Stress vector

1. Aug 7, 2008

leofur

Hi all,
I'm doing a MEMS project, I have a cantilever beam with a mass at its end, I need to calculate the stress tensor at the beam contact point, there is a piezoelectric matirial there, and I want to calculate the voltage it generates. somebody can please help me and explain how to calculate the stress tensor there, I don't know solid state physics that good, and the last 2 days I was searching the web for this, but couldn't find anything.

2. Aug 7, 2008

Modey3

leofur,

Not to pull hairs, but stress isn't a vector (first rank tensor) quantity. It is a second-rank tensor. Let me try to put the picture together. You have a piezoelectric material, which is actuating a cantilever beam and you want to calculate the stress at the beam/piezoelectric material contact point when a mass is loaded to the cantilever. Is that correct? Or is the beam being used to generate an electric field within piezoelectric material? Be very careful in how you phrase questions and don't be afraid to write a lot of detail.

Either way, the stress tensor in a cantilever beam will vary with distance from the neutral axis of bending. The stress in your piezoelectric material will depend where is situated with reference to the beam's neutral axis. The voltage generated in a piezoelectric material is proportional to the stress state. There must be some constitutive relationship in a text book. Or look up the ginzburg-landau theory for piezoelectric phase transformations. This theory is the basis for developing a constitutive relationship between stress and electric field.

modey3

3. Aug 9, 2008

Andy Resnick

Well, if you know the cantiliever geometry and boundary conditions (built-in cantilever, for example), you can calculate the deformation (or approximate it fairly easily), and from the material properties, the local stress. Plug that into the appropriate piezo-electric coefficient, and you are done.

Can you more simply empirically determine the relationship- using a series of cantilevers, or masses, or...?