Add reference, fix equation and indent, fix prm in doc

Author: Wang-yijun

cookbooks/CPO_induced_anisotropic_viscosity/doc/cpo_particle_property.part.prm

@@ -3,7 +3,7 @@ subsection Postprocess
 
     subsection Visualization
         set Time between graphical output = 0.1
-        set List of output variables = material properties, strain rate,  named additional outputs,  shear stress,  stress
+        set List of output variables = material properties, strain rate, named additional outputs, shear stress, stress
 
       subsection Material properties
         set List of material properties = density, viscosity
@@ -18,13 +18,13 @@ subsection Postprocess
         set Time between data output = 0.1
         set Write in background thread = true
         set Compress cpo data files = false
-        set Write out raw cpo data = mineral 0: volume fraction, mineral 0: Euler angles #, mineral 1: volume fraction, mineral 1: Euler angles
-        set Write out draw volume weighted cpo data = mineral 0: volume fraction, mineral 0: Euler angles #, mineral 1: volume fraction, mineral 1: Euler angles
+        set Write out raw cpo data = mineral 0: volume fraction, mineral 0: Euler angles
+        set Write out draw volume weighted cpo data = mineral 0: volume fraction, mineral 0: Euler angles
     end
 end
 
 subsection Particles
-    set List of particle properties =  integrated strain, integrated strain invariant, velocity, pT path, strain rate, crystal preferred orientation, cpo bingham average, cpo elastic tensor #integrated strain, integrated strain invariant, velocity, pT path, strain rate, velocity gradient, stress, crystal preferred orientation, cpo bingham average, cpo bingham average euler angle, cpo elastic tensor
+    set List of particle properties =  integrated strain, integrated strain invariant, velocity, pT path, strain rate, crystal preferred orientation, cpo bingham average, cpo elastic tensor
     set Allow cells without particles = false
     set Interpolation scheme = nearest neighbor
     set Minimum particles per cell = 1
@@ -42,15 +42,15 @@ subsection Particles
             set Minerals = Olivine: A-fabric
             set Volume fractions minerals = 1.0
         end
-        set Number of grains per particle = 1000 ## Annotation grain count
-        set Property advection method = Backward Euler ## Annotation Property advection method
+        set Number of grains per particle = 1000
+        set Property advection method = Backward Euler
         set Property advection tolerance = 1e-15
         set CPO derivatives algorithm = D-Rex 2004
         subsection D-Rex 2004
-            set Mobility = 10 ## Annotation LPO Mobility
+            set Mobility = 10
             set Stress exponents = 3.5
             set Exponents p = 1.5
-            set Threshold GBS = 0.3 ## Annotation TGBS
+            set Threshold GBS = 0.3
         end
     end
     subsection CPO Bingham Average

cookbooks/CPO_induced_anisotropic_viscosity/plugin/anisotropic_stress.cc

@@ -112,16 +112,17 @@ namespace aspect
     {
       ASPECT_REGISTER_VISUALIZATION_POSTPROCESSOR(AnisotropicStress,
                                                   "Anisotropic stress",
-                                                  "A visualization output object that generates output "
-                                                  "for the 6 (in 3d) components of the anisotropic stress "
-                                                  "tensor. The anisotropic stress is defined as $2 \eta "
-                                                  "(\varepsilon(\mathbf u) - \tfrac 13 \textrm{trace}\ "
-                                                  "\varepsilon(\mathbf u) \mathbf 1) = 2\eta (\varepsilon(\mathbf u) - "
-                                                      "\frac 13 (\nabla \cdot \mathbf u) \mathbf I)$ * stress_strain_directors, and differs from the "
-                                                      "full stress by the absence of the pressure.  The second term in the "
-                                                      "difference is zero if the model is incompressible. "
-                                                      "This particle property plugin should only be activated when using the "
-                                                      "CPO induced anisotropic viscosity material model from the cookbook. ")
-                                                    }
-                                                    }
-                                                    }
+                                                  "A visualization output object that generates "
+                                                  "the 3 or 6 independent components (in 2d and 3d, respectively) "
+                                                  "of the anisotropic stress tensor. "
+                                                  "The anisotropic stress is defined as $2 \\eta "
+                                                  "(\\varepsilon(\\mathbf u) - \\tfrac 13 \\text{trace} "
+                                                  "\\varepsilon(\\mathbf u) \\mathbf 1) = 2\\eta (\\varepsilon(\\mathbf u) - "
+                                                  "\\frac 13 (\\nabla \\cdot \\mathbf u) \\mathbf I)$ * stress_strain_directors, "
+                                                  "and differs from the full stress by the absence of the pressure. "
+                                                  "The second term in the difference is zero if the model is incompressible. "
+                                                  "This particle property plugin should only be activated when using "
+                                                  "the CPO induced anisotropic viscosity material model from the cookbook.")
+    }
+  }
+}

doc/sphinx/references.bib

@@ -12633,4 +12633,32 @@ @article{gleason:tullis:1995
   pages={1--23},
   year={1995},
   publisher={Elsevier B.V.}
+}
+
+@article{signorelli:etal:2021,
+  title={An effective parameterization of texture-induced viscous anisotropy in orthotropic materials with application for modeling geodynamical flows},
+  author={Signorelli, Javier and Hassani, Riad and Tommasi, Andréa and Mameri, Lucan},
+  journal={Journal of Theoretical, Computational and Applied Mechanics},
+  pages={6737},
+  year={2021}
+}
+
+@article{hansen:etal:2016,
+  title={Viscous anisotropy of textured olivine aggregates: 2. Micromechanical model},
+	author={Hansen, Lars N. and Conrad, Clinton P. and Boneh, Yuval and Skemer, Philip and Warren, Jessica M. and Kohlstedt, David L.},
+  journal={Journal of Geophysical Research: Solid Earth},
+  volume={121},
+  number={10},
+  pages = {7137--7160},
+  year={2016}
+}
+
+@article{hill:1948,
+  title={A theory of the yielding and plastic flow of anisotropic metals},
+  author={Hill, Rodney},
+  journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
+  volume={193},
+  number={1033},
+  pages={281--297},
+  year={1948}
 }