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A question about strain in graphene

  1. Jul 10, 2015 #1
    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|?
     

    Attached Files:

  2. jcsd
  3. Jul 15, 2015 #2

    jedishrfu

    Staff: Mentor

    Are you uncertain of how to do a matrix addition and then a matrix x vector?
     
  4. Jul 16, 2015 #3
    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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