]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Fix some theory in step-44 introduction
authorJean-Paul Pelteret <jppelteret@gmail.com>
Thu, 11 Aug 2022 22:16:31 +0000 (00:16 +0200)
committerJean-Paul Pelteret <jppelteret@gmail.com>
Thu, 11 Aug 2022 22:16:31 +0000 (00:16 +0200)
The deviator tensor involves the  4th-order symmetric identity tensor, not the "normal" 4th-order identity tensor.

examples/step-44/doc/intro.dox

index 30660874aa9e65f1632590c126dde827cbf2710f..edd216beb7fa6b4a38f991bdce83606b6fb8752a 100644 (file)
@@ -260,7 +260,7 @@ Similarly, the Kirchhoff stress can be decomposed into volumetric and isochoric
        \boldsymbol{\tau}_{\text{iso}} &=
                2 \mathbf{b} \dfrac{\partial \Psi_{\textrm{iso}} (\overline{\mathbf{b}})}{\partial \mathbf{b}}
                \\
-               &= \underbrace{( \mathcal{I} - \dfrac{1}{3} \mathbf{I} \otimes \mathbf{I})}_{\mathbb{P}} : \overline{\boldsymbol{\tau}} \, ,
+               &= \underbrace{( \mathcal{S} - \dfrac{1}{3} \mathbf{I} \otimes \mathbf{I})}_{\mathbb{P}} : \overline{\boldsymbol{\tau}} \, ,
 @f}
 where
 $p \dealcoloneq \dfrac{\partial \Psi_{\text{vol}}(J)}{\partial J}$ is the pressure response.

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