Merge pull request #112 from TheGreatCid/ductiletutorial

Add a tutorial for ductile fracture.

doc/content/tutorials/08_ductile_fracture.md

@@ -3,4 +3,109 @@
 # Tutorial 8: Ductile fracture
 
 !content pagination previous=tutorials/07_elastoplasticity.md
-                    next=tutorials/09_three_point_bending.md
+next=tutorials/09_three_point_bending.md
+This tutorial covers the implementation of ductile fracture
+
+For simplicity, we will consider a single element 3 dimensional homogeneous cube under tension. For this tutorial we will apply J2 plasticity with a linear hardening model, but in the tutorial folder you will find examples with other configurations.
+
+## `elastoplasticity.i`: The displacement subproblem
+
+Similar to previous tutorials, we need to define parameters.
+We define additional parameters related to plasticity.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/elastoplasticity.i
+  start=E
+  end=H
+  include-end=True
+  link=False
+  language=python
+
+Where `H` is hardening modulus and `sigma_y` is the yield stress.
+
+
+  `GeneratedMeshGenerator` is utilized to create a 3 dimensional cube.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/elastoplasticity.i
+    block=Mesh
+    link=False
+    language=python
+
+
+We are now transferring an additional variable to the fracture multi-app, psip_active. This is the active plastic energy. In this model active plastic energy contributes to the fracture driving energy.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/elastoplasticity.i
+    block=Transfers
+    link=False
+    language=python
+
+
+
+We have an additional auxiliary variable defined, `F`. This is a consequence of utilizing large deformation models. Previous tutorials utilized small deformation models.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/elastoplasticity.i
+    block=AuxVariables
+    link=False
+    language=python
+
+Plasticity is added through constitutive updates in the Materials block.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/elastoplasticity.i
+    block=Materials
+    link=False
+    language=python
+
+Here we add the blocks for `HenckyIsotropicElasticity`, `linearhardening`, `LargeDeformationJ2Plasticity`, and `ComputeLargeDeformationStress`.
+
+`LargeDeformationJ2Plasticity`: This utilizes the selected hardening model to calculate the value of the yield surface and determine whether the material has begun plastic deformation.
+
+`HenckyIsotropicElasticity:` This calculates elastic stress using the hencky model. Returns the Mandel stress to `ComputeLargeDeformationStress`
+
+`LinearHardening:`This performs plastic hardening following a linear isotropic law. It returns plastic energy to `LargeDeformationJ2Plasticity`
+
+`ComputeLargeDeformationStress:`This computes stress given an elasticity model and a plasticity model. It uses the elasticity model to compute Cauchy stress and the plasticity model to update the plastic deformation to bring the stress state back unto the yield surface.
+
+## Modifications
+
+The elasticity model and hardening law used can be changed.
+
+Currently available hyperelasticity models
+
+1. `HenckyIsotropicElasticity`
+2. `CNHIsotropicElasticity`
+
+Currently available hardening models
+
+1. `ArrheniusLawHardening`
+2. `LinearHardening`
+3. `PowerLawHardening`
+
+
+## `fracture.i`: The phase-field subproblem
+
+There are two minor changes to be made to the fracture input file seen in previous tutorials.
+
+First, we add an auxiliary variable for active plastic energy. This is to receive the value from the main app.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/fracture.i
+    block=AuxVariables
+    link=False
+    language=python
+
+
+
+Second, we add the active plastic energy into the fracture driving energy
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/fracture.i
+    block=psi
+    link=False
+    language=python
+
+
+## Alternating Minimization
+
+Like in previous tutorials, we rely on on MOOSE's Picard iteration to create an alternating minimization scheme.
+
+!listing tutorials/homogeneous_cube/Hencky_J2_linearhardening/fracture.i
+    block=Executioner
+    link=False
+    language=python