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bmcs_course/4_1_PO_multilinear_unloading.ipynb
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%% Cell type:markdown id: tags:
# Example 4.1: Pull-out multilinear bond-slip law unloading
This notebook uses the `bmcs` package to show the unphysical
nature of a model without physical representation of irreversible
processes in the material structure. It unloads along the original
pull-out curve.
Further, the notebook shows how to define non-monotonic loading scenario
using a time-function and how to use the function of the `PullOutModel`
to plot the results into a prepared plotting area.
%% Cell type:code id: tags:
``` python
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from bmcs.api import PullOutModel
```
%% Cell type:markdown id: tags:
## Model parameters
Let us consider the case of the CFRP sheet debonding from concrete
%% Cell type:code id: tags:
``` python
A_f = 16.67 # [mm^2]
A_m = 1540.0 # [mm^2]
p = 1.0 #
E_f = 170000 # [MPa]
E_m = 28000 # [MPa]
```
%% Cell type:markdown id: tags:
## Construct the finite element pullout model
The model uses a multilinear bond-slip law specified by the attributes
s_arr and tau_arr specifying the pairs of slip and bond stress values.
%% Cell type:code id: tags:
``` python
pm = PullOutModel(mats_eval_type='multilinear',
n_e_x=50, k_max=200, w_max=1.84)
pm.sim.tline.step = 0.001
pm.mats_eval.s_tau_table = [[0, 0.1, 0.4, 4],
[0, 800, 0, 0]]
# w = pm.get_window()
# w.configure_traits()
pm
```
%% Output
\begin{array}{lrrl}\hline
\textrm{k_max} & k_{\max} = 200 & \textrm{[-]} & \textrm{maximum number of iterations} \\
\textrm{tolerance} & \epsilon = 0.0001 & \textrm{[-]} & \textrm{required accuracy} \\
\textrm{n_e_x} & n_\mathrm{E} = 50 & \textrm{[-]} & \textrm{number of finite elements along the embedded length} \\
\textrm{mats_eval_type} & \textrm{multilinear} & & \textrm{material model type} \\
\textrm{control_variable} & \textrm{u} & & \textrm{displacement or force control: [u|f]} \\
\textrm{w_max} & w_{\max} = 1.84 & \textrm{[mm]} & \textrm{maximum pullout slip} \\
\textrm{fixed_boundary} & \textrm{non-loaded end (matrix)} & & \textrm{which side of the specimen is fixed [non-loaded end [matrix], loaded end [matrix], non-loaded end [reinf]]} \\
\hline
\textbf{loading_scenario} & \textrm{LoadingScenario} & & \textrm{object defining the loading scenario} \\
\textbf{cross_section} & \textrm{CrossSection} & & \textrm{cross section parameters} \\
\textbf{geometry} & \textrm{Geometry} & & \textrm{geometry parameters of the boundary value problem} \\
\textbf{mats_eval} & \textrm{MATSBondSlipMultiLinear} & & \textrm{material model of the interface} \\
\hline
\end{array}
<bmcs.pullout.pullout_sim.PullOutModel at 0x7f8ead32b2f0>
<bmcs.pullout.pullout_sim.PullOutModel at 0x7f971674c9f0>
%% Cell type:code id: tags:
``` python
pm.loading_scenario.plot(plt.axes())
pm.loading_scenario
```
%% Output
\begin{array}{lrrl}\hline
\textrm{loading_type} & option = monotonic & \textrm{[-]} & \textrm{possible values: [monotonic, cyclic]} \\
\textrm{number_of_cycles} & n_\mathrm{cycles} = 1 & \textrm{[-]} & \textrm{for cyclic loading} \\
\textrm{maximum_loading} & \phi_{\max} = 1.0 & \textrm{[-]} & \textrm{load factor at maximum load level} \\
\textrm{unloading_ratio} & \phi_{\mathrm{unload}} = 0.5 & \textrm{[-]} & \textrm{fraction of maximum load at lowest load level} \\
\textrm{number_of_increments} & n_{\mathrm{incr}} = 20 & \textrm{[-]} & \textrm{number of values within a monotonic load branch} \\
\textrm{amplitude_type} & option = increasing & \textrm{[-]} & \textrm{possible values: [increasing, constant]} \\
\textrm{loading_range} & option = non-symmetric & \textrm{[-]} & \textrm{possible values: [non-symmetric, symmetric]} \\
\hline
\hline
\end{array}
<bmcs.time_functions.loading_scenario.LoadingScenario at 0x7f8eb1ee5b30>
<bmcs.time_functions.loading_scenario.LoadingScenario at 0x7f971342fd10>
%% Cell type:code id: tags:
``` python
pm.loading_scenario.loading_type='cyclic'
pm.loading_scenario.trait_set(number_of_cycles=2,
unloading_ratio=0.0,
amplitude_type='constant',
loading_range='non-symmetric')
pm.loading_scenario
```
%% Output
\begin{array}{lrrl}\hline
\textrm{loading_type} & option = cyclic & \textrm{[-]} & \textrm{possible values: [monotonic, cyclic]} \\
\textrm{number_of_cycles} & n_\mathrm{cycles} = 2 & \textrm{[-]} & \textrm{for cyclic loading} \\
\textrm{maximum_loading} & \phi_{\max} = 1.0 & \textrm{[-]} & \textrm{load factor at maximum load level} \\
\textrm{unloading_ratio} & \phi_{\mathrm{unload}} = 0.0 & \textrm{[-]} & \textrm{fraction of maximum load at lowest load level} \\
\textrm{number_of_increments} & n_{\mathrm{incr}} = 20 & \textrm{[-]} & \textrm{number of values within a monotonic load branch} \\
\textrm{amplitude_type} & option = constant & \textrm{[-]} & \textrm{possible values: [increasing, constant]} \\
\textrm{loading_range} & option = non-symmetric & \textrm{[-]} & \textrm{possible values: [non-symmetric, symmetric]} \\
\hline
\hline
\end{array}
<bmcs.time_functions.loading_scenario.LoadingScenario at 0x7f8eb1ee5b30>
<bmcs.time_functions.loading_scenario.LoadingScenario at 0x7f971342fd10>
%% Cell type:code id: tags:
``` python
pm.loading_scenario.plot(plt.axes())
```
%% Output
%% Cell type:code id: tags:
``` python
pm.cross_section.trait_set(A_f=A_f, P_b=p, A_m=A_m)
pm.cross_section # display the cross section parameters
```
%% Output
\begin{array}{lrrl}\hline
\textrm{A_m} & A_\mathrm{m} = 1540.0 & \textrm{[$\mathrm{mm}^2$]} & \textrm{matrix area} \\
\textrm{A_f} & A_\mathrm{f} = 16.67 & \textrm{[$\mathrm{mm}^2$]} & \textrm{reinforcement area} \\
\textrm{P_b} & p_\mathrm{b} = 1.0 & \textrm{[$\mathrm{mm}$]} & \textrm{perimeter of the bond interface} \\
\hline
\hline
\end{array}
<bmcs.pullout.pullout_sim.CrossSection at 0x7f8eacdf6530>
%% Cell type:code id: tags:
``` python
pm.geometry # geometry of the boundary value problem
```
%% Output
\begin{array}{lrrl}\hline
\textrm{L_x} & L = 45 & \textrm{[$\mathrm{mm}$]} & \textrm{embedded length} \\
\hline
\hline
\end{array}
<bmcs.pullout.pullout_sim.Geometry at 0x7f8eacdf6470>
%% Cell type:markdown id: tags:
## Plot the current bond-slip law
%% Cell type:code id: tags:
``` python
pm.mats_eval # configuration of the material model
```
%% Output
\begin{array}{lrrl}\hline
\textrm{E_m} & E_\mathrm{m} = 28000.0 & \textrm{[MPa]} & \textrm{E-modulus of the matrix} \\
\textrm{E_f} & E_\mathrm{f} = 170000.0 & \textrm{[MPa]} & \textrm{E-modulus of the reinforcement} \\
\textrm{s_data} & s = & \textrm{[mm]} & \textrm{slip values} \\
\textrm{tau_data} & \tau = & \textrm{[MPa]} & \textrm{shear stress values} \\
\hline
\hline
\end{array}
<ibvpy.mats.mats1D5.vmats1D5_bondslip1D.MATSBondSlipMultiLinear at 0x7f8eacdbb2f0>
%% Cell type:code id: tags:
``` python
pm.mats_eval.bs_law.plot(plt, color='green')
```
%% Output
%% Cell type:code id: tags:
``` python
c='red'
pm.geometry.L_x = 200
pm.sim.run()
```
%% Cell type:code id: tags:
``` python
fig, ax = plt.subplots(1,1,figsize=(7,4))
pm.hist.plot_Pw(ax,0.68)
```
%% Output
%% Cell type:code id: tags:
``` python
ax = plt.axes()
for t in np.linspace(0.,0.62,4):
pm.plot_sf(ax,t)
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
ax = plt.axes()
for t in np.linspace(0.,.99,5):
pm.plot_s(ax,t)
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
ax = plt.axes()
for t in np.linspace(0.,.99,5):
pm.plot_eps_p(ax,t)
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
ax = plt.axes()
for t in np.linspace(0.,.99,5):
pm.plot_sig_p(ax,t)
plt.show()
```
%% Output
%% Cell type:markdown id: tags:
# Questions and Tasks
%% Cell type:markdown id: tags:
### 1 Define a symmetric loading scenario with increasing amplitude and 3 cycles
%% Cell type:code id: tags:
``` python
```
%% Cell type:code id: tags:
``` python
```
%% Cell type:code id: tags:
``` python
```
......
bmcs_course/4_3_BS_EP_SH_IK_A.ipynb 0 → 100644
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bmcs_course/4_3_BS_EP_SH_IK_N.ipynb → bmcs_course/4_4_BS_EP_SH_IK_N.ipynb
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......@@ -5091,7 +5091,7 @@
"cell_type": "code",
"execution_count": 30,
"metadata": {
"hide_input": true,
"hide_input": false,
"scrolled": false,
"slideshow": {
"slide_type": "fragment"
......
index.ipynb
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%% Cell type:markdown id: tags:
# BMCS applications
Collection of notebooks accompanying the course on brittle-matrix composite structures.
@author: rosoba
## Rule of mixtures for elastic composites
- [J0101 - Elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)
# BOND
## Constant bond-slip law
- [J0201 - Pull-out of long fiber from rigid matrix](bmcs_course/2_1_PO_LF_LM_RG.ipynb)
- [J0202 - Pull-out of long fiber from long elastic matrix](bmcs_course/2_2_PO_LF_LM_EL.ipynb)
- [J0203 - Pull-out of short fiber from rigid matrix](bmcs_course/2_3_PO_SF_M_RG.ipynb)
- [J0204 - Comparison of several models](bmcs_course/2_4_PO_comparison.ipynb)
## Nonlinear bond-slip law
- [J0301 - Pull-out with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb)
- [J0302 - EXTRA - Newton iterative scheme](extras/newton_method.ipynb)
- [J0303 - EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb)
## Unloading, reloading and inelasticity
- [J0401 - Unloading with multi-linear bond-slip law](bmcs_course/4_1_PO_multilinear_unloading.ipynb) (PO_BS_ML)
- [J0402 - Basic concept of plasticity](bmcs_course/4_2_BS_EP_SH_I_A.ipynb) (BS_EP_SH_I_A)
- [J0403 - EXTRA - General time-stepping algorithm](bmcs_course/4_3_BS_EP_SH_IK_N.ipynb) (BS_EP_SH_IK_N)
- [J0402 - Basic concept of plasticity, ideal and isotopic hardening](bmcs_course/4_2_BS_EP_SH_I_A.ipynb) (BS_EP_SH_I_A)
- [J0403 - Basic concept of plasticity, kinematic hardening](bmcs_course/4_3_BS_EP_SH_IK_A.ipynb) (BS_EP_SH_I_A)
- [J0404 - EXTRA - Generalization of the algorithm using vectors](bmcs_course/4_4_BS_EP_SH_IK_N.ipynb) (BS_EP_SH_IK_N)
## Inelasticity modeled as damage
- [J0404 - Damage framework](bmcs_course)
- [J0405 - Iterative numerical simulation](bmcs_course)
# CRACK
## Energy dissipation
%% Cell type:code id: tags:
``` python
```
......
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