From: bangerth Date: Tue, 21 Feb 2012 16:51:15 +0000 (+0000) Subject: Add a note about the sense or nonsense of the model. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=b34244ca97e857b8f7eaad891d8af5ca4fa236d7;p=dealii-svn.git Add a note about the sense or nonsense of the model. git-svn-id: https://svn.dealii.org/trunk@25132 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-18/doc/intro.dox b/deal.II/examples/step-18/doc/intro.dox index b9908c5813..2c37a1d863 100644 --- a/deal.II/examples/step-18/doc/intro.dox +++ b/deal.II/examples/step-18/doc/intro.dox @@ -101,7 +101,27 @@ variable, but only a time-like parameter that governs the evolution of the problem. While these equations are sufficient to describe small deformations, computing -large deformations is a little more complicated. To do so, let us first +large deformations is a little more complicated and, in general, leads +to nonlinear equations such as those treated in step-44. In the +following, let us consider some of the tools one would employ when +simulating problems in which the deformation becomes large. + +@note The model we will consider below is not founded on anything that +would be mathematical sound: we will consider a model in which we +produce a small deformation, deform the physical coordinates of the +body by this deformation, and then consider the next loading step +again as a linear problem. This isn't consistent, since the assumption +of linearity implies that deformations are infinitesimal and so moving +around the vertices of our mesh by a finite amount before solving the +next linear problem is an inconsistent approach. We should therefore +note that it is not surprising that the equations discussed below +can't be found in the literature: The model considered here has +little to do with reality! On the other hand, the implementational +techniques we consider are very much what one would need to use when +implementing a real model, as we will see in step-44. + + +To come back to defining our "artificial" model, let us first introduce a tensorial stress variable $\sigma$, and write the differential equations in terms of the stress: @f{eqnarray*}