3. Substitute the result into the kinematic relation stating that the pull-out displacement is equal to the integral of fiber strain along the debonded length
4. Identify the integration constants by applying boundary conditions: equilibrium at loaded end and compatibility and smoothness at the end of the debonded zone $x = a$
These step deliver the pull-out curve as a square root function
\begin{align}
P = \sqrt{p \bar{\tau} E_\mathrm{f} A_\mathrm{f} w}
Let us utilize the the derived model to simulate the test results of the RILEM pull-out test
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| Symbol | Unit |Description |
|:- |:- |:- |
| $E_\mathrm{f}$ | MPa | Young's modulus of reinforcement |
| $\bar{\tau}$ | MPa | Bond stress |
| $A_\mathrm{f}$ | mm$^2$ | Cross-sectional area of reinforcement |
| $p$ | mm | Perimeter of contact between concrete and reinforcement |
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### **Observation**
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- The measured displament at the loaded and unloaded end are different
- Their difference increases with increasing bond length $L_\mathrm{b}$
- The shape of the pull-out curve has a shape of a square root function
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### **Question**
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- Can the above derived model describe the debonding process correctly?
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# Look inside the specimen using the model
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The parameters of the above experiment are specified as follows
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``` python
ds=16
A_f=(ds/2)**2*3.14# mm^2 - reinforcement area
L_b=5*ds# mm - bond length
E_f=210000# MPa - reinforcement stiffness
p_b=3.14*ds# mm - bond perimeter
w_max=0.12# mm - maximum displacement
```
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**Construct the model:** To study the model behavior import the class `PO_ELF_RLM`, construct it with the defined parameters and run the `interact` method
**Remark:** that the length $L_b$ is not the end of the bond zone. It only measures the slip at the position $x = L_\mathrm{b}$ from the loadedend. However, the debonding process can continue beyond this length.
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``` python
po.interact()
```
%% Output
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## Let's learn from the model
Exercise the relation between $P$ and $\tau(x)$ and between $w$ and $\varepsilon(x)$.
1. What is the meaning of the green area?
2. What is the meaning of the red area?
3. What is the meaning of the slope of the green curve?
4. Is it possible to reproduce the shown RILEM test response using this "frictional" model?
4. What is the role of debonded length $a$ in view of general non-linear simulation?
