From 7fc3a2448df89ba866f3a654ff38abfccd6f0a0f Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Thu, 6 Jan 2022 04:49:17 -0700 Subject: [PATCH] Update step-44 documentation. --- examples/step-44/doc/intro.dox | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/examples/step-44/doc/intro.dox b/examples/step-44/doc/intro.dox index 886720ef59..30660874aa 100644 --- a/examples/step-44/doc/intro.dox +++ b/examples/step-44/doc/intro.dox @@ -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} \, , \\ -- 2.39.5