]> https://gitweb.dealii.org/ - dealii.git/commitdiff
Clarify a couple of things in the introduction to step-44. 18376/head
authorWolfgang Bangerth <bangerth@colostate.edu>
Tue, 22 Apr 2025 17:11:25 +0000 (11:11 -0600)
committerWolfgang Bangerth <bangerth@colostate.edu>
Tue, 22 Apr 2025 17:11:25 +0000 (11:11 -0600)
examples/step-44/doc/intro.dox

index 20e0e99782e97aff4efce73fe2c028aab9a4f677..85ef54a2256756e448dcabd4a73a988466b20005 100644 (file)
@@ -374,8 +374,11 @@ The boundary of the current configuration  $\partial \Omega$ is composed into tw
 $\partial \Omega = \partial \Omega_{\mathbf{u}} \cup \partial \Omega_{\sigma}$,
 where
 $\partial \Omega_{\mathbf{u}} \cap \partial \Omega_{\boldsymbol{\sigma}} = \emptyset$.
-The prescribed Cauchy traction, denoted $\mathbf{t}^\text{p}$, is applied to $ \partial \Omega_{\boldsymbol{\sigma}}$ while the motion is prescribed on the remaining portion of the boundary $\partial \Omega_{\mathbf{u}}$.
+The externally prescribed Cauchy traction, denoted $\mathbf{t}^\text{p}$, is applied to $ \partial \Omega_{\boldsymbol{\sigma}}$ while the motion (displacement) is prescribed on the remaining portion of the boundary $\partial \Omega_{\mathbf{u}}$.
 The body force per unit current volume is denoted $\mathbf{b}^\text{p}$.
+(In these terms, the superscript $\text{p}$ is meant to suggest that a
+quantity is *prescribed*, not that it is related to the unknown pressure
+$\tilde p$.)
 
 
 
@@ -494,7 +497,7 @@ Thus,
 @f}
 where
 @f{align*}{
-       D_{d \mathbf{u}} R( \mathbf{\Xi}; \delta \mathbf{\Xi})
+       D_{d \mathbf{u}} R( \mathbf{\Xi}; \delta \mathbf{\Xi}) \cdot d \mathbf{u}
        &=
        \int_{\Omega_0} \bigl[ \textrm{grad}\ \delta \mathbf{u} :
                        \textrm{grad}\ d \mathbf{u} [\boldsymbol{\tau}_{\textrm{iso}} + \boldsymbol{\tau}_{\textrm{vol}}]
@@ -505,12 +508,12 @@ where
                \\
        &\quad + \int_{\Omega_0} \delta \widetilde{p} J \mathbf{I} : \textrm{grad}\ d \mathbf{u} ~\textrm{d}V
        \\
-       D_{d \widetilde{p}} R( \mathbf{\Xi}; \delta \mathbf{\Xi})
+       D_{d \widetilde{p}} R( \mathbf{\Xi}; \delta \mathbf{\Xi})  d \widetilde{p}
        &=
        \int_{\Omega_0} \textrm{grad}\ \delta \mathbf{u} : J \mathbf{I} d \widetilde{p} ~\textrm{d}V
                -  \int_{\Omega_0} \delta \widetilde{J} d \widetilde{p}  ~\textrm{d}V \, ,
        \\
-       D_{d \widetilde{J}} R( \mathbf{\Xi}; \delta \mathbf{\Xi})
+       D_{d \widetilde{J}} R( \mathbf{\Xi}; \delta \mathbf{\Xi})  d \widetilde{J}
        &=  -\int_{\Omega_0} \delta \widetilde{p} d \widetilde{J}~\textrm{d}V
         + \int_{\Omega_0} \delta \widetilde{J}  \dfrac{\textrm{d}^2 \Psi_{\textrm{vol}}(\widetilde{J})}{\textrm{d} \widetilde{J}\textrm{d}\widetilde{J}} d \widetilde{J} ~\textrm{d}V \, .
 @f}

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