From: Joerg Frohne Date: Sun, 27 Oct 2013 23:00:07 +0000 (+0000) Subject: add the rhs in the linearized inequality X-Git-Tag: v8.1.0~485 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=66f64202d454452e5867cd15e71d9099099dee65;p=dealii.git add the rhs in the linearized inequality git-svn-id: https://svn.dealii.org/trunk@31449 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-42/doc/intro.dox b/deal.II/examples/step-42/doc/intro.dox index a263359ead..a7d4ab3e5b 100644 --- a/deal.II/examples/step-42/doc/intro.dox +++ b/deal.II/examples/step-42/doc/intro.dox @@ -23,7 +23,7 @@ elasto-plastic material behavior with isotropic hardening in three dimensions. In other words, it considers how a three-dimensional body deforms if one pushes into it a rigid obstacle (the contact problem) where deformation is governed by an elasto-plastic material law (a material that can only accommodate a certain -maximal stress) that hardens as deformation accumulates. To show we we intend to +maximal stress) that hardens as deformation accumulates. To show what we intend to do before going into too many details, let us just show a picture of what the solution will look like (the deformable body is a cube - only half of which is actually shown -, the obstacle corresponds @@ -197,7 +197,11 @@ the following equation (still an inequality, but linearized): @f{align*} \label{eq:linearization} \left(I_{\Pi}\varepsilon(\tilde {\mathbf u}^{i}), - \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) \geq 0, + \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) \geq + \left(\left(I_{\Pi}\varepsilon(\tilde {\mathbf u}^{i-1}), + \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) - + \left(P_{\Pi}(C\varepsilon(\tilde {\mathbf u}^{i-1})), + \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right)\right), \quad \forall \varphi\in V^+, @f} where the rank-4 tensor $I_\Pi=I_\Pi(\varepsilon^D(\mathbf u^{i-1}))$ given by