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Update step-44 documentation. #13174

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Jan 6, 2022
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Update step-44 documentation. #13174

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7 changes: 3 additions & 4 deletions examples/step-44/doc/intro.dox
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Original file line number Diff line number Diff line change
Expand Up @@ -319,9 +319,8 @@ The fourth-order elasticity tensor in the spatial description $\mathfrak{c}$ is
\qquad \text{and thus} \qquad
J\mathfrak{c} = 4 \mathbf{b} \dfrac{\partial^2 \Psi(\mathbf{b})} {\partial \mathbf{b} \partial \mathbf{b}} \mathbf{b} \, .
@f]
The fourth-order elasticity tensors (for hyperelastic materials) possess both major and minor symmetries.

The fourth-order spatial elasticity tensor can be written in the following decoupled form:
This tensor (for hyperelastic materials) possesses both major and minor symmetries, and it
can be written in the following decoupled form:
@f[
\mathfrak{c} = \mathfrak{c}_{\text{vol}} + \mathfrak{c}_{\text{iso}} \, ,
@f]
Expand All @@ -330,7 +329,7 @@ where
J \mathfrak{c}_{\text{vol}}
&= 4 \mathbf{b} \dfrac{\partial^2 \Psi_{\text{vol}}(J)} {\partial \mathbf{b} \partial \mathbf{b}} \mathbf{b}
\\
&= J[\widehat{p}\, \mathbf{I} \otimes \mathbf{I} - 2p \mathcal{I}]
&= J[\widehat{p}\, \mathbf{I} \otimes \mathbf{I} - 2p \mathcal{S}]
\qquad \text{where} \qquad
\widehat{p} \dealcoloneq p + \dfrac{\textrm{d} p}{\textrm{d}J} \, ,
\\
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