A question about strain in graphene

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SUMMARY

The discussion focuses on calculating the positions of carbon atoms in graphene under uniaxial strain using the elastic theory framework. The equation ri'=(I+ε).ri is central to the calculations, where ri and ri' represent the positions before and after strain, respectively. The strain tensor ε is crucial for determining the new positions of the atoms. The user seeks assistance in computing the magnitudes |δ1|, |δ2|, and |δ3| based on the provided equations, highlighting confusion regarding matrix operations involved in the calculations.

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Materials scientists, mechanical engineers, and researchers working with graphene or other carbon-based materials will benefit from this discussion, particularly those focusing on the effects of strain on atomic structures.

barana
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Dear forum people
The new position of the carbon atoms under uniaxial strain r in the framework of elastic theory is shown by the following equation:
ri'=(I+ε).ri
in which ri and ri' are the position of the carbon atoms before and after the strain is applied, respectively.
I is the unit matrix and ε is the strain tensor which is attached.
I can't calculate ri' .
For example:

δ1=a(√3/2,-1/2) δ2=a(0,1) δ3=a(-√3/2,-1/2)
|δ1|=1+(3/4)ε11-(√3/2)ε12+(1/4)ε22
|δ2|=1+ε22
|δ3|=1+(3/4)ε11+(√3/2)ε12+(1/4)ε22

Can help me?
How calculate |δ1|,|δ2|,|δ3|?
 

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Are you uncertain of how to do a matrix addition and then a matrix x vector?
 
jedishrfu said:
Are you uncertain of how to do a matrix addition and then a matrix x vector?
I don't know how obtained |δ1|,|δ2|,|δ3|.
δ1=( √3/2*a(1-ε11)-a/2*ε12 ; √3/2a*ε21-a/2*(1-ε22))
According to δ1, |δ1| not equal with |δ1| above maintained.
 

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