hoomanya
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Could someone please tell me what the tilde sign stands for in this equation:$$w_{0}\left(e_{ij}\right)=\int s_{ij}d\tilde{e_{ij}}=\frac{1}{2}\,\underline{\underline{s}}:\underline{\underline{e}}$$
where and ##\underline{\underline{e}}## is the Green Lagrangian strain tensor and ##\underline{\underline{s}}## is the 2nd Piola-Kirchoff stress tensor, if I'm not mistaken ##w_{0}## is the strain energy in the material reference frame.
I have been trying to find out but no luck yet. I thought it was the Voigt notation but apparently it isn't. I have seen this notation in a lot of literature related to hyperelastic materials which I think uses the same symbol, for instance:
p.s. I am not sure how to create inline equations here. I would appreciate it if someone edited this or told me how.
[example_paper][1] [1]: http://www.mse.berkeley.edu/groups/morris/MSE205/Extras/Elastic.pdf
where and ##\underline{\underline{e}}## is the Green Lagrangian strain tensor and ##\underline{\underline{s}}## is the 2nd Piola-Kirchoff stress tensor, if I'm not mistaken ##w_{0}## is the strain energy in the material reference frame.
I have been trying to find out but no luck yet. I thought it was the Voigt notation but apparently it isn't. I have seen this notation in a lot of literature related to hyperelastic materials which I think uses the same symbol, for instance:
p.s. I am not sure how to create inline equations here. I would appreciate it if someone edited this or told me how.
[example_paper][1] [1]: http://www.mse.berkeley.edu/groups/morris/MSE205/Extras/Elastic.pdf
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