.

Okay... I just found this: www-sop.inria.fr/asclepios/Publications/Herve.Delingette/Picinbono-GM03.pdf
How does nonlinearity work with anisotropy? For a linear response, you have: σij = Eijkl ϵkl with implicit summation over repeated indices. But with nonlinear, you'd have: σij = Eijkl ϵjk + E'ijklmn ϵmn ϵkl where E' is the 2nd order contribution Sure, there's symmetry reduction, but that's a lot of coefficients. Okay... I just found this: http://www-sop.inria.fr/asclepios/Publications/Herve.Delingette/Picinbono-GM03.pdf

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