From: wolf Date: Sun, 10 Apr 2005 18:16:57 +0000 (+0000) Subject: Write some more docs. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=613b9af300de6b5e531b738da28a4abc64add727;p=dealii-svn.git Write some more docs. git-svn-id: https://svn.dealii.org/trunk@10467 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-18/step-18.cc b/deal.II/examples/step-18/step-18.cc index 4016d22861..dda4b6ef8f 100644 --- a/deal.II/examples/step-18/step-18.cc +++ b/deal.II/examples/step-18/step-18.cc @@ -113,7 +113,20 @@ namespace QuasiStaticElasticity }; - // + // @sect3{The stress-strain tensor} + + // Next, we define the linear relationship + // between the stress and the strain in + // elasticity. It is given by a tensor of + // rank 4 that is usually written in the + // form ``C_{ijkl} = \mu (\delta_{ik} + // \delta_{jl} + \delta_{il} \delta_{jk}) + + // \lambda \delta_{ij} \delta_{kl}''. This + // tensor maps symmetric tensor of rank 2 + // to symmetric tensors of rank 2. A + // function implementing its creation for + // given values of the Lame constants + // lambda and my is straightforward: template SymmetricTensor<4,dim> get_stress_strain_tensor (const double lambda, const double mu) @@ -129,10 +142,36 @@ namespace QuasiStaticElasticity return tmp; } + // With this function, we can define a + // variable that will be used throughout + // the program as the stress-strain tensor, + // with values for the Lame constants that + // are appropriate for steel: const SymmetricTensor<4,deal_II_dimension> stress_strain_tensor = get_stress_strain_tensor (/*lambda = */ 9.695e10, /*mu = */ 7.617e10); + // In more elaborate programs, this will + // probably be a member variable of some + // class instead, or a function that + // returns the stress-strain relationship + // depending on other input. For example in + // damage theory models, the Lame constants + // are considered a function of the prior + // stress/strain history of a + // point. Conversely, in plasticity the + // form of the stress-strain tensor is + // modified if the material has reached the + // yield stress in a certain point, and + // possibly also depending on its prior + // history. + // + // In the present program, however, we + // assume that the material is completely + // elastic and linear, and a constant + // stress-strain tensor is sufficient for + // our present purposes. + // @sect3{Auxiliary functions}