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Principal Stretches  


am16d200
Posts: 3
(@am16d200)
New Member
Joined: 3 years ago

Hi Sir

I am working in modelling of hyper elastic materials

I have a doubt why the stretch invariants are expressed in terms of squares as compared to strain or stress invariants expressed in terms of linear terms of strain or stress

Thanks in advance

Rams

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3 Replies
Melly
(@melly)
Joined: 1 year ago

Eminent Member
Posts: 27
Posted by: @am16d200

Hi Sir

I am working in modelling of hyper elastic materials

I have a doubt why the stretch invariants are expressed in terms of squares as compared to strain or stress invariants expressed in terms of linear terms of strain or stress

Thanks in advance

Rams

It would be better if you can include the said expressions for easier understanding.

~Melly

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am16d200
(@am16d200)
Joined: 3 years ago

New Member
Posts: 3

@melly

The below one is principal invariants expressed i terms of squares of principal stretches in hyper elasticity

the below one is the stress invariant is expressed in terms of summation of principal stresses in elasticity

Why is the difference so

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Melly
(@melly)
Joined: 1 year ago

Eminent Member
Posts: 27
Posted by: @am16d200

@melly

The below one is principal invariants expressed i terms of squares of principal stretches in hyper elasticity

the below one is the stress invariant is expressed in terms of summation of principal stresses in elasticity

Why is the difference so

Well, this is pretty straight forward. 

In the first case, they are known as 'strain invariants' because they are based on the Cauchy-Green deformation tensors (both the left and the right result to the same values) whereas the second case are known as 'stress invariants' and are based on the Cauchy stress tensor. 

From the attached file, you can see how to get the strain invariants. The same method applies to stress invariants. 

Hope it helps. 

~Melly

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am16d200
Posts: 3
(@am16d200)
New Member
Joined: 3 years ago

@melly

Thank you for the reply

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