Stress/strain tensor for anisotropic materials

[chiraganand]

Hi,

I understand stress, strain but when it moves on to 3 dimension anisotropic materials using tensors and stiffness matrices I get confused with einstein's notation. can someone please help me out in this regard to undrstand how stiffness and compliance matrices get reduced for monoclinic, orthotropic materials?

 

[Chestermiller]

Hi,

I understand stress, strain but when it moves on to 3 dimension anisotropic materials using tensors and stiffness matrices I get confused with einstein's notation. can someone please help me out in this regard to undrstand how stiffness and compliance matrices get reduced for monoclinic, orthotropic materials?

Are you trying to do it for a stack of uni's?

 

[chiraganand]

i wan to start off with a stack of uni's and then move on to bi-directionals. The main problem is i am unable to visualise einstein's notation and to differentiate when it is that and when it is not.

 

[Chestermiller]

i wan to start off with a stack of uni's and then move on to bi-directionals. The main problem is i am unable to visualise einstein's notation and to differentiate when it is that and when it is not.

This is einstein's summation convention?

 

[chiraganand]

This is einstein's summation convention?

yep..

 

[Chestermiller]

Please tell us what your understanding of the einstein summation convention is so that we can better pinpoint what your difficulty is.

 

[chiraganand]

Please tell us what your understanding of the einstein summation convention is so that we can better pinpoint what your difficulty is.

Ok einstein summation is that for when an index is being repeated in the forumlation for example a₁₁+a_{12/SUB]+a13+a14 then it can be written as aij j=1,2,3} and also for orthotropic materials the compliance/stiffness matrix reduces to 21 constants. Can someone please explain how??

 

[Chestermiller]

Ok einstein summation is that for when an index is being repeated in the forumlation for example a₁₁+a_{12/SUB]+a13+a14 then it can be written as aij j=1,2,3} and also for orthotropic materials the compliance/stiffness matrix reduces to 21 constants. Can someone please explain how??

That's not the Einstein summation convention. The Einstein convention says that, if an index is repeated in an expression, summation over that index is implied. It's the same as if you had a summation sign in front of the expression. The Einstein summation convention is typically used in stress-strain contexts to concisely represent matrix multiplication (without having to include the summation sign). An example is a_ijb_jk.