From 159226977049f184b4f610ea7a476bc176e0defb Mon Sep 17 00:00:00 2001
From: rch <rostislav.chudoba@rwth-aachen.de>
Date: Mon, 17 May 2021 22:39:56 +0200
Subject: [PATCH] lecture four with videos

---
 index.ipynb                                   |    2 +-
 tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb | 1843 ++++++++++++++++-
 .../3_2_anchorage_length.ipynb                |   27 +-
 .../4_1_PO_multilinear_unloading.ipynb        |  128 +-
 tour4_plastic_bond/4_2_BS_EP_SH_I_A.ipynb     |  487 +++--
 .../4_3_PO_trc_cfrp_cyclic.ipynb              |  173 +-
 tour4_plastic_bond/plastic_app/bs_ep_ikh.py   |   14 +-
 tour4_plastic_bond/plastic_app/bs_history.py  |   12 +-
 8 files changed, 2420 insertions(+), 266 deletions(-)

diff --git a/index.ipynb b/index.ipynb
index 4e21b35..7e94c4c 100644
--- a/index.ipynb
+++ b/index.ipynb
@@ -301,7 +301,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.8"
+   "version": "3.9.1"
   },
   "toc": {
    "base_numbering": 1,
diff --git a/tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb b/tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb
index 4526af7..0387f31 100644
--- a/tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb
+++ b/tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb
@@ -182,9 +182,1846 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
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+       "ZGlyYXBwbAAAAAAAAAAAAAAAAC1pbHN0AAAAJal0b28AAAAdZGF0YQAAAAEAAAAATGF2ZjU4LjQ1\n",
+       "LjEwMA==\n",
+       "\">\n",
+       "  Your browser does not support the video tag.\n",
+       "</video>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "from IPython.display import HTML\n",
     "html_video_file = open('../extras/pull_out_animation.html','r')\n",
diff --git a/tour3_nonlinear_bond/3_2_anchorage_length.ipynb b/tour3_nonlinear_bond/3_2_anchorage_length.ipynb
index 38d4c39..6e69977 100644
--- a/tour3_nonlinear_bond/3_2_anchorage_length.ipynb
+++ b/tour3_nonlinear_bond/3_2_anchorage_length.ipynb
@@ -179,18 +179,7 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/rch/miniconda3/lib/python3.9/site-packages/traits/observation/_has_traits_helpers.py:70: RuntimeWarning: Trait '_wrappers' (trait type: List) on class ActionItem is defined with comparison_mode=<ComparisonMode.equality: 2>. Mutations and extended traits cannot be observed if a new container compared equally to the old one is set. Redefine the trait with List(..., comparison_mode=<ComparisonMode.identity: 1>) to avoid this.\n",
-      "  warnings.warn(\n",
-      "/home/rch/miniconda3/lib/python3.9/site-packages/traits/observation/_has_traits_helpers.py:70: RuntimeWarning: Trait '_wrappers' (trait type: List) on class ActionItem is defined with comparison_mode=<ComparisonMode.equality: 2>. Mutations and extended traits cannot be observed if a new container compared equally to the old one is set. Redefine the trait with List(..., comparison_mode=<ComparisonMode.identity: 1>) to avoid this.\n",
-      "  warnings.warn(\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%matplotlib widget\n",
     "import matplotlib.pylab as plt\n",
@@ -206,7 +195,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "b60f01b1c01f4c3086332ce256e83d22",
+       "model_id": "401e3a35b31f4caab4a2ba7a2972fb08",
        "version_major": 2,
        "version_minor": 0
       },
@@ -253,7 +242,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -294,7 +283,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -303,7 +292,7 @@
        "21.71"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -332,13 +321,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "fe9e1cc79fba4002ad3e12295ff34565",
+       "model_id": "2f74227dcb8f4d2d9e571d0bafe45f2c",
        "version_major": 2,
        "version_minor": 0
       },
@@ -861,7 +850,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.8"
+   "version": "3.9.1"
   },
   "toc": {
    "base_numbering": 1,
diff --git a/tour4_plastic_bond/4_1_PO_multilinear_unloading.ipynb b/tour4_plastic_bond/4_1_PO_multilinear_unloading.ipynb
index 6af7571..ae2c11f 100644
--- a/tour4_plastic_bond/4_1_PO_multilinear_unloading.ipynb
+++ b/tour4_plastic_bond/4_1_PO_multilinear_unloading.ipynb
@@ -8,6 +8,13 @@
     "# **4.1: Loading, unloading and reloading**"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=551829) part 1"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -50,7 +57,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Consider again the test double-sided pullout test introduced in [3.2](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#trc_pullout_study). Within this test series studying the nonlinear bond behavior of carbon fabrics, a loading scenario with introducing several **unloading and reloading steps** has been included for the specimen with the length of 300 mm. The obtained measured response looked as follows \n",
+    "Consider again the test double-sided pullout test introduced in [notebook 3.2](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#trc_pullout_study). Within this test series studying the nonlinear bond behavior of carbon fabrics, a loading scenario with introducing several **unloading and reloading steps** has been included for the specimen with the total length of 300 and 400 mm. The obtained measured response looked as follows \n",
     "![image](../fig/test_unloading.png)"
    ]
   },
@@ -72,40 +79,21 @@
     "<a id=\"trc_study_monotonic\"></a>\n",
     "### **Example 1:** TRC specimen with unloading\n",
     "\n",
-    "Reusing the [case study](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#case_study_1)\n",
-    "\n",
-    "This notebook uses the `bmcs` package to show the unphysical \n",
-    "nature of a model without physical representation of irreversible\n",
-    "processes in the material structure. It unloads along the original\n",
-    "pull-out curve.\n",
-    "\n",
-    "Further, the notebook shows how to define non-monotonic loading scenario\n",
-    "using a time-function and how to use the function of the `PullOutModel`\n",
-    "to plot the results into a prepared plotting area."
+    "Let us reuse the geometrical, material and algorithmic parameters already specified in the  \n",
+    "[case study on carbon fabric bond](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#case_study_1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 12,
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/home/rch/miniconda3/lib/python3.9/site-packages/traits/observation/_has_traits_helpers.py:70: RuntimeWarning: Trait '_wrappers' (trait type: List) on class ActionItem is defined with comparison_mode=<ComparisonMode.equality: 2>. Mutations and extended traits cannot be observed if a new container compared equally to the old one is set. Redefine the trait with List(..., comparison_mode=<ComparisonMode.identity: 1>) to avoid this.\n",
-      "  warnings.warn(\n",
-      "/home/rch/miniconda3/lib/python3.9/site-packages/traits/observation/_has_traits_helpers.py:70: RuntimeWarning: Trait '_wrappers' (trait type: List) on class ActionItem is defined with comparison_mode=<ComparisonMode.equality: 2>. Mutations and extended traits cannot be observed if a new container compared equally to the old one is set. Redefine the trait with List(..., comparison_mode=<ComparisonMode.identity: 1>) to avoid this.\n",
-      "  warnings.warn(\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "%matplotlib widget\n",
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
     "from bmcs_cross_section.pullout import PullOutModel1D\n",
-    "po_trc = PullOutModel1D(n_e_x=100, w_max=6) # mm \n",
+    "po_trc = PullOutModel1D(n_e_x=100, w_max=3) # mm \n",
     "po_trc.geometry.L_x=150 # [mm]\n",
     "po_trc.time_line.step = 0.02\n",
     "po_trc.cross_section.trait_set(A_m=1543, A_f=16.7, P_b=10)\n",
@@ -117,15 +105,28 @@
     ");"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In addition, let us now change the `loading_scenario` to `cyclic` load.\n",
+    "Note that this polymorphic attribute changes the 'shadowed' object\n",
+    "which generates the time function for the scaling of the load. The \n",
+    "shadowed object representing the cyclic loading scenario can then \n",
+    "be accessed as an attribute `loading_scenario_`. It can be rendered \n",
+    "using the `interact` method, like any other model component in the\n",
+    "model tree"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "c0bcf32e93c340918fda7a39e22f2884",
+       "model_id": "6b42f230c60d40e898e60ae02cc02d8d",
        "version_major": 2,
        "version_minor": 0
       },
@@ -139,32 +140,87 @@
    ],
    "source": [
     "po_trc.loading_scenario = 'cyclic'\n",
+    "po_trc.loading_scenario_.interact()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The parameters of the loading scenario are now visible in the rendered window. They can be \n",
+    "assigned through the `trait_set` method."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
     "po_trc.loading_scenario_.trait_set(number_of_cycles=2,\n",
     "                              unloading_ratio=0.0,\n",
     "                               numbe_of_increments=200,\n",
     "                              amplitude_type='constant',\n",
-    "                              loading_range='non-symmetric')\n",
+    "                              loading_range='non-symmetric');"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The model can now be executed and rendered."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "1bb807c6e671474cb0ae9947069e0307",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "po_trc.run()\n",
     "po_trc.interact()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Apparently, there is no significant difference directly visible. However, if you browse through the history, it will be obvious that unloading is running along the same path as loading, which contradicts to the behavior observed in experiments."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### **Example 2:** CFRP with unloading\n",
     "\n",
-    "Even more evident demonstration of the non-physicality of the model can be provided by reusing the calibrated CFRP model. Let us apply the same loading scenario again"
+    "Even more evident demonstration of the non-physicality of the applied model can be provided by reusing the calibrated CFRP model. Let us apply the same loading scenario again"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "95ad1c680f5947d0a3f0e59002d97c36",
+       "model_id": "1811bef380224201a0b173161ea5649f",
        "version_major": 2,
        "version_minor": 0
       },
@@ -197,9 +253,17 @@
     "                               numbe_of_increments=200,\n",
     "                              amplitude_type='constant',\n",
     "                              loading_range='non-symmetric')\n",
+    "pm.run()\n",
     "pm.interact()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Browsing through the history will reveal that the debonded zone gets recovered upon unloading as the process zone travels back through the bond zone and the pullout tests gets completely healed once $w = 0$. This motivates the question: **How to introduce irreversible changes in the material structure** so that we reflect the physics behind the scenes in a correct way."
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -212,7 +276,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=551829)"
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=551829) part 2"
    ]
   },
   {
diff --git a/tour4_plastic_bond/4_2_BS_EP_SH_I_A.ipynb b/tour4_plastic_bond/4_2_BS_EP_SH_I_A.ipynb
index f457e14..0937471 100644
--- a/tour4_plastic_bond/4_2_BS_EP_SH_I_A.ipynb
+++ b/tour4_plastic_bond/4_2_BS_EP_SH_I_A.ipynb
@@ -1,5 +1,20 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<a id=\"top\"></a>\n",
+    "# **4.2 Basic concept of plasticity**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712) part 1"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -8,9 +23,6 @@
     }
    },
    "source": [
-    "<a id=\"top\"></a>\n",
-    "# **4.2 Basic concept of plasticity**\n",
-    "\n",
     "<div style=\"background-color:lightgray;text-align:left\"> <img src=\"../icons/start_flag.png\" alt=\"Previous trip\" width=\"40\" height=\"40\">\n",
     "    &nbsp; &nbsp; <b>Starting point</b> </div> "
    ]
@@ -48,22 +60,38 @@
     "| Parameter name | Symbol | Description |\n",
     "| - | - | - |\n",
     "| E | $E$ | material stiffness |\n",
-    "| bartau | $\\bar{\\tau}$ | yield stress |\n",
+    "| tau_bar | $\\bar{\\tau}$ | yield stress |\n",
     "| K | $K$ | isotropic hardening modulus |\n",
     "| gamma | $\\gamma$ | kinematic hardening modulus | "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 5,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "4929672100d54cafb00c2e82609b6dbc",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "%matplotlib widget\n",
     "from plastic_app.bs_model_explorer import BSModelExplorer\n",
-    "bs = BSModelExplorer(name='plasticity explorer', delta_s=2)\n",
-    "bs.bs_model.trait_set(E=28000, K=3, gamma=9, bartau=20)\n",
-    "bs.n_steps=100"
+    "bs = BSModelExplorer(name='plasticity explorer')\n",
+    "bs.bs_model.trait_set(E=100, K=3, gamma=9, tau_bar=20)\n",
+    "bs.n_steps=200\n",
+    "bs.interact()"
    ]
   },
   {
@@ -76,13 +104,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "61f129c8f3b0477fa82f77582692ce55",
+       "model_id": "5c0b66a4e6b247b48d91968de33a92ff",
        "version_major": 2,
        "version_minor": 0
       },
@@ -128,7 +156,7 @@
     "## **Observations**\n",
     " * By setting the parameters $K$ and $\\gamma$ equal to zero, yielding is horizontal, and recovers the case of **ideal plasticity**, or the already known stick-slip bond behavior discussed in **Tour 2**\n",
     "\n",
-    " * The hardening moduli $K$ and $\\gamma$  both **enlarge the yield stress during the yielding**.\n",
+    " * The hardening moduli $K$ and $\\gamma$  both **change the size of the elastic domain during the yielding**.\n",
     "\n",
     " * While **isotropic hardening** controlled by $K$ enlarges the whole elastic domain upon yielding, the **kinematic hardening** $\\gamma$ keeps the size of the elastic domain constant. Instead, it induces the shift of the whole elastic domain in the direction of yielding."
    ]
@@ -144,7 +172,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712)"
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712) part 2"
    ]
   },
   {
@@ -186,8 +214,20 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# **Plastic model with kinematic hardening**\n",
-    "\n",
+    "# **Plastic model with isotropic and kinematic hardening**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712) part 3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "Let us now express the manual derivation of the ideally plastic behavior using the algebra system. This step will help us to apply the same logic to more general assumptions including changes of elastic domain during the yielding process. In particular, we want to use the same skeleton of derivation to include the effects of hardening, both isotropic and kinematic."
    ]
   },
@@ -200,7 +240,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 11,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -276,7 +316,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 12,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -295,7 +335,7 @@
        "-τ_Y + ╲╱  \\tau  "
       ]
      },
-     "execution_count": 4,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -326,14 +366,14 @@
     "\n",
     "![image.png](attachment:image.png)\n",
     "\\begin{align}\n",
-    "\\tau = E_\\mathrm{b} s(s - s_\\mathrm{pl})\n",
+    "\\tau = E_\\mathrm{b} (s - s_\\mathrm{pl})\n",
     "\\label{eq:elastic_behavior}\n",
     "\\end{align}"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 13,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -350,7 +390,7 @@
        "E_b⋅(s - sₚₗ)"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -435,7 +475,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 14,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -456,7 +496,7 @@
        "       \\tau       "
       ]
      },
-     "execution_count": 6,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -566,7 +606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 15,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -583,7 +623,7 @@
        "E_b⋅(\\dot{s} - \\dot{s}__\\mathrm{pl})"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -609,7 +649,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 16,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -630,7 +670,7 @@
        "                  \\tau                 "
       ]
      },
-     "execution_count": 8,
+     "execution_count": 16,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -653,7 +693,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 17,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -674,7 +714,7 @@
        " ╲╱  \\tau   "
       ]
      },
-     "execution_count": 9,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -738,7 +778,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 18,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -747,21 +787,21 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAOCAYAAAASVl2WAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVQYGX2R0Q3CMAxEU8QA7QqwAWKEskFZhX4mv7BBuwIjwAqwASMgZYPwDtVpQAhL7tnni+0mLqXkSvfeP/DBuIUrLIRQk67wbaZNacjp2mJhpc8/+xjxS7gsSXY4kj8nbg32eQTFiwjwLgHYAvv3CBJt3lpRAqzHb98j1OWMXxHvwPkvIDT/IHKyE9y8g7GQmq32wqbiYnSyo6Cts5HrghotKeWQKwQUO2AEozpsSCSKuN5CFimOCl6sFGokXwcxmgAAAABJRU5ErkJggg==\n",
+      "image/png": "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\n",
       "text/latex": [
-       "$\\displaystyle \\dot{s}$"
+       "$\\displaystyle \\left\\{ \\dot{s}^\\mathrm{pl} : \\dot{s}\\right\\}$"
       ],
       "text/plain": [
-       "\\dot{s}"
+       "{\\dot{s}__\\mathrm{pl}: \\dot{s}}"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "dot_s_pl_.subs(lambda_, lambda_solved)"
+    "{dot_s_pl : dot_s_pl_.subs(lambda_, lambda_solved) }"
    ]
   },
   {
@@ -800,7 +840,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 19,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -817,7 +857,7 @@
        "{\\dot{\\tau}: 0}"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -841,6 +881,8 @@
    "source": [
     "## **Hardening - elastic domain changes during yielding**\n",
     "\n",
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712) part 4\n",
+    "\n",
     "The derivation scheme presented above can be used for more general assumptions describing the inelastic range of the material behavior. In this section, we will include the next dissipative mechanism, namely isotropic hardening. In simple terms we now allow the growth of the elastic domain with a variable $Z$.\n",
     "\n",
     "![image.png](attachment:image.png)\n",
@@ -858,12 +900,16 @@
    "source": [
     "Using `sympy`, we introduce this variable and define the yield function as `f_tau_Z_`. \n",
     "\n",
-    "**Side remark:** <font color=\"gray\"> To document that the derivation is systematic and can incorporate further assumption, we prepare also the variable $X$ for inclusion of kinematic hardening. In the accompanying video, we will show the procedure of extending the model with the kinematic hardening behavior. The model can be extended by uncommenting the lines referring to kinematic hardening</font> "
+    "**Side remark:** <font color=\"gray\"> To document that the derivation is systematic and can incorporate further assumption, we prepare also the variable $X$ for inclusion of kinematic hardening. In the accompanying video, we will show the procedure of extending the model with the kinematic hardening behavior. The model can be extended by uncommenting the lines referring to kinematic hardening, i.e.\n",
+    "\\begin{align}\n",
+    "[f = | \\tau - X | - (\\tau_Y + Z)]\n",
+    "\\label{eq:f_iso_hardening}\n",
+    "\\end{align}</font> "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 50,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -872,25 +918,25 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "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\n",
       "text/latex": [
-       "$\\displaystyle - Z - \\tau_{Y} + \\sqrt{\\tau^{2}}$"
+       "$\\displaystyle - Z - \\tau_{Y} + \\sqrt{\\left(- X + \\tau\\right)^{2}}$"
       ],
       "text/plain": [
-       "              _______\n",
-       "             ╱     2 \n",
-       "-Z - τ_Y + ╲╱  \\tau  "
+       "              ______________\n",
+       "             ╱            2 \n",
+       "-Z - τ_Y + ╲╱  (-X + \\tau)  "
       ]
      },
-     "execution_count": 12,
+     "execution_count": 50,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "Z = sp.symbols('Z')\n",
-    "# X = sp.symbols('X') # prepared for kinematic hardening\n",
-    "f_tau_Z_ = sp.sqrt(tau**2) - (tau_Y + Z) # extend the definition of elastic domain with to kinematic hardening\n",
+    "X = sp.symbols('X') # prepared for kinematic hardening\n",
+    "f_tau_Z_ = sp.sqrt( (tau-X)**2 ) - (tau_Y + Z) # extend the definition of elastic domain with to kinematic hardening\n",
     "f_tau_Z_"
    ]
   },
@@ -907,7 +953,7 @@
     "<a id=\"hardening_law\"></a>\n",
     "\\begin{align}\n",
     " Z = K z \\\\\n",
-    "\\color{gray}{ X = \\gamma \\alpha }\n",
+    "\\color{gray}{ [X = \\gamma \\alpha] }\n",
     "\\label{eq:isotropic_hardening}\n",
     "\\end{align}\n",
     "This relation will be needed to solve for the consistency condition in the rate form. Thus, in `sympy` we shall introduce directly $\\dot{Z} = K \\dot{z}$"
@@ -915,7 +961,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 51,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -924,15 +970,16 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "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\n",
       "text/latex": [
-       "$\\displaystyle \\left\\{ \\dot{Z} : K \\dot{z}, \\  \\dot{\\tau} : E_{b} \\left(\\dot{s} - \\dot{s}^\\mathrm{pl}\\right)\\right\\}$"
+       "$\\displaystyle \\left\\{ \\dot{X} : \\dot{\\alpha} \\gamma, \\  \\dot{Z} : K \\dot{z}, \\  \\dot{\\tau} : E_{b} \\left(\\dot{s} - \\dot{s}^\\mathrm{pl}\\right)\\right\\}$"
       ],
       "text/plain": [
-       "{\\dot{Z}: K⋅\\dot{z}, \\dot{\\tau}: E_b⋅(\\dot{s} - \\dot{s}__\\mathrm{pl})}"
+       "{\\dot{X}: \\dot{\\alpha}⋅\\gamma, \\dot{Z}: K⋅\\dot{z}, \\dot{\\tau}: E_b⋅(\\dot{s} - \n",
+       "\\dot{s}__\\mathrm{pl})}"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 51,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -943,9 +990,12 @@
     "Z_ = K * z\n",
     "dot_z, dot_Z = sp.symbols(r'\\dot{z}, \\dot{Z}')\n",
     "dot_Z_ = K * dot_z\n",
-    "#gamma = sp.symbols(r'\\gamma', positive=True)\n",
-    "#dot_alpha = sp.symbols(r'\\dot{\\alpha}')\n",
-    "{dot_Z: dot_Z_, dot_tau: dot_tau_}"
+    "gamma = sp.symbols(r'\\gamma', positive=True)\n",
+    "alpha = sp.symbols(r'alpha')\n",
+    "X_ = gamma * alpha\n",
+    "dot_alpha, dot_X = sp.symbols(r'\\dot{\\alpha}, \\dot{X}')\n",
+    "dot_X_ = gamma * dot_alpha\n",
+    "{dot_Z: dot_Z_, dot_tau: dot_tau_, dot_X: dot_X_}"
    ]
   },
   {
@@ -987,7 +1037,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 53,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -996,19 +1046,25 @@
    "outputs": [
     {
      "data": {
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+      "image/png": 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\n",
       "text/latex": [
-       "$\\displaystyle \\left\\{ \\dot{s}^\\mathrm{pl} : \\frac{\\lambda \\sqrt{\\tau^{2}}}{\\tau}, \\  \\dot{z} : \\lambda\\right\\}$"
+       "$\\displaystyle \\left\\{ \\dot{\\alpha} : - \\frac{\\lambda \\sqrt{\\left(X - \\tau\\right)^{2}}}{X - \\tau}, \\  \\dot{s}^\\mathrm{pl} : \\frac{\\lambda \\sqrt{\\left(- X + \\tau\\right)^{2}}}{- X + \\tau}, \\  \\dot{z} : \\lambda\\right\\}$"
       ],
       "text/plain": [
-       "⎧                                 _______                  ⎫\n",
-       "⎪                                ╱     2                   ⎪\n",
-       "⎨                      \\lambda⋅╲╱  \\tau                    ⎬\n",
-       "⎪\\dot{s}__\\mathrm{pl}: ──────────────────, \\dot{z}: \\lambda⎪\n",
-       "⎩                             \\tau                         ⎭"
+       "⎧                          _____________                                    __\n",
+       "⎪                         ╱           2                                    ╱  \n",
+       "⎨              -\\lambda⋅╲╱  (X - \\tau)                           \\lambda⋅╲╱  (\n",
+       "⎪\\dot{\\alpha}: ──────────────────────────, \\dot{s}__\\mathrm{pl}: ─────────────\n",
+       "⎩                       X - \\tau                                         -X + \n",
+       "\n",
+       "____________                  ⎫\n",
+       "          2                   ⎪\n",
+       "-X + \\tau)                    ⎬\n",
+       "────────────, \\dot{z}: \\lambda⎪\n",
+       "\\tau                          ⎭"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1016,9 +1072,9 @@
    "source": [
     "dot_s_pl_ = lambda_ * f_tau_Z_.diff(tau)\n",
     "dot_z_ = - lambda_ * f_tau_Z_.diff(Z)\n",
-    "#dot_alpha_ = - lambda_ * f_tau_Z_.diff(X)\n",
+    "dot_alpha_ = - lambda_ * f_tau_Z_.diff(X)\n",
     "# let us show the result as a dictionary to see associate the obtained expression to the coresponding state variable\n",
-    "{dot_s_pl: dot_s_pl_, dot_z: dot_z_ } "
+    "{dot_s_pl: dot_s_pl_, dot_z: dot_z_, dot_alpha: sp.simplify(dot_alpha_) } "
    ]
   },
   {
@@ -1042,7 +1098,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 56,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1051,26 +1107,33 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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+AAAAAElFTkSuQmCC\n",
+      "image/png": "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\n",
       "text/latex": [
-       "$\\displaystyle \\left\\{ \\dot{f} : \\frac{E_{b} \\left(\\dot{s} - \\dot{s}^\\mathrm{pl}\\right) \\sqrt{\\tau^{2}}}{\\tau} - K \\dot{z}\\right\\}$"
+       "$\\displaystyle \\left\\{ \\dot{f} : \\frac{- E_{b} \\left(\\dot{s} - \\dot{s}^\\mathrm{pl}\\right) \\sqrt{\\left(X - \\tau\\right)^{2}} - K \\dot{z} \\left(X - \\tau\\right) + \\dot{\\alpha} \\gamma \\sqrt{\\left(X - \\tau\\right)^{2}}}{X - \\tau}\\right\\}$"
       ],
       "text/plain": [
-       "⎧                                                 _______            ⎫\n",
-       "⎪                                                ╱     2             ⎪\n",
-       "⎨         E_b⋅(\\dot{s} - \\dot{s}__\\mathrm{pl})⋅╲╱  \\tau              ⎬\n",
-       "⎪\\dot{f}: ─────────────────────────────────────────────── - K⋅\\dot{z}⎪\n",
-       "⎩                               \\tau                                 ⎭"
+       "⎧                                                   _____________             \n",
+       "⎪                                                  ╱           2              \n",
+       "⎨         - E_b⋅(\\dot{s} - \\dot{s}__\\mathrm{pl})⋅╲╱  (X - \\tau)   - K⋅\\dot{z}⋅\n",
+       "⎪\\dot{f}: ────────────────────────────────────────────────────────────────────\n",
+       "⎩                                                                X - \\tau     \n",
+       "\n",
+       "                                    _____________⎫\n",
+       "                                   ╱           2 ⎪\n",
+       "(X - \\tau) + \\dot{\\alpha}⋅\\gamma⋅╲╱  (X - \\tau)  ⎬\n",
+       "─────────────────────────────────────────────────⎪\n",
+       "                                                 ⎭"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 56,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "dot_f = sp.symbols(r'\\dot{f}')\n",
-    "dot_f_tau_Z_ = f_tau_Z_.diff(tau) * dot_tau_ + f_tau_Z_.diff(Z) * dot_Z_\n",
+    "dot_f_tau_Z_ = f_tau_Z_.diff(tau) * dot_tau_ + f_tau_Z_.diff(Z) * dot_Z_ + + f_tau_Z_.diff(X) * dot_X_ \n",
+    "dot_f_tau_Z_ = sp.simplify(dot_f_tau_Z_)\n",
     "{dot_f : dot_f_tau_Z_}"
    ]
   },
@@ -1087,7 +1150,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 57,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -1096,25 +1159,35 @@
    "outputs": [
     {
      "data": {
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\n",
       "text/latex": [
-       "$\\displaystyle \\left\\{ \\dot{f} : \\frac{E_{b} \\dot{s} \\sqrt{\\tau^{2}}}{\\tau} - E_{b} \\lambda - K \\lambda\\right\\}$"
+       "$\\displaystyle \\left\\{ \\dot{f} : - \\frac{E_{b} \\left(\\dot{s} \\left(X - \\tau\\right) + \\lambda \\sqrt{\\left(X - \\tau\\right)^{2}}\\right) \\sqrt{\\left(X - \\tau\\right)^{2}} + \\lambda \\left(K + \\gamma\\right) \\left(X - \\tau\\right)^{2}}{\\left(X - \\tau\\right)^{2}}\\right\\}$"
       ],
       "text/plain": [
-       "⎧                        _______                          ⎫\n",
-       "⎪                       ╱     2                           ⎪\n",
-       "⎨         E_b⋅\\dot{s}⋅╲╱  \\tau                            ⎬\n",
-       "⎪\\dot{f}: ────────────────────── - E_b⋅\\lambda - K⋅\\lambda⎪\n",
-       "⎩                  \\tau                                   ⎭"
+       "⎧          ⎛    ⎛                                _____________⎞    ___________\n",
+       "⎪          ⎜    ⎜                               ╱           2 ⎟   ╱           \n",
+       "⎪         -⎝E_b⋅⎝\\dot{s}⋅(X - \\tau) + \\lambda⋅╲╱  (X - \\tau)  ⎠⋅╲╱  (X - \\tau)\n",
+       "⎨\\dot{f}: ────────────────────────────────────────────────────────────────────\n",
+       "⎪                                                                   2         \n",
+       "⎪                                                         (X - \\tau)          \n",
+       "⎩                                                                             \n",
+       "\n",
+       "__                                   ⎞ ⎫\n",
+       "2                                   2⎟ ⎪\n",
+       "   + \\lambda⋅(K + \\gamma)⋅(X - \\tau) ⎠ ⎪\n",
+       "───────────────────────────────────────⎬\n",
+       "                                       ⎪\n",
+       "                                       ⎪\n",
+       "                                       ⎭"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 57,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "dot_f_lambda_ = dot_f_tau_Z_.subs(dot_s_pl, dot_s_pl_).subs(dot_z, dot_z_)\n",
+    "dot_f_lambda_ = dot_f_tau_Z_.subs(dot_s_pl, dot_s_pl_).subs(dot_z, dot_z_).subs(dot_alpha, dot_alpha_)\n",
     "{dot_f : sp.simplify(dot_f_lambda_)}"
    ]
   },
@@ -1131,7 +1204,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 59,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1140,26 +1213,26 @@
    "outputs": [
     {
      "data": {
-      "image/png": "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\n",
+      "image/png": "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\n",
       "text/latex": [
-       "$\\displaystyle \\frac{E_{b} \\dot{s} \\sqrt{\\tau^{2}}}{\\tau \\left(E_{b} + K\\right)}$"
+       "$\\displaystyle - \\frac{E_{b} \\dot{s} \\sqrt{X^{2} - 2 X \\tau + \\tau^{2}}}{E_{b} X - E_{b} \\tau + K X - K \\tau + X \\gamma - \\gamma \\tau}$"
       ],
       "text/plain": [
-       "               _______\n",
-       "              ╱     2 \n",
-       "E_b⋅\\dot{s}⋅╲╱  \\tau  \n",
-       "──────────────────────\n",
-       "    \\tau⋅(E_b + K)    "
+       "                        _______________________         \n",
+       "                       ╱  2                  2          \n",
+       "        -E_b⋅\\dot{s}⋅╲╱  X  - 2⋅X⋅\\tau + \\tau           \n",
+       "────────────────────────────────────────────────────────\n",
+       "E_b⋅X - E_b⋅\\tau + K⋅X - K⋅\\tau + X⋅\\gamma - \\gamma⋅\\tau"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 59,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "lambda_solved = sp.solve(dot_f_lambda_, lambda_)[0] # the solution is returned as a list with one entry, therefore [0] \n",
-    "lambda_solved "
+    "sp.simplify(lambda_solved) "
    ]
   },
   {
@@ -1183,7 +1256,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 60,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -1192,19 +1265,25 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/latex": [
-       "$\\displaystyle \\left\\{ \\dot{s}^\\mathrm{pl} : \\frac{E_{b} \\dot{s}}{E_{b} + K}, \\  \\dot{z} : \\frac{E_{b} \\dot{s} \\sqrt{\\tau^{2}}}{\\tau \\left(E_{b} + K\\right)}\\right\\}$"
+       "$\\displaystyle \\left\\{ \\dot{\\alpha} : \\frac{E_{b} \\dot{s}}{E_{b} + K + \\gamma}, \\  \\dot{s}^\\mathrm{pl} : \\frac{E_{b} \\dot{s}}{E_{b} + K + \\gamma}, \\  \\dot{z} : - \\frac{E_{b} \\dot{s} \\sqrt{X^{2} - 2 X \\tau + \\tau^{2}}}{E_{b} X - E_{b} \\tau + K X - K \\tau + X \\gamma - \\gamma \\tau}\\right\\}$"
       ],
       "text/plain": [
-       "⎧                                                           _______⎫\n",
-       "⎪                                                          ╱     2 ⎪\n",
-       "⎨                      E_b⋅\\dot{s}           E_b⋅\\dot{s}⋅╲╱  \\tau  ⎬\n",
-       "⎪\\dot{s}__\\mathrm{pl}: ───────────, \\dot{z}: ──────────────────────⎪\n",
-       "⎩                        E_b + K                 \\tau⋅(E_b + K)    ⎭"
+       "⎧                                                                             \n",
+       "⎪                                                                             \n",
+       "⎨                E_b⋅\\dot{s}                             E_b⋅\\dot{s}          \n",
+       "⎪\\dot{\\alpha}: ────────────────, \\dot{s}__\\mathrm{pl}: ────────────────, \\dot{\n",
+       "⎩              E_b + K + \\gamma                        E_b + K + \\gamma       \n",
+       "\n",
+       "                            _______________________         ⎫\n",
+       "                           ╱  2                  2          ⎪\n",
+       "            -E_b⋅\\dot{s}⋅╲╱  X  - 2⋅X⋅\\tau + \\tau           ⎬\n",
+       "z}: ────────────────────────────────────────────────────────⎪\n",
+       "    E_b⋅X - E_b⋅\\tau + K⋅X - K⋅\\tau + X⋅\\gamma - \\gamma⋅\\tau⎭"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 60,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1212,7 +1291,9 @@
    "source": [
     "dot_s_pl_solved = dot_s_pl_.subs(lambda_, lambda_solved)\n",
     "dot_z_solved = dot_z_.subs(lambda_, lambda_solved)\n",
-    "{dot_s_pl: sp.simplify(dot_s_pl_solved), dot_z: sp.simplify(dot_z_solved)}"
+    "dot_alpha_solved = dot_alpha_.subs(lambda_, lambda_solved)\n",
+    "{dot_s_pl: sp.simplify(dot_s_pl_solved), dot_z: sp.simplify(dot_z_solved), \n",
+    " dot_alpha: sp.simplify(dot_alpha_solved)}"
    ]
   },
   {
@@ -1227,22 +1308,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 61,
    "metadata": {},
    "outputs": [
     {
      "data": {
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+      "image/png": "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\n",
       "text/latex": [
-       "$\\displaystyle \\left\\{ \\dot{\\tau} : \\frac{E_{b} K \\dot{s}}{E_{b} + K}\\right\\}$"
+       "$\\displaystyle \\left\\{ \\dot{\\tau} : \\frac{E_{b} \\dot{s} \\left(K + \\gamma\\right)}{E_{b} + K + \\gamma}\\right\\}$"
       ],
       "text/plain": [
-       "⎧            E_b⋅K⋅\\dot{s}⎫\n",
-       "⎨\\dot{\\tau}: ─────────────⎬\n",
-       "⎩               E_b + K   ⎭"
+       "⎧            E_b⋅\\dot{s}⋅(K + \\gamma)⎫\n",
+       "⎨\\dot{\\tau}: ────────────────────────⎬\n",
+       "⎩                E_b + K + \\gamma    ⎭"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 61,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1272,7 +1353,7 @@
     "the evolution of two state variables $\\dot{s}_\\mathrm{pl}$ and $\\dot{z}$ depending on the rate of prescribed slip $\\dot{s}$.\n",
     " - We have derived a direct relation between the rate of stress and the rate of slip using differentials.</br>\n",
     " <font color=\"darkblue\">To simulate the behavior for a particular loading history we have to integrate these differential rate equations over the whole time line.</font>\n",
-    " - In a way, we have just rediscovered the well known wisdom:</br> <font color=\"red\"> It is impossible to say something about the future without accounting for the burden of the past.</a>\n",
+    " - In a way, we have just mathematically rediscovered the wheel:</br> <font color=\"red\"> It is impossible to predict something about the future without accounting for what happened in the past.</a>\n",
     " - Thus, the question remains:</br>\n",
     "<font color=\"green\">**How to transform the differential continuous evolution equations into an algorithm that can simulate the material response to variable loading?**</font>"
    ]
@@ -1285,13 +1366,38 @@
     }
    },
    "source": [
-    "## **Numerical iterative solution**\n",
+    "# **Numerical iterative solution**\n",
+    "\n",
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712) part 5\n",
     "\n",
     "<div style=\"background-color:lightgray;text-align:left\"> <img src=\"../icons/evaluate.png\" alt=\"Evaluate\" width=\"40\" height=\"40\">\n",
-    "    &nbsp; &nbsp; <b>How to get numbers?</b> </div>\n",
-    "    \n",
-    "So far, we have expressed the change of the yield condition as a time derivative without considering the history that a material point went through. To move through an inelastic space of a material, let us now consider a discrete instance of time $t_n$ with the history represented by known values of $s_{n}$ and $s^{\\mathrm{pl}}_{n}$ and $z_n$ for which the \n",
-    "[Kuhn-Tucker conditions](#kuhn_tucker) are fulfilled."
+    "    &nbsp; &nbsp; <b>How to get numbers?</b> </div>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To move through an inelastic space of a material, let us now consider a discrete instance of time $t_n$ with the history represented by known values of $s_{n}$ and $s^{\\mathrm{pl}}_{n}$ and $z_n$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Discrete integration of evolution equations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Relaxing the yield condition\n",
+    "In a continuous case we used the consistency condition to explicitly glue the state onto the yield surface \n",
+    "\\begin{align}\n",
+    " \\dot{f}(\\tau(s, s_\\mathrm{pl}(\\lambda), z(\\lambda)) &= 0.\n",
+    "\\end{align}\n",
+    "Thus, it was impossible to reach an inadmissible state beyond the yield locus. In discrete case, we have to relax this requirement and allow intermediate steps into the inadmissible region during iterations."
    ]
   },
   {
@@ -1307,13 +1413,13 @@
     }
    },
    "source": [
-    "Let us now prescribe an increment of total control slip $\\Delta s$ to achieve the state at $t_{n+1}$ as\n",
+    "To introduce discrete time stepping procedure, let us prescribe an increment of total control slip $\\Delta s$ to achieve the state at $t_{n+1}$ as\n",
     "\\begin{align}\n",
     "s_{n+1} = s_n + \\Delta s.\n",
     "\\end{align}\n",
-    "Since the state variables $s^\\mathrm{pl}_{n+1}, z_{n+1}$ are unknown, we start the search for an admissible state by evaluating the yield function with the values known from the previous step\n",
+    "Since the state variables $s^\\mathrm{pl}_{n+1}, z_{n+1}$ are unknown, we start the search for an admissible state by evaluating the yield function with the values known from the previous step, which will result in a step into an inadmissible range\n",
     "\\begin{align}\n",
-    "f(s_{n+1}, s^{\\mathrm{pl}}_n, z_n)\n",
+    "f(s_{n+1}, s^{\\mathrm{pl}}_n, z_n) > 0\n",
     "\\end{align}\n",
     "![image.png](attachment:image.png)"
    ]
@@ -1326,16 +1432,18 @@
     }
    },
    "source": [
-    "### Discrete yield condition\n",
-    "In a continuous case we used the consistency condition to explicitly glue the state onto the yield surface \n",
-    "\\begin{align}\n",
-    " \\dot{f}(\\tau(s, s_\\mathrm{pl}(\\lambda), z(\\lambda)) &= 0.\n",
-    "\\end{align}\n",
-    "Thus, it was impossible to reach an inadmissible state beyond the yield locus. In discrete case, we have to relax this requirement and allow intermediate steps into the inadmissible region during iterations. Indeed, by taking the state variables $s^\\mathrm{pl}_n, z_n$ from the last step as a first estimate, the yield function $f(s_{n+1}, s^{\\mathrm{pl}}_n, z_n)$ can deliver positive values in this trial iteration step.\n",
+    "Indeed, by taking the state variables $s^\\mathrm{pl}_n, z_n$ from the last step as a first estimate, the yield function $f(s_{n+1}, s^{\\mathrm{pl}}_n, z_n)$ can deliver positive values in this trial iteration step.\n",
     "\n",
     "**The \"trial\" step beyond the admissible domain $f \\le 0$ must be accompanied with a \"return mapping\" algorithm that iteratively returns back to an admissible state located on the yield surface.**"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Return mapping using discrete consistency condition"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -1348,7 +1456,7 @@
     "\\begin{align}\n",
     " f_{k+1} &= f_{k} + \\left. \\frac{\\partial f}{\\partial \\lambda} \\right|_k \\Delta \\lambda\n",
     "\\end{align}\n",
-    "In this form, we can search for an admissible state $f_{n+1} = 0$ by iterating over $k$ to identify the value of the plastic multiplier $\\lambda$ which recovers an admissible state of yielding.\n",
+    "In this form, we can reach an admissible state of yielding recovering the condition $f_{n+1} = 0$ by iterating over $k$ to identify the value of the plastic multiplier $\\lambda$.\n",
     "Note that in initial iteration $k = 0$ the state from previous step is reused, i.e. $f(s_{n+1}, s_n^\\mathrm{pl}, z_n)$."
    ]
   },
@@ -1413,7 +1521,7 @@
     }
    },
    "source": [
-    "### State update\n",
+    "### State update using evolution equations\n",
     "In every iteration step the state variables $s_\\mathrm{pl}$ and $z$ must be updated using the discrete [evolution equations](#evolution_equations), i.e. \n",
     "\n",
     "<a id=\"discrete_evolution_equations\"></a>\n",
@@ -1489,22 +1597,21 @@
     " \\Delta \\lambda = \\frac{f_k}{E_\\mathrm{b}+K}\n",
     "\\end{align}\n",
     "\n",
-    "Apparently, the derivative of $f$ with respect to $\\lambda$ is linear in the present model. This means that the solution can be found in a single iteration step. This gives us the chance to derive an explicit analytical formulas for return mapping in a time step $s_{n+1} = s_n + \\Delta s$ using the state variables $s^\\mathrm{pl}_n, z_n$ from the last time step as follows:\n",
+    "Apparently, the derivative of $f$ with respect to $\\lambda$ is constant in the present model. This means that the solution can be found in a single iteration step. This gives us the chance to derive an explicit analytical formulas for return mapping in a time step $s_{n+1} = s_n + \\Delta s$ using the state variables $s^\\mathrm{pl}_n, z_n$ from the last time step as follows:\n",
     "<div style=\"background-color:#dfffef;text-align:left\">\n",
     "    <a id='return_mapping'></a>\n",
-    "Algorithm\n",
-    "Given $s_{n+1}, s^{\\mathrm{pl}_n}, z_n$\n",
+    "Given $s_{n+1}, s^{\\mathrm{pl}}_n, z_n$\n",
     "\\begin{align}\n",
     " \\tau_{k} &= E_b(s_{n+1} - s^{\\mathrm{pl}}_n) \\nonumber \\\\\n",
-    " Z_k &= K z_n\n",
+    " Z_k &= K z_n \\\\\n",
+    " f_k &= | \\tau_k | - Z_k - \\tau_{\\mathrm{Y}} \\nonumber \n",
     "\\end{align}\n",
     "if $f_k > 0$\n",
     "\\begin{align}\n",
-    " f_k &= | \\tau_k | - Z_k - \\tau_{\\mathrm{Y}} \\nonumber \\\\\n",
     " \\Delta \\lambda &= \\frac{f_k}{E_\\mathrm{b} + K} \\\\\n",
-    "s^\\mathrm{pl}_{n+1} &= \\Delta \\lambda \\; \\mathrm{sign}(\\tau_k)\n",
+    "s^\\mathrm{pl}_{n+1} &= s^\\mathrm{pl}_{n} + \\Delta \\lambda \\; \\mathrm{sign}(\\tau_k)\n",
     "\\nonumber \\\\\n",
-    "z_{n+1} &= \\Delta \\lambda \\nonumber \\\\\n",
+    "z_{n+1} &= z_{n} + \\Delta \\lambda \\nonumber \\\\\n",
     "n &= n+1 \\nonumber \\\\\n",
     "\\tau_{n+1} &= E_\\mathrm{b} (s_{n+1} - s^\\mathrm{pl}_{n+1})\n",
     "\\end{align}</font></div>"
@@ -1523,7 +1630,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**Cyclic loading history:** Consider a loading prescribed in terms of the slip function $s(t)$ in the form\n",
+    "## Example implementation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Cyclic loading history\n",
+    "\n",
+    "Consider a loading prescribed in terms of the slip function $s(t)$ in the form\n",
     "\\begin{align}\n",
     " s(t) = s_\\max \\, \\theta(t)\n",
     "\\end{align}\n",
@@ -1537,35 +1653,68 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The next cell delivers an array with 10 cycles, i.e. $n_\\mathrm{cycles} = 10$, with an amplitude of 10 mm, i.e. $s_\\max = 3$ with 500 data points, i.e. `n_steps` = 500.  "
+    "The next cell delivers an array with 10 cycles, i.e. $n_\\mathrm{cycles} = 10$, with an amplitude of $s_\\max = 3$ with 500 data points, i.e. `n_steps` = 500.  "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 45,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "array([0.        , 0.30168648, 0.60031433, 0.89285593, 1.17634535,\n",
-       "       1.44790846, 1.70479204, 1.94439167, 2.16427819, 2.3622223 ])"
+       "array([0.        , 0.37674922, 0.74753308, 1.10648066, 1.44790846,\n",
+       "       1.76641039, 2.05694336, 2.31490712, 2.53621714, 2.71736924])"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "import numpy as np\n",
-    "n_cycles, s_max, n_steps = 8, 3, 500 # load history parameters\n",
+    "n_cycles, s_max, n_steps = 10, 3, 500 # load history parameters\n",
     "t_arr = np.linspace(0,1,n_steps) # time range t in (0,1)\n",
     "theta = np.sin(2*n_cycles * np.pi * t_arr) # load history with unloading\n",
     "s_n1_arr = s_max * theta # load history\n",
     "s_n1_arr[:10] # show just the 10 first entries in the array"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f9fd6807670>]"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 720x216 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1,1, figsize=(10,3))\n",
+    "ax.plot(t_arr, s_n1_arr)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1582,12 +1731,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "### Example of the time integration loop\n",
+    "\n",
     "The following loop is evaluating the admissible state for all entries from the load history `s_n1_arr`. First, the trial state is evaluated using the values of `s_pl_k` and `z_k` from the previous step. If the yield condition is violated, the [return mapping](#return_mapping) formulas are evaluated. The resulting stress is appended to the recorded stress history in `tau_list`"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 47,
    "metadata": {
     "scrolled": true,
     "slideshow": {
@@ -1623,21 +1774,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 49,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "4e806da334c848baa8d168a8fe80711e",
-       "version_major": 2,
-       "version_minor": 0
-      },
+      "image/png": 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\n",
       "text/plain": [
-       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
+       "<Figure size 720x360 with 2 Axes>"
       ]
      },
-     "metadata": {},
+     "metadata": {
+      "needs_background": "light"
+     },
      "output_type": "display_data"
     }
    ],
@@ -1649,6 +1798,13 @@
     "ax_t.set_title('loading history'); ax_tau.set_title('stress-slip'); "
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Material model implemented"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -1667,7 +1823,17 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    " 1. Extend the model with kinematic hardening $X = \\gamma \\alpha$ following the lecture video V0403."
+    "<div style=\"background-color:lightgray;text-align:left\"> <img src=\"../icons/enhancement.png\" alt=\"Question\" width=\"50\" height=\"50\">\n",
+    "    &nbsp; &nbsp; <b>DIY extension</b> </div> "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Task:** To show that the derivation procedure is general, let us now extend the with kinematic hardening $X = \\gamma \\alpha$. The following video shows how to do it.\n",
+    "\n",
+    "[![title](../fig/bmcs_video.png)](https://moodle.rwth-aachen.de/mod/page/view.php?id=615712) part 6"
    ]
   },
   {
@@ -1696,11 +1862,20 @@
    "metadata": {},
    "source": [
     "<div style=\"background-color:lightgray;text-align:left\"> <img src=\"../icons/exercise.png\" alt=\"Run\" width=\"40\" height=\"40\">\n",
-    "    &nbsp; &nbsp; <a href=\"../exercises/X0401 - Bond-slip model classification (unloading and reloading).pdf\"><b>Exercise X0401:</b></a> <b>Bond-slip model classification (unloading and reloading</b> \n",
+    "    &nbsp; &nbsp; <a href=\"../exercises/X0401 - Bond-slip model classification (unloading and reloading).pdf\"><b>Exercise X0401:</b></a> <b>Bond-slip model classification (unloading and reloading)</b> \n",
     "<a href=\"https://moodle.rwth-aachen.de/mod/page/view.php?id=551831\"><img src=\"../icons/bmcs_video.png\" alt=\"Run\" height=\"130\"></a>\n",
     "</div>"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<div style=\"background-color:lightgray;text-align:left\"> <img src=\"../icons/exercise.png\" alt=\"Run\" width=\"40\" height=\"40\">\n",
+    "    &nbsp; &nbsp; <a href=\"../exercises/X0402 - Nonlinear bond behavior modeled using plasticity.pdf\"><b>Exercise X0402:</b></a> <b>Nonlinear bond behavior modeled using plasticity</b> \n",
+    "</div>"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
diff --git a/tour4_plastic_bond/4_3_PO_trc_cfrp_cyclic.ipynb b/tour4_plastic_bond/4_3_PO_trc_cfrp_cyclic.ipynb
index 19bf145..1c28fa8 100644
--- a/tour4_plastic_bond/4_3_PO_trc_cfrp_cyclic.ipynb
+++ b/tour4_plastic_bond/4_3_PO_trc_cfrp_cyclic.ipynb
@@ -52,12 +52,19 @@
     "# **TRC pullout test modeled using plastic material model**"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test results"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<a id=\"trc_test_results\"></a>\n",
-    "Consider again the test double-sided pullout test that was used to motivate the development of plastic material model in [notebook 4.1](4_1_PO_multilinear_unloading.ipynb#trc_study_monotonic) which demonstrated that no unloading branch could be reproduced. We reprint the test results for convenience here with the goal to examine the ability of the plastic model to reproduce the unloading stiffness of the specimen with the length of 300 mm.\n",
+    "Consider again the test double-sided pullout test that was used to motivate the development of plastic material model in [notebook 4.1](4_1_PO_multilinear_unloading.ipynb#trc_study_monotonic) which demonstrated that no unloading branch could be reproduced. We reprint the test results for convenience here with the goal to examine the ability of the plastic model to reproduce the unloading stiffness of the specimen with the total length of 300 mm, i.e. $L_\\mathrm{b} = 150$ mm.\n",
     "\n",
     "![image](../fig/test_unloading.png)"
    ]
@@ -66,13 +73,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Pullout model setup\n",
+    "\n",
     "<a id=\"trc_test\"></a>\n",
-    "Let us first construct the model with the same geometry as specified in [notebook 3.2](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#trc_parameters)"
+    "Let us first construct the model with the same geometry as specified in [notebook 3.2](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#trc_parameters). Note again that the maximum control displacement $w_\\mathrm{max}$ is \n",
+    "the half of the crack opening displacement measured in the test. Therefore `w_max` has been set to 3 mm."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -80,8 +90,8 @@
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
     "from bmcs_cross_section.pullout import PullOutModel1D\n",
-    "po_trc = PullOutModel1D(n_e_x=100, w_max=6) # mm \n",
-    "po_trc.geometry.L_x=300 # [mm]\n",
+    "po_trc = PullOutModel1D(n_e_x=100, w_max=3) # mm \n",
+    "po_trc.geometry.L_x=150 # [mm]\n",
     "po_trc.time_line.step = 0.02\n",
     "po_trc.cross_section.trait_set(A_m=1543, A_f=16.7, P_b=10);"
    ]
@@ -90,44 +100,71 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "and set the the `elasto-plasticity` option for the `material_model` attribute. Then, the plastic model with the parameters $\\tau_Y = \\bar{\\tau}, K, \\gamma$ introduced in the notebook [3.2](3_2_anchorage_length.ipynb) can be set to the attribute `material_model_` using the `trait_set` method as follows \n",
+    "## Material model with kinematic hardening\n",
+    "\n",
+    "To apply the elastic-plastic model in this pullout model, set the the `elasto-plasticity` option for the `material_model` attribute. Then, the plastic model with the parameters $\\tau_Y = \\bar{\\tau}, K, \\gamma$ introduced in the [notebook 3.2](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#trc_pullout_study) can be set to the attribute `material_model_` using the `trait_set` method as follows \n",
     "| parameter | name | value | unit |\n",
     "| - | - | -: | - |\n",
     "| bond stiffness | `E_b` | 6.4 | MPa |\n",
-    "| elastic limit stress | `tau_bar` | 5 | MPa |\n",
+    "| elastic limit stress | `tau_bar` | 4 | MPa |\n",
     "| isotropic hardening modulus | `K` | 0 | MPa |\n",
-    "| kinematic hardening modulus | `gamma` | 0.8 | MPa |"
+    "| kinematic hardening modulus | `gamma` | 1.0 | MPa |"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Using these parameters, we aim to reproduce the same shape of the [bond slip law that was used previously in notebook 3.2](../tour3_nonlinear_bond/3_2_anchorage_length.ipynb#trc_parameters), represented as a tri-linear function for the simulation of the monotonically increasing load."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "de0c91dd8b8c47418f2eacdbe18b441d",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "po_trc.material_model='elasto-plasticity'\n",
     "po_trc.material_model_.trait_set(\n",
-    "    E_m=28000, E_f=170000, E_b=6.4, K = 0, gamma=0.8, tau_bar=5\n",
-    ");"
+    "    E_m=28000, E_f=170000, E_b=6.4, K = 0, gamma=1.0, tau_bar=4\n",
+    ");\n",
+    "po_trc.material_model_.interact()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Load scenario\n",
+    "\n",
     "Finally, following the same mimic, we change the loading scenario from `monotonic` to `cyclic` and can set the parameters of the cyclic loading through the attribute with the trailing underscore `loading_scenario_`.\n",
     "To verify the loading scenario we directly render the model component using the `interact` method. "
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "b9d1d80e16154e288ef2a861969fb46f",
+       "model_id": "2e63d89c7a7a4dcca2b93d88b1905279",
        "version_major": 2,
        "version_minor": 0
       },
@@ -142,7 +179,7 @@
    "source": [
     "po_trc.loading_scenario = 'cyclic'\n",
     "po_trc.loading_scenario_.trait_set(number_of_cycles=2,\n",
-    "                              unloading_ratio=0.7,\n",
+    "                              unloading_ratio=0.8,\n",
     "                            number_of_increments=200,\n",
     "                              amplitude_type='constant',\n",
     "                              loading_range='non-symmetric');\n",
@@ -153,19 +190,20 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Apparently, we apply directly the full control displacement, then reduce it to 70% and reload again to the maximum. Our intention is not to simulate the whole history displayed in the [test results](trc_test_results) but to compare the unloading stiffness reproduced by the model.\n",
+    "## Run the simulation\n",
+    "Apparently, we apply directly the full control displacement, then reduce it to 80% and reload again to the maximum. Our intention is not to simulate the whole history displayed in the [test results](trc_test_results) but to compare the unloading stiffness reproduced by the model.\n",
     "The model is now ready for execution so that let us run it and render the user interface to inspect the results."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "1214ef7707d2407cba1bb49f005d621c",
+       "model_id": "5c8a30ea2e44496485084cad200fe067",
        "version_major": 2,
        "version_minor": 0
       },
@@ -183,6 +221,17 @@
     "po_trc.interact()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Discussion of the study\n",
+    "\n",
+    " - The predicted response reproduces the experimental response reasonably well. For the **short bond length** used in the test, the slip and shear profiles are nearly uniform along the bond zone.  - **Task:** Change the bond length to 200 mm and compare the response with the pull-out curve depicted in the [test results](#trc_test_results)\n",
+    " - The main focus of the study at hand was the question, if the **unloading stiffness** corresponds to the initial stiffness, similarly to the test response. Since this is the case, the conclusion can be made, that the bond behavior in the tested TRC specimens is primarily governed by plasticity.\n",
+    " - Since the model uses **linear hardening**, the pull-out response has a linear inelastic branch up to the point of unloading. The non-linear shape of the experimentally obtained curve cannot be reproduced in a better way. **Non-linear hardening** function instead of a single hardening modulus $\\gamma$ can be theoretically included into the framework of plasticity. However, such enhancement requires a non-trivial systematic calibration procedure which would be able to uniquely associate the inelastic mechanisms governing the response to the hardening process, which is a non-trivial task. Such effort would only be justified for a material combination with large amount of practical applications. "
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -192,27 +241,59 @@
     "\n",
     "It is interesting to examine the ability of the plastic model with negative hardening, i.e. softening, to simulate the cyclic response of the CFRP sheets.\n",
     "\n",
-    "Indeed, the bond-slip law identified during the [**Tour 3:** (CFRP sheet test)](../tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb#cfrp_bond_slip) can be reproduced by setting the parameters of\n",
+    "## Pullout model setup\n",
+    "Let us construct the model with these parameters and check the shape of the bond-slip relation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "from bmcs_cross_section.pullout import PullOutModel1D\n",
+    "\n",
+    "A_f = 16.67 # [mm^2]\n",
+    "A_m = 1540.0 # [mm^2]\n",
+    "p_b = 100.0 #\n",
+    "E_f = 170000 # [MPa]\n",
+    "E_m = 28000 # [MPa]\n",
+    "pm = PullOutModel1D()\n",
+    "pm.sim.tline.step = 0.01 # 100 time increments\n",
+    "pm.cross_section.trait_set(A_f=A_f, P_b=p_b, A_m=A_m)\n",
+    "pm.geometry.L_x = 300 # length of the specimen [mm]\n",
+    "pm.w_max = 2.8 # maximum control displacement [mm]\n",
+    "pm.n_e_x = 100 # number of finite elements"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Material model with isotropic softening\n",
+    "\n",
+    "The bond-slip law identified during the [**Tour 3:** (CFRP sheet test)](../tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb#cfrp_bond_slip) can be reproduced by setting the parameters of\n",
     "the plastic material model with isotropic hardening to:\n",
     "| parameter | name | value | unit |\n",
     "| - | - | -: | - |\n",
     "| bond stiffness | `E_b` | 80 | MPa |\n",
     "| elastic limit stress | `tau_bar` | 8 | MPa |\n",
     "| isotropic hardening modulus | `K` | -20 | MPa |\n",
-    "| kinematic hardening modulus | `gamma` | 0 | MPa |\n",
-    "\n",
-    "Let us construct the model with these parameters and check the shape of the bond-slip relation"
+    "| kinematic hardening modulus | `gamma` | 0 | MPa |\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "1fca9b713fa6498d9ec8fdbbfffa5563",
+       "model_id": "faff8b6240794172971ea1f7f97c91db",
        "version_major": 2,
        "version_minor": 0
       },
@@ -225,17 +306,6 @@
     }
    ],
    "source": [
-    "%matplotlib widget\n",
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "from bmcs_cross_section.pullout import PullOutModel1D\n",
-    "\n",
-    "A_f = 16.67 # [mm^2]\n",
-    "A_m = 1540.0 # [mm^2]\n",
-    "p_b = 100.0 #\n",
-    "E_f = 170000 # [MPa]\n",
-    "E_m = 28000 # [MPa]\n",
-    "pm = PullOutModel1D()\n",
     "pm.material_model='elasto-plasticity'\n",
     "pm.material_model_.trait_set(\n",
     "    E_m=28000, E_f=170000, E_b=80, K = -20, gamma=0, tau_bar=8\n",
@@ -269,15 +339,27 @@
     "With the material model at hand, let us explore the response of the CFRP sheets in a cyclic loading scenario with symmetric, increasing amplitudes"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Load scenario\n",
+    "\n",
+    "To see the effect of propagating softening plasticity upon unloading, let us apply four loading cycles oscillating applying the pull-out and push-in load in each cycle. Note that with this, \n",
+    "a compressive stress is transferred by the FRP sheet upon push-in loading, which is unrealistic. \n",
+    "Such response might be expected from a test on CFRP bars. Still the purpose of the study is \n",
+    "to show the consequences of the applied assumptions on a broad scale of loading configuration and check the plausibility of the model response for a wider range of loading scenarios."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "672ff3bc071e43a296b93f1aafccf4ef",
+       "model_id": "fdfa0b5fafd741eca3ad9ba0cfc7474f",
        "version_major": 2,
        "version_minor": 0
       },
@@ -290,11 +372,6 @@
     }
    ],
    "source": [
-    "pm.sim.tline.step = 0.01 # 100 time increments\n",
-    "pm.cross_section.trait_set(A_f=A_f, P_b=p_b, A_m=A_m)\n",
-    "pm.geometry.L_x = 300 # length of the specimen [mm]\n",
-    "pm.w_max = 2.8 # maximum control displacement [mm]\n",
-    "pm.n_e_x = 100 # number of finite elements\n",
     "pm.loading_scenario = 'cyclic'\n",
     "pm.loading_scenario_.trait_set(number_of_cycles=4,\n",
     "                              unloading_ratio=0.5,\n",
@@ -305,6 +382,18 @@
     "pm.interact()"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Discussion of the study\n",
+    "\n",
+    " - By checking the `history` showing the field variables along the bond zone, we can observe the the alternating tension and compression profiles in the reinforcement and in the matrix.\n",
+    " - The shear transfer is again taking place only on a short length due to the softening nature of the bond behavior.\n",
+    " - The yielding of the bond within the process zone occurs both under pullout and under push-in load as apparent from the existence of the hysteretic loop.\n",
+    " - In contrast to the [study of TRC test](#trc_results), the unloading stiffness does not correspond to the initial stiffness. This question is discussed in a more detail below.  "
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
diff --git a/tour4_plastic_bond/plastic_app/bs_ep_ikh.py b/tour4_plastic_bond/plastic_app/bs_ep_ikh.py
index fde27be..f382b66 100644
--- a/tour4_plastic_bond/plastic_app/bs_ep_ikh.py
+++ b/tour4_plastic_bond/plastic_app/bs_ep_ikh.py
@@ -22,13 +22,13 @@ class BS_EP_IKH(bu.Model):
     E = bu.Float(28000, MAT=True)
     gamma = bu.Float(10, MAT=True)
     K = bu.Float(8, MAT=True)
-    bartau = bu.Float(9, MAT=True)
+    tau_bar = bu.Float(9, MAT=True)
 
     ipw_view = bu.View(
         bu.Item('E', latex='E', minmax=(0.5, 100)),
         bu.Item('gamma', latex=r'\gamma_\mathrm{T}', minmax=(-20, 20)),
         bu.Item('K', minmax=(-20, 20)),
-        bu.Item('bartau', latex=r'\bar{\tau}', minmax=(0.5, 20)),
+        bu.Item('tau_bar', latex=r'\bar{\tau}', minmax=(0.5, 20)),
     )
 
     def get_sig_n1(self, s_n1, Sig_n, Eps_n, k_max):
@@ -43,7 +43,7 @@ class BS_EP_IKH(bu.Model):
         _E_b = self.E
         _K = self.K
         _gamma = self.gamma
-        _tau_Y = self.bartau  # material parameters
+        _tau_Y = self.tau_bar  # material parameters
         s_pl_k, z_k, alpha_k = Eps_k  # initialization of trial states
         tau_k = _E_b * (s_n1 - s_pl_k)  # elastic trial step
         Z_k = _K * z_k  # isotropic hardening
@@ -84,8 +84,8 @@ class BS_EP_IKH(bu.Model):
     def plot_f_state(self, ax, Eps, Sig):
         lower = -self.f_c * 1.05
         upper = self.f_t + 0.05 * self.f_c
-        lower_tau = -self.bartau * 2
-        upper_tau = self.bartau * 2
+        lower_tau = -self.tau_bar * 2
+        upper_tau = self.tau_bar * 2
         lower_tau = 0
         upper_tau = 10
         tau_x, tau_y, sig = Sig[:3]
@@ -119,8 +119,8 @@ class BS_EP_IKH(bu.Model):
     def plot_f(self, ax):
         lower = -self.f_c * 1.05
         upper = self.f_t + 0.05 * self.f_c
-        lower_tau = -self.bartau * 2
-        upper_tau = self.bartau * 2
+        lower_tau = -self.tau_bar * 2
+        upper_tau = self.tau_bar * 2
         sig_ts, tau_x_ts  = np.mgrid[lower:upper:201j,lower_tau:upper_tau:201j]
         Sig_ts = np.zeros((len(self.symb.Eps),) + tau_x_ts.shape)
         Sig_ts[0,:] = tau_x_ts
diff --git a/tour4_plastic_bond/plastic_app/bs_history.py b/tour4_plastic_bond/plastic_app/bs_history.py
index 9b91fa4..f131556 100644
--- a/tour4_plastic_bond/plastic_app/bs_history.py
+++ b/tour4_plastic_bond/plastic_app/bs_history.py
@@ -23,7 +23,7 @@ class BSHistory(bu.Model):
     )
 
     def plot_Sig_Eps(self, axes):
-        ax1, ax11, ax3, ax33 = axes
+        ax1, ax11, ax33, ax3 = axes
         colors = ['blue', 'red', 'green', 'black', 'magenta']
         t = self.t_arr
         s_pi_, z_, alpha_ = self.Eps_arr.T
@@ -37,15 +37,15 @@ class BSHistory(bu.Model):
         tau_pi_t = tau_pi_
 
         ax1.set_title('stress - displacement');
-        ax1.plot(t, tau_pi_t, '--', color='darkgreen', label=r'$||\tau||$')
+        ax1.plot(t, tau_pi_t, '--', color='darkgreen', label=r'$\tau$')
         ax1.fill_between(t, tau_pi_t, 0, color='limegreen', alpha=0.1)
-        ax1.set_ylabel(r'$|| \tau ||, \sigma$')
+        ax1.set_ylabel(r'$ \tau')
         ax1.set_xlabel('$t$');
         ax1.plot(t[idx], 0, marker='H', color='red')
         ax1.legend()
-        ax11.plot(t, s_t, color='darkgreen', label=r'$||s||$')
-        ax11.plot(t, s_pi_t, '--', color='orange', label=r'$||s^\pi||$')
-        ax11.set_ylabel(r'$|| s ||, w$')
+        ax11.plot(t, s_t, color='darkgreen', label=r'$s$')
+        ax11.plot(t, s_pi_t, color='orange', label=r'$s_\mathrm{pl}$')
+        ax11.set_ylabel(r'$s$')
         ax11.legend()
         mpl_align_yaxis(ax1,0,ax11,0)
 
-- 
GitLab