From 5e88e947d96513529bf809eefb06c9293657312c Mon Sep 17 00:00:00 2001
From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Tue, 6 Oct 2015 16:46:47 -0500
Subject: [PATCH] Update to the step-42 documentation.

This implements a suggestion by Korosh Taebi.
---
 examples/step-42/doc/intro.dox |  2 ++
 examples/step-42/step-42.cc    | 18 ++++++++++++------
 2 files changed, 14 insertions(+), 6 deletions(-)

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
+  // <code>PlasticityContactProblem::residual_nl_system()</code> 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
-- 
2.39.5