From f59fdde606780c3bd7cc3998915dfa223c6ad983 Mon Sep 17 00:00:00 2001
From: rch <rostislav.chudoba@rwth-aachen.de>
Date: Wed, 2 Jun 2021 11:30:54 +0200
Subject: [PATCH] finished 5.1
---
index.ipynb | 5 +-
.../2_2_1_PO_configuration_explorer.ipynb | 14 ++--
tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb | 67 +++++++----------
.../3_2_anchorage_length.ipynb | 2 +-
...t_Damage_Evolution_Damage_initiation.ipynb | 75 ++++++++++++-------
5 files changed, 91 insertions(+), 72 deletions(-)
diff --git a/index.ipynb b/index.ipynb
index 062fc46..22d0528 100644
--- a/index.ipynb
+++ b/index.ipynb
@@ -244,6 +244,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "<a id=\"tour5\"></a>\n",
"## **Tour 5:** Irreversibility due to damage\n",
"\n",
"### 5.1 Damage initiation, damage evolution, 2D bond behavior\n",
@@ -267,6 +268,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "<a id=\"tour6\"></a>\n",
"## **Tour 6:** From debonding to cracking \n",
"\n",
"- 6.1 Crack propagation"
@@ -276,6 +278,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "<a id=\"tour7\"></a>\n",
"## **Tour 7:** Reinforced bended cross section\n",
"\n",
"- 7.1 Beam bending "
@@ -305,7 +308,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.10"
+ "version": "3.9.1"
},
"toc": {
"base_numbering": 1,
diff --git a/tour2_constant_bond/2_2_1_PO_configuration_explorer.ipynb b/tour2_constant_bond/2_2_1_PO_configuration_explorer.ipynb
index c23d777..414a816 100644
--- a/tour2_constant_bond/2_2_1_PO_configuration_explorer.ipynb
+++ b/tour2_constant_bond/2_2_1_PO_configuration_explorer.ipynb
@@ -70,13 +70,13 @@
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "aa679c9a134f4afa9e5e06a6d61c16b9",
+ "model_id": "735610fd27ee461aad640614c65a260f",
"version_major": 2,
"version_minor": 0
},
@@ -129,7 +129,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "a20f4260c8f54ab59d4d9ad7c2474cca",
+ "model_id": "3c276ea1bffe428b92bf854b313990bd",
"version_major": 2,
"version_minor": 0
},
@@ -176,7 +176,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "291aa713915840b5a850713f697d8a43",
+ "model_id": "de56fdd2d67142f2b15e7f6ba2ac28a7",
"version_major": 2,
"version_minor": 0
},
@@ -217,13 +217,13 @@
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "922c5f729a8a411eb475c7e346c77815",
+ "model_id": "45fd75c0b31545b0bd41d1a7ef251c5e",
"version_major": 2,
"version_minor": 0
},
@@ -300,7 +300,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.10"
+ "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 92972ee..0e7e22d 100644
--- a/tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb
+++ b/tour3_nonlinear_bond/3_1_nonlinear_bond.ipynb
@@ -2154,6 +2154,7 @@
"outputs": [
{
"data": {
+ "image/png": "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\n",
"text/latex": [
"$\\displaystyle \\begin{cases} \\frac{s \\tau_{1}}{s_{1}} & \\text{for}\\: s \\leq s_{1} \\\\\\tau_{1} + \\frac{\\left(s - s_{1}\\right) \\left(- \\tau_{1} + \\tau_{2}\\right)}{- s_{1} + s_{2}} & \\text{for}\\: s \\leq s_{2} \\\\\\tau_{2} & \\text{otherwise} \\end{cases}$"
],
@@ -2207,6 +2208,7 @@
"outputs": [
{
"data": {
+ "image/png": "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\n",
"text/latex": [
"$\\displaystyle \\begin{cases} \\frac{\\tau_{1}}{s_{1}} & \\text{for}\\: s \\leq s_{1} \\\\\\frac{- \\tau_{1} + \\tau_{2}}{- s_{1} + s_{2}} & \\text{for}\\: s \\leq s_{2} \\\\0 & \\text{otherwise} \\end{cases}$"
],
@@ -2317,7 +2319,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": 21,
"metadata": {
"slideshow": {
"slide_type": "fragment"
@@ -2327,7 +2329,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "5118f6505f734c4da338d9e842066940",
+ "model_id": "7ff0053380a04c4eb079d443b2eff9cd",
"version_major": 2,
"version_minor": 0
},
@@ -2365,20 +2367,9 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": 22,
"metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "/opt/conda/lib/python3.8/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",
- "/opt/conda/lib/python3.8/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": [
"from bmcs_cross_section.pullout import PullOutModel1D"
]
@@ -2392,7 +2383,7 @@
},
{
"cell_type": "code",
- "execution_count": 9,
+ "execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
@@ -2458,13 +2449,13 @@
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "b153348aa4f04a05a049ee827652ca3b",
+ "model_id": "e2f41101cb4645eebf1f2eeac18da437",
"version_major": 2,
"version_minor": 0
},
@@ -2533,7 +2524,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "slide"
@@ -2558,7 +2549,7 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
@@ -2581,7 +2572,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
@@ -2600,13 +2591,13 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "6d13585e6a254deb88e7db59663b8781",
+ "model_id": "1e9b77ee250c42548ff7c95ac5b45a61",
"version_major": 2,
"version_minor": 0
},
@@ -2657,13 +2648,13 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "b12be47f59f84d8488947f50c95429bf",
+ "model_id": "a86dc7e1965f445781bd785f155b8e6c",
"version_major": 2,
"version_minor": 0
},
@@ -2740,13 +2731,13 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "7ba35505666945fc9f3a55c6069ffdda",
+ "model_id": "517ab704ab66459b93cf02b39a3f9a86",
"version_major": 2,
"version_minor": 0
},
@@ -2898,12 +2889,12 @@
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
- "image/png": "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\n",
+ "image/png": "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\n",
"text/latex": [
"$\\displaystyle 25.3$"
],
@@ -2911,7 +2902,7 @@
"25.3"
]
},
- "execution_count": 22,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -2962,13 +2953,13 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "bc1b76a9c2274dd388de224f171ca721",
+ "model_id": "18cc21ed4c0e49b69746cfc3ed4377ce",
"version_major": 2,
"version_minor": 0
},
@@ -3003,12 +2994,12 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
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+ "image/png": "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\n",
"text/latex": [
"$\\displaystyle 39.05$"
],
@@ -3016,7 +3007,7 @@
"39.05"
]
},
- "execution_count": 25,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -3055,13 +3046,13 @@
},
{
"cell_type": "code",
- "execution_count": 26,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
- "model_id": "0bd0b493db484d8cbdbd8c0415b15606",
+ "model_id": "5996458965984c958d127bd5eafa8970",
"version_major": 2,
"version_minor": 0
},
@@ -3152,7 +3143,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.10"
+ "version": "3.9.1"
},
"toc": {
"base_numbering": 1,
diff --git a/tour3_nonlinear_bond/3_2_anchorage_length.ipynb b/tour3_nonlinear_bond/3_2_anchorage_length.ipynb
index cf7830e..17e33dd 100644
--- a/tour3_nonlinear_bond/3_2_anchorage_length.ipynb
+++ b/tour3_nonlinear_bond/3_2_anchorage_length.ipynb
@@ -849,7 +849,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.8.10"
+ "version": "3.9.1"
},
"toc": {
"base_numbering": 1,
diff --git a/tour5_damage_bond/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb b/tour5_damage_bond/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb
index ed5e01b..23829a1 100644
--- a/tour5_damage_bond/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb
+++ b/tour5_damage_bond/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb
@@ -47,14 +47,21 @@
"Summarizing, in the present notebook, we are going to\n",
"* describe and visualize examples of damage functions in 1D\n",
"* show how to use an isotropic damage model to represent \n",
- " the material behavior of a 2D interface? "
+ " the material behavior of a 2D interface"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "# **Motivation: Fiber bundle behavior described using a damage function**"
+ "# **Motivation and general aspects of damage**"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fiber bundle behavior described using a damage function"
]
},
{
@@ -132,9 +139,21 @@
"in tension and in shear. The damage function explained below are applicable in \n",
"both situations. Moreover, they can be used also in two- and three dimensional\n",
"configurations as well.\n",
- "\n",
- "\n",
- "Thus, we can express the tensile response of a yarn as\n",
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Mathematical framework for the definition of damage models"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The tensile response of a yarn can be expressed as\n",
"\\begin{align}\n",
"\\sigma &= \\psi E_\\mathrm{b} s = (1 - \\omega) E_\\mathrm{b} \\varepsilon\n",
"\\end{align}"
@@ -171,14 +190,13 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "In the elastic regime with no damage, the value of $\\omega$ remains zero $\\omega = 0$. After the breakage of the first filament, it starts to grow up to a complete damage with $\\omega = 1$. Having used the fiber bundles as suitable pictures for the motivation of damage by explaining their tensile response, we will return to the bond-slip law $\\tau(s)$ in the sequel with the goal to mathematically describe the bond and pullout behavior within the damage framework. "
+ "In the elastic regime with no damage, the value of $\\omega$ remains zero $\\omega = 0$. After the breakage of the first filament, it starts to grow up to a complete damage with $\\omega = 1$. Having used the fiber bundles as a suitable picture to motivate the damage modeling for tensile response, we will return to the bond-slip law $\\tau(s)$ in the sequel with the goal to mathematically describe the bond and pullout behavior within the damage framework. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "# **Mathematical framework for the definition of damage models**\n",
"\n",
"Instead of explicitly prescribing the nonlinear bond slip law as a nonlinear curve let us prescribe \n",
"a nonlinear curve governing the evolution of stiffness.\n",
@@ -191,36 +209,22 @@
"\n",
"where $\\omega(\\kappa)$ is the nonlinear damage function and $\\kappa$ is the state variable\n",
"that is equivalent to maximum slip $s$ (or strain $\\varepsilon$) attained during \n",
- "the loading history. The only difference with respect to the models\n",
- "used in Tour 2 is that the bond slip model introduces the \n",
- "initial bond stiffness $E_\\mathrm{b}$ and prescribes its reduction in terms of the \n",
- "damage function $\\omega(\\kappa)$."
+ "the loading history."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "**What is the shape of the damage function?** The answer to this question is not unique\n",
- "and depends on the particular type of material. Let us distinguish three ways how to define it\n",
- "\n",
- " 1. **Definition based on an experiment:** Given a measured $\\sigma(\\epsilon)$ curve, the damage level $\\omega$ can be resolved directly by rearranging the [stress-strain equation](#damage_general), i.e. \n",
- " \\begin{align}\n",
- " \\omega = \\left(1 - \\dfrac{1}{E_\\mathrm{b}} \\right) \\dfrac{\\tau}{s}\n",
- " \\end{align}\n",
- " or the integrity function\n",
- " \\begin{align}\n",
- " \\psi = \\dfrac{\\tau}{E_\\mathrm{b} s}\n",
- " \\end{align}\n",
- " 2. **Definition based on probabilistic density function of fiber strength**: Let us remark, that a the properties of a damage function as a non-decreasing function within a range (0,1) are equal to a cumulative probability density function. This fact provides the possibility to introduce the damage function as an integrated probability density function of a filament strength within the fiber bundle model as indicated in the [stress strain response](#sig_eps_damage). \n",
- " 3. **Definition based on the amount of dissipated energy**: To narrow down the possible shapes of the damage profile, theoretical arguments based on energetic interpretation of the damage process can be used to scale the damage function to a obtain the desired amount of energy dissipation. This aspect will be addressed more in detail in Tour 6 introducing energy dissipation as an effective means of describing the localization and fracture of material exhibiting damage."
+ "<div style=\"background-color:lightgray;text-align:left\"> <img src=\"../icons/remark.png\" alt=\"Previous trip\" width=\"50\" height=\"50\">\n",
+ " <b>Apparent and effective stress</b> </div> "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "**Apparent and effective stress:** By rearranging the terms in the [above damage equation](#damage_general) we can introduce the notion of effective stress as \n",
+ "By rearranging the terms in the [above damage equation](#damage_general) we can introduce the notion of effective stress as \n",
"\n",
"\\begin{equation}\n",
"\\tilde{\\tau} = \\frac{\\tau}{1-\\omega} = E_b \\; s\n",
@@ -229,6 +233,27 @@
"Note that effective stress $\\tilde{\\tau} \\geq \\tau$. While the apparent stress is related to the original material area, the effective stress is related to the undamaged material area. In other words, it can be interpreted as the stress acting on the remaining fraction of springs. The effective stress is related to the instantaneous, or still effective, cross section and not to the initial cross sectional area of the unit material zone."
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## How to identify the shape of the damage function?\n",
+ "\n",
+ "There are several ways how to justify a particular shape of the damage function. \n",
+ "Let us distinguish three ways in which the damage functions are introduced.\n",
+ "\n",
+ " 1. **Definition based on an experiment:** Given a measured $\\sigma(\\epsilon)$ curve, the damage level $\\omega$ can be resolved directly by rearranging the [stress-strain equation](#damage_general), i.e. \n",
+ " \\begin{align}\n",
+ " \\omega = \\left(1 - \\dfrac{1}{E_\\mathrm{b}} \\right) \\dfrac{\\tau}{s}\n",
+ " \\end{align}\n",
+ " or the integrity function\n",
+ " \\begin{align}\n",
+ " \\psi = \\dfrac{\\tau}{E_\\mathrm{b} s}\n",
+ " \\end{align}\n",
+ " 2. **Definition based on probabilistic density function of fiber strength**: Let us remark, that a the properties of a damage function as a non-decreasing function within a range (0,1) are equal to a cumulative probability density function. This fact provides the possibility to introduce the damage function as an integrated probability density function of a filament strength within the fiber bundle model as indicated in the [stress strain response](#sig_eps_damage). \n",
+ " 3. **Definition based on the amount of dissipated energy**: To narrow down the possible shapes of the damage profile, theoretical arguments based on energetic interpretation of the damage process can be used to scale the damage function to a obtain the desired amount of energy dissipation. This aspect will be addressed more in detail in Tour 6 introducing energy dissipation as an effective means of describing the localization and fracture of material exhibiting damage."
+ ]
+ },
{
"cell_type": "code",
"execution_count": 1,
--
GitLab