{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Example 4.1: Pull-out multilinear bond-slip law unloading\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."
]
},
{
"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",
"/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"
]
}
],
"source": [
"%matplotlib widget\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from bmcs_cross_section.api import PullOutModel"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model parameters\n",
"Let us consider the case of the CFRP sheet debonding from concrete"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"A_f = 16.67 # [mm^2]\n",
"A_m = 1540.0 # [mm^2]\n",
"p = 1.0 #\n",
"E_f = 170000 # [MPa]\n",
"E_m = 28000 # [MPa]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Construct the finite element pullout model\n",
"The model uses a multilinear bond-slip law specified by the attributes \n",
"s_arr and tau_arr specifying the pairs of slip and bond stress values."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"REGENERATE DOMAIN\n",
"REGENERATE DOMAIN\n",
"REGENERATE DOMAIN\n"
]
}
],
"source": [
"pm = PullOutModel()\n",
"pm.mat_mod_.s_data = \"0, 0.1, 0.4, 4\"\n",
"pm.mat_mod_.tau_data = \"0, 800, 0, 0\"\n",
"pm.sim.tline.step = 0.01\n",
"pm.cross_section.trait_set(A_f=A_f, P_b=p, A_m=A_m)\n",
"pm.geometry.L_x = 100\n",
"pm.w_max = 2\n",
"pm.n_e_x = 100"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
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"application/vnd.jupyter.widget-view+json": {
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"version_minor": 0
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"text/plain": [
"VBox(children=(HBox(children=(VBox(children=(Tree(layout=Layout(align_items='stretch', border='solid 1px black…"
]
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.interact()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
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"application/vnd.jupyter.widget-view+json": {
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"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/latex": [
"\n",
" \\begin{array}{lrrl}\\hline\n",
" \\textrm{number_of_cycles} & n_\\mathrm{cycles} = 1 & \\textrm{[-]} & \\textrm{for cyclic loading} \\\\\n",
" \\textrm{maximum_loading} & \\phi_{\\max} = 1.0 & \\textrm{[-]} & \\textrm{load factor at maximum load level} \\\\\n",
" \\textrm{number_of_increments} & n_{\\mathrm{incr}} = 20 & \\textrm{[-]} & \\textrm{number of values within a monotonic load branch} \\\\\n",
" \\textrm{unloading_ratio} & \\phi_{\\mathrm{unload}} = 0.5 & \\textrm{[-]} & \\textrm{fraction of maximum load at lowest load level} \\\\\n",
" \\textrm{amplitude_type} & option = increasing & \\textrm{[-]} & \\textrm{possible values: [increasing, constant]} \\\\\n",
" \\textrm{loading_range} & option = non-symmetric & \\textrm{[-]} & \\textrm{possible values: [non-symmetric, symmetric]} \\\\\n",
" \\hline\n",
" \\hline\n",
" \\end{array}\n",
" "
],
"text/plain": [
"<ibvpy.tfunction.loading_scenario.CyclicLoadingScenario at 0x7fdbc3ba7f40>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"pm.loading_scenario_.plot(ax)\n",
"pm.loading_scenario_"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"\n",
" \\begin{array}{lrrl}\\hline\n",
" \\textrm{loading_type} & option = cyclic & \\textrm{[-]} & \\textrm{possible values: [monotonic, cyclic]} \\\\\n",
" \\textrm{number_of_cycles} & n_\\mathrm{cycles} = 2 & \\textrm{[-]} & \\textrm{for cyclic loading} \\\\\n",
" \\textrm{maximum_loading} & \\phi_{\\max} = 1.0 & \\textrm{[-]} & \\textrm{load factor at maximum load level} \\\\\n",
" \\textrm{unloading_ratio} & \\phi_{\\mathrm{unload}} = 0.0 & \\textrm{[-]} & \\textrm{fraction of maximum load at lowest load level} \\\\\n",
" \\textrm{number_of_increments} & n_{\\mathrm{incr}} = 20 & \\textrm{[-]} & \\textrm{number of values within a monotonic load branch} \\\\\n",
" \\textrm{amplitude_type} & option = constant & \\textrm{[-]} & \\textrm{possible values: [increasing, constant]} \\\\\n",
" \\textrm{loading_range} & option = non-symmetric & \\textrm{[-]} & \\textrm{possible values: [non-symmetric, symmetric]} \\\\\n",
" \\hline\n",
" \\hline\n",
" \\end{array}\n",
" "
],
"text/plain": [
"<ibvpy.tfunction.loading_scenario.LoadingScenario at 0x7f4d73abd0e0>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.loading_scenario.loading_type='cyclic'\n",
"pm.loading_scenario.trait_set(number_of_cycles=2,\n",
" unloading_ratio=0.0,\n",
" amplitude_type='constant',\n",
" loading_range='non-symmetric')\n",
"pm.loading_scenario"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"<ipython-input-7-a80ba1790c48>:1: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance. In a future version, a new instance will always be created and returned. Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.\n",
" pm.loading_scenario.plot(plt.axes())\n"
]
}
],
"source": [
"pm.loading_scenario.plot(plt.axes())"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"\n",
" \\begin{array}{lrrl}\\hline\n",
" \\textrm{A_m} & A_\\mathrm{m} = 1540.0 & \\textrm{[$\\mathrm{mm}^2$]} & \\textrm{matrix area} \\\\\n",
" \\textrm{A_f} & A_\\mathrm{f} = 16.67 & \\textrm{[$\\mathrm{mm}^2$]} & \\textrm{reinforcement area} \\\\\n",
" \\textrm{P_b} & p_\\mathrm{b} = 1.0 & \\textrm{[$\\mathrm{mm}$]} & \\textrm{perimeter of the bond interface} \\\\\n",
" \\hline\n",
" \\hline\n",
" \\end{array}\n",
" "
],
"text/plain": [
"<bmcs.pullout.pullout_sim.CrossSection at 0x7f8eacdf6530>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.cross_section.trait_set(A_f=A_f, P_b=p, A_m=A_m)\n",
"pm.cross_section # display the cross section parameters"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"\n",
" \\begin{array}{lrrl}\\hline\n",
" \\textrm{L_x} & L = 45 & \\textrm{[$\\mathrm{mm}$]} & \\textrm{embedded length} \\\\\n",
" \\hline\n",
" \\hline\n",
" \\end{array}\n",
" "
],
"text/plain": [
"<bmcs.pullout.pullout_sim.Geometry at 0x7f8eacdf6470>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.geometry # geometry of the boundary value problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot the current bond-slip law"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"\n",
" \\begin{array}{lrrl}\\hline\n",
" \\textrm{E_m} & E_\\mathrm{m} = 28000.0 & \\textrm{[MPa]} & \\textrm{E-modulus of the matrix} \\\\\n",
" \\textrm{E_f} & E_\\mathrm{f} = 170000.0 & \\textrm{[MPa]} & \\textrm{E-modulus of the reinforcement} \\\\\n",
" \\textrm{s_data} & s = 0, 0.1, 0.4, 4 & \\textrm{[mm]} & \\textrm{slip values} \\\\\n",
" \\textrm{tau_data} & \\tau = 0, 800, 0, 0 & \\textrm{[MPa]} & \\textrm{shear stress values} \\\\\n",
" \\hline\n",
" \\hline\n",
" \\end{array}\n",
" "
],
"text/plain": [
"<ibvpy.tmodel.mats1D5.vmats1D5_bondslip1D.MATSBondSlipMultiLinear at 0x7f1f25718810>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.mat_mod_ # configuration of the material model"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
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"application/vnd.jupyter.widget-view+json": {
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"version_major": 2,
"version_minor": 0
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"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"pm.mat_mod_.plot(ax, color='green')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"c='red'\n",
"pm.geometry.L_x = 200\n",
"pm.sim.run()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "3399b8c10dc540369e2282ed2a5dad7c",
"version_major": 2,
"version_minor": 0
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"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"pm.hist.plot_Pw(ax,0.68)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "0aaabc9a67844b0b801d026243f8fb32",
"version_major": 2,
"version_minor": 0
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"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"for t in np.linspace(0.,0.62,4):\n",
" pm.hist.t_slider = t\n",
" pm.hist.plot_sf(ax)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "f8316fff884f47d4b59a27f8879206fc",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"for t in np.linspace(0.,0.62,4):\n",
" pm.hist.t_slider = t\n",
" pm.hist.plot_s(ax)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "cafa3ab8f561421e899e6f2b0ba7eff9",
"version_major": 2,
"version_minor": 0
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"text/plain": [
"Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"for t in np.linspace(0.,.99,5):\n",
" pm.hist.t_slider = t\n",
" pm.hist.plot_eps_p(ax)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
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"model_id": "8b62d46e22af412cb0926afbb213a01e",
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"text/plain": [
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"_, ax = plt.subplots(1,1,figsize=(7,4))\n",
"for t in np.linspace(0.,.99,5):\n",
" pm.hist.t_slider = t\n",
" pm.hist.plot_sig_p(ax)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Questions and Tasks"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1 Define a symmetric loading scenario with increasing amplitude and 3 cycles"
]
},
{
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"source": []
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