Calculating Stress Tensor and Voltage for MEMS Project

In summary: There is a constitutive relationship between stress and electric field in piezoelectric materials, but it is not easy to empirically determine. You can try to empirically determine the relationship by loading a series of cantilevers and measuring the deformation. Alternatively, you can measure the stress state in a piezoelectric material by using a tensiometer.
  • #1
leofur
2
0
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.
 
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  • #2
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 textbook. 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
leofur said:
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.

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...?
 

1. How is the stress tensor calculated for MEMS devices?

The stress tensor for MEMS devices is typically calculated using finite element analysis (FEA) software. This involves dividing the device into small elements and solving for the stress and strain in each element. The results are then combined to generate a complete stress tensor map for the device.

2. What factors influence the stress tensor in MEMS devices?

The stress tensor in MEMS devices is influenced by a variety of factors, including the geometry and material properties of the device, as well as any external forces or loads applied to the device. The fabrication process and any residual stresses from manufacturing also play a role in determining the stress tensor.

3. How is the voltage calculated for MEMS devices?

The voltage for MEMS devices can be calculated using the piezoresistive effect, which describes the change in electrical resistance of a material under mechanical stress. By measuring the change in resistance of a piezoresistive material on the MEMS device, the applied stress can be determined and converted into a voltage value.

4. What is the significance of the stress tensor and voltage in MEMS devices?

The stress tensor and voltage are important parameters in the design and operation of MEMS devices. They provide valuable information about the mechanical and electrical performance of the device, and can help identify areas of potential failure or optimization. Additionally, these values are used in the design process to ensure the device can withstand expected stresses and function properly.

5. How can the stress tensor and voltage be used to improve MEMS device performance?

By accurately calculating and analyzing the stress tensor and voltage in MEMS devices, engineers can identify areas of high stress or weak points in the design. This information can then be used to make improvements to the device, such as altering the material or geometry, to enhance its performance and durability. Additionally, the stress tensor and voltage can be used to optimize the design for specific applications or environments.

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