Definition of the Lagrangian finite strain tensor

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The Lagrangian finite strain tensor is defined using a specific formula that incorporates partial derivatives and the Kronecker delta. The discussion clarifies that the expression is indeed in Einstein notation, implying that a summation over the index k is understood. It emphasizes that the summation symbol can be omitted due to the convention, which can lead to confusion due to the complexity of indices in mechanics. Understanding this notation is crucial for correctly interpreting the tensor's definition. The conversation highlights the importance of clarity in tensor notation for effective communication in mechanics.
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The Lagrangian finite strain tensor is defined as:

E_{i,j}=\frac{1}{2}\left(\frac{\partial x_k}{\partial X_i}\frac{\partial x_k}{\partial X_j}-\delta _{i,j}\right)

Is it in Einstein Notation so that there is a summation symbol missing, i.e. would it be the same thing if one wrote it as:

E_{i,j}=\frac{1}{2}\left(\sum _k \left(\frac{\partial x_k}{\partial X_i}\frac{\partial x_k}{\partial X_j}\right)-\delta _{i,j}\right)

It's that there is too many indices in mechanics, and it always gets me confused. Thanks a lot! :smile:
 
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Yes. this would involve use of the Einstein summation convention.
 
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