From: Wolfgang Bangerth Date: Tue, 6 Oct 2015 21:46:47 +0000 (-0500) Subject: Update to the step-42 documentation. X-Git-Tag: v8.4.0-rc2~334^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=5e88e947d96513529bf809eefb06c9293657312c;p=dealii.git Update to the step-42 documentation. This implements a suggestion by Korosh Taebi. --- diff --git a/examples/step-42/doc/intro.dox b/examples/step-42/doc/intro.dox index 0a2397871e..93573cbff0 100644 --- a/examples/step-42/doc/intro.dox +++ b/examples/step-42/doc/intro.dox @@ -169,6 +169,8 @@ condition: \left\{ \mathbf u\in V: \mathbf n \cdot \mathbf u\leq g \text{ on } \Gamma_C \right\}. @f} +In the actual code, we will use the abbreviation $\gamma=\dfrac{\gamma^{\text{iso}}}{2\mu + \gamma^{\text{iso}}}$. + Given this formulation, we will apply two techniques: - Run a Newton method to iterate out the nonlinearity in the projector. - Run an active set method for the contact condition, in much the same diff --git a/examples/step-42/step-42.cc b/examples/step-42/step-42.cc index 077e1ee229..54ebb04827 100644 --- a/examples/step-42/step-42.cc +++ b/examples/step-42/step-42.cc @@ -176,12 +176,18 @@ namespace Step42 // @sect4{ConstitutiveLaw::get_stress_strain_tensor} - // This is the principal component of the constitutive law. It projects the - // deviatoric part of the stresses in a quadrature point back to the yield - // stress (i.e., the original yield stress $\sigma_0$ plus the term that - // describes linear isotropic hardening). We need this function to calculate - // the nonlinear residual in PlasticityContactProblem::residual_nl_system. The - // computations follow the formulas laid out in the introduction. + // This is the principal component of the constitutive law. It + // computes the fourth order symmetric tensor that relates the + // strain to the stress according to the projection given above, + // when evaluated at a particular strain point. We need this + // function to calculate the nonlinear residual in + // PlasticityContactProblem::residual_nl_system() where + // we multiply this tensor with the strain given in a quadrature + // point. The computations follow the formulas laid out in the + // introduction. In comparing the formulas there with the + // implementation below, recall that $C_\mu : \varepsilon = \tau_D$ + // and that $C_\kappa : \varepsilon = \kappa + // \text{trace}(\varepsilon) I = \frac 13 \text{trace}(\tau) I$. // // The function returns whether the quadrature point is plastic to allow for // some statistics downstream on how many of the quadrature points are