]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Update step-44 documentation. 13174/head
authorWolfgang Bangerth <bangerth@colostate.edu>
Thu, 6 Jan 2022 11:49:17 +0000 (04:49 -0700)
committerWolfgang Bangerth <bangerth@colostate.edu>
Thu, 6 Jan 2022 11:49:17 +0000 (04:49 -0700)
examples/step-44/doc/intro.dox

index 886720ef59d24fe23af3791dc3bbdecfc8979b5d..30660874aa9e65f1632590c126dde827cbf2710f 100644 (file)
@@ -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]
@@ -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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