From: Wolfgang Bangerth Date: Tue, 22 Apr 2025 17:11:25 +0000 (-0600) Subject: Clarify a couple of things in the introduction to step-44. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F18376%2Fhead;p=dealii.git Clarify a couple of things in the introduction to step-44. --- diff --git a/examples/step-44/doc/intro.dox b/examples/step-44/doc/intro.dox index 20e0e99782..85ef54a225 100644 --- a/examples/step-44/doc/intro.dox +++ b/examples/step-44/doc/intro.dox @@ -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}