From: Daniel Garcia-Sanchez Date: Fri, 21 Feb 2020 17:36:50 +0000 (+0100) Subject: Fix equation X-Git-Tag: v9.2.0-rc1~476^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=96778903e503555c2c4aabc7a15b307c621bd3c8;p=dealii.git Fix equation The equation \partial_j (c_{ijkl} \partial_k u_l) is only valid if c_{ijkl} = c_{ijlk} --- diff --git a/examples/step-8/doc/intro.dox b/examples/step-8/doc/intro.dox index 5e538797e2..a982951eea 100644 --- a/examples/step-8/doc/intro.dox +++ b/examples/step-8/doc/intro.dox @@ -20,15 +20,21 @@ vector-valued, meaning that in each point it has a direction and an absolute value. The elastic equations are the following: @f[ - - \partial_j (c_{ijkl} \partial_k u_l) + \partial_j (c_{ijkl} \varepsilon_{kl}) = f_i, \qquad i=1\ldots d, @f] -where the values $c_{ijkl}$ are the stiffness coefficients and -will usually depend on the space coordinates. In -many cases, one knows that the material under consideration is +where the values $c_{ijkl}$ are the stiffness coefficients that +usually depend on the space coordinates and the strain $\varepsilon_{kl}$ is +the symmetrized gradient of the displacement, +given by +@f[ +\varepsilon_{kl} =\frac{1}{2}(\partial_k u_l + \partial_l u_k) +@f] + +In many cases, one knows that the material under consideration is isotropic, in which case by introduction of the two coefficients $\lambda$ and $\mu$ the coefficient tensor reduces to @f[