Clarification on Definition of Green Strain

In summary, the conversation is about a question regarding continuum mechanics and the definition of green strain. The person is seeking help from others and mentions that the equation includes a 2, but they do not understand its purpose. It is explained that the 2 is necessary for the equation to reduce to the linear strain tensor for small displacements.
  • #1
EvanZ
1
0
Hey, everyone. I'm new here. This is a continuum mechanics question. If it's the wrong forum, please let me know, of course.

The question is pretty simple, but since I haven't been able to find an answer, I'm looking for "crowd help". Green strain [itex]\mathbf{E}[/itex] is usually defined implicitly by the following equation:

[itex]ds^2-dS^2=2\mathbf{dX}\cdot \mathbf{E}\cdot\mathbf{dX}[/itex]

For the life of me, I can't explain why the 2 is necessary or where it comes from. I assume there's a good reason, though. Any thoughts are appreciated.
 
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  • #2
The two is there so that it reduces to the usual linear strain tensor in the limit of small displacements.
 

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