{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 2.1: PO_ELF_RLM\n",
    "Pull-out (PO) of a elastic long fiber (ELF) from rigid long matrix (RLG)\n",
    "\n",
    "[Video - pullout with constant bond](https://moodle.rwth-aachen.de/mod/page/view.php?id=551807)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Observation\n",
    "Let us try to utilize the depicted idealization for the derivation of a model that can help us simulate the test results of the RILEM pull-out test\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A look inside the specimen using the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pull_out import PullOutAModel, PO_ELF_RLM_Symb\n",
    "po = PullOutAModel(symb_class=PO_ELF_RLM_Symb)\n",
    "po.interact()"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Idealization of the pull-out problem\n",
    "This notebook explains the derivation of the pullout model and provides also its executable form.\n",
    "The one-dimensional idealization of the pull-out is introduced in the figure\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "**Remark**: The origin of the coordinate system is placed at the transition between the bond zone and free zone of the fiber. The domain in the bond zone is defined as $x \\in (-L_\\mathrm{b},0)$. As a result, in the bond domain $x < 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The meaning of the variables defining the idealization is summarized in the table"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The pull-out test is controlled by the displacement at the end of the fiber $w$. \n",
    "\n",
    "The force $P$ is measured to obtain the pull-out curve $P(w)$\n",
    "\n",
    "**Simple and trivial question:** What is the purpose of measuring the pull-out curve?"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simplifications\n",
    "\n",
    "Before referring to advanced possibilities how to solve this problem, let us show that we can derive a rather simple, yet useful model by putting together the conditions of \n",
    " * local equilibrium, kinematics and the constitutive laws, and \n",
    " * boundary and compatibility conditions\n",
    "to analytically solve the pull-out problem.  \n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Simplification 1: Matrix ridigity**\n",
    "\n",
    "The dimensions of the concrete block are 100 $\\times$ 100 mm so that $A_\\mathrm{m} = $10000 mm. Let us consider the diameter of the steel rebar 16 mm so that we get $A_\\mathrm{f}$ = 201 mm. Considering Young's modulus of concrete $E_\\mathrm{m}=$ 28 GPa and  of steel $E_\\mathrm{f} = $ 210 GPa we see that the effective tensile stiffness of these components in the test reads\n",
    "\\begin{align}\n",
    "E_\\mathrm{m} A_\\mathrm{m} &= 280000 \\; \\mathrm{kN/mm} \\\\\n",
    "E_\\mathrm{f} A_\\mathrm{f} &=  42210 \\; \\mathrm{kN/mm} \\\\\n",
    "\\end{align}\n",
    "The stiffness of concrete cross section is thus almost seven times larger than that of concrete. To simplify the construction of the model, let us assume that its stiffness infinite, i.e. $E_\\mathrm{m} A_\\mathrm{m} = \\infty$. This means that the matrix displacement is zero everywhere, i.e. $u_\\mathrm{m}(x) = 0, \\forall x \\in (-L_\\mathrm{b}, 0)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Simplification 2: Constant bond stress** \n",
    "\n",
    "Further, we assume that the interface between steel and concrete transfers a constant shear stress independently on the amount of slip, i.e.\n",
    "\\begin{align}\n",
    " \\tau(s) = \\bar{\\tau}\n",
    "\\end{align}\n",
    "were $\\tau$ is a constant material parameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Simplification 3: Infinite bond length** \n",
    "\n",
    "We consider $L_\\mathrm{b} = \\infty$. Thus, the pull-out process can continue infinitely."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![image.png](attachment:image.png)\n",
    "\n",
    "## Boundary value problem\n",
    "This example shows the analytically solvable model - the simplest possible configuration of the pullout test.\n",
    "By applying the simplifying assumptions, the model parameters specified in the table above reduce to the following symbols that we now define as variables within the `sympy` package. This will allow us to apply the `sympy` package to perform algebraic manipulation, to integrate and to differentiate automatically and concentrate on the model construction instead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "It is convenient to classify the parameters and variables involved in the model into the groups related to parameters describing the geometry, material behavior, measured response, internal state and subsidiary integration parameters that will be resolved during the model derivation. In this classification we also associate the mathematical symbols with the Python variable name introduced in the next cell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Geometrical variables:**\n",
    "\n",
    "| Python | Parameter | Description | \n",
    "| :- | :-: | :- |\n",
    "| `A_f` | $A_\\mathrm{f}$ |  Cross section area modulus of the reinforcement |\n",
    "| `p`   | $p$            |  Perimeter of the reinforcement                  |\n",
    "| `L_b` | $L_\\mathrm{b}$ |  Length of the bond zone of the pulled-out bar   |\n",
    "| `x`   | $x$            |  Longitudinal coordinate |\n",
    "\n",
    "**Material parameters:**\n",
    "\n",
    "| Python | Parameter | Description | \n",
    "| :- | :-: | :- |\n",
    "| `E_f`     | $E_\\mathrm{f}$ |  Young's modulus of the reinforcement |\n",
    "| `tau_bar` | $\\bar{\\tau}$   |  Frictional bond stress               |\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Control parameter:**\n",
    "\n",
    "| Python | Parameter | Description | \n",
    "| :- | :-: | :- |\n",
    "| `P` | $P$ | Pullout force |\n",
    "| `w` | $w$ | pullout control  displacement\n",
    "\n",
    "**State parameter:**\n",
    "\n",
    "| Python | Parameter | Description | \n",
    "| :- | :-: | :- |\n",
    "| `a` | $a$ | Length of the debonded zone |\n",
    "\n",
    "**Integration constants:**\n",
    "\n",
    "| Python | Parameter | Description | \n",
    "| :- | :-: | :- |\n",
    "| `C`, `D` | $C,D$ | Integration constants to be resolved through boundary and continuity conditions |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**Let's import the packages:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "import sympy as sp # symbolic algebra package\n",
    "import numpy as np # numerical package\n",
    "import matplotlib.pyplot as plt # plotting package\n",
    "sp.init_printing() # enable nice formating of the derived expressions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we tell `sympy` to remember these variables for further use. The parameter of the `symbols( str )` is a string that contains comma-separated printable symbol definition. One can use latex commands in this string to introduce e.g. Greek symbols like `\\gamma, \\beta`, etc. The number of symbols in `str` must be equal to the number of variables assigned on the left hand side of the `=` sign"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "E_f, A_f = sp.symbols(r'E_\\mathrm{f}, A_\\mathrm{f}', positive = True )\n",
    "E_m, A_m = sp.symbols(r'E_\\mathrm{m}, A_\\mathrm{m}', positive = True )\n",
    "tau, p = sp.symbols(r'\\bar{\\tau}, p', positive = True)\n",
    "C, D = sp.symbols(r'C, D')\n",
    "P, w = sp.symbols(r'P, w', positive=True)\n",
    "x, a, L_b = sp.symbols(r'x, a, L_b')"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Infinitesimal bond segment\n",
    "Let us now consider an infinitely small segment of the bond zone and employ the usual model ingredients, i.e. equilibrium, constitutive laws of the components and then the kinematics\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "\\begin{align}\n",
    "\\mathrm{d} \\sigma_\\mathrm{f} A_\\mathrm{f} = p \\bar{\\tau} \\, \\mathrm{d}x\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Equilibrium \n",
    "In the halfspace $x \\in (-\\infty, 0)$ the governing equations take the folowing form:<br>\n",
    "\n",
    "The equilibrium equation along the free length of the bar introduces the equivalence between the normal force in the reinforcement $\\sigma_\\mathrm{f} A_\\mathrm{f}$ and and the bond intensity within an ifinitesimal element $\\mathrm{d}x$\n",
    "\\begin{align}\n",
    "\\frac{\\mathrm{d} \\sigma_\\mathrm{f}}{\\mathrm{d} x} &= \\frac{p \\bar{\\tau}}{A_\\mathrm{f}}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "d_sig_f = p * tau / A_f\n",
    "d_sig_f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We have expressed the derivative of tensile strain in the fiber in terms of the constant shear $\\bar{\\tau}$.\n",
    "By integrating this expression we obtain the stress as \n",
    "\\begin{align}\n",
    "\\sigma_\\mathrm{f}(x) &= \\int \\frac{p\\bar{\\tau}}{A_\\mathrm{f}} \\, \\mathrm{d}x = \\frac{p \\bar{\\tau}}{A_\\mathrm{f}} x + C\n",
    "\\end{align}\n",
    "with $C$ as an unknown integration constant. In `sympy` we can issue the `sp.integrate` method to perform the automatic integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sig_f = sp.integrate(d_sig_f, x) + C\n",
    "sig_f "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Constitutive laws: \n",
    "Assuming linear elastic behavior with the Young's modulus $E_\\mathrm{f}$ we obtain the strain $\\varepsilon$ as\n",
    "\\begin{align}\n",
    "\\varepsilon_\\mathrm{f}(x) = \\frac{1}{E_\\mathrm{f}} \\sigma_{\\mathrm{f}} = \\frac{1}{E_\\mathrm{f}} \\left(\\frac{p \\tau}{A_\\mathrm{f}} x + C \\right).\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "eps_f = sig_f / E_f\n",
    "eps_f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Kinematics: \n",
    "Realizing that\n",
    "\\begin{align}\n",
    "\\varepsilon_\\mathrm{f} &= \\frac{\\mathrm{d} u}{\\mathrm{d} x}\n",
    "\\implies \n",
    "u_\\mathrm{f} = \\int\n",
    "\\varepsilon_\\mathrm{f} \\mathrm{d} x\n",
    "\\end{align}\n",
    "we obtain the displacement of the bar as an integral\n",
    "\\begin{align}\n",
    "u_\\mathrm{f}(x) &= \n",
    "\\int \n",
    "\\frac{1}{E_\\mathrm{f}} \\left(\\frac{p \\tau}{A_\\mathrm{f}} x + C \\right) \\; \\mathrm{d}x =\n",
    "\\frac{p \\tau x^{2}}{2 A_\\mathrm{f} E_\\mathrm{f}} + \\frac{C x}{E_{\\mathrm{f}}} + D \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "u_f = sp.integrate(eps_f, x) + D\n",
    "u_f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**What's next?**\n",
    "\n",
    "We obtained a function that describes the displacement along the bond zone $x < 0$. Moreover, it implicitly satisfies the local equilibrium conditions and constitutive laws in each material point. \n",
    "\n",
    "However, there are still two unknown integration constants $C$ and $D$. Thus, our local solution can be fulfilled for various boundary conditions. In other words, the obtained solution is valid no matter if we load the pull-out specimen on right or on the left hand side. To resolve these constants we have to find further equilibrium or compatibility conditions. "
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Resolving integration constants \n",
    "### Equilibrium at the loaded end\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "__Condition 1__: Stress in the free length must be equal to load over area: $\\sigma_\\mathrm{f}(0) = P/A_\\mathrm{f} \\; \\implies \\; P - \\sigma_\\mathrm{f}(0) A_\\mathrm{f} = 0 \\implies C = P / A_\\mathrm{f}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "eq_C = {P - sig_f.subs({x:0}) * A_f}\n",
    "C_subs = sp.solve(eq_C,C)   \n",
    "C_subs # display the result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**`sympy` explanation**: Let us explain the two lines\n",
    "\n",
    "__Line 1__: Defines the equation to solve $P - \\sigma_\\mathrm{f}(x=0) A_\\mathrm{f} = 0$ in curly braces `{}`. The resulting data type is a set. Set is an unordered container. The set was assigned to a variable `eq_C`. \n",
    "\n",
    "__Line 2__: Then we used the `sp.solve` method available in `sympy` package with two parameters. The first parameter is the equation to solve `eq_C` and the second is the variable `C` that we want to resolve. The result is obtained in form of a dictionary defining a key-value pair of the variable and the resolved expression. "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compatibility condition requiring the continuity of slip\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "The solution for the integration constant $D$ requires a second thought. Can we say something about how does the displacement approach zero within the embedded length? The figure shows the geometrical meaning of the applied conditions. With condition 1 we required that the slope of the curve $u_\\mathrm{f}$, i.e the stress must be equal to the external load. Thus all the parabolic curves must have the same slope at the point $x = 0$. Now the parameter $D$ can stretch and scale the curve along the $x$ axis. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Condition 2__: We can postulate, that at some unknown position $a < 0$, the slip between the reinforcement and the matrix will be zero, i.e. $u_\\mathrm{f}(a) = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "eqns_D = {u_f.subs(C_subs).subs(x,a)}\n",
    "D_subs = sp.solve(eqns_D,D)\n",
    "D_subs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**`sympy` explanation:** The function `u_f` still contains the unknown parameter $C$. Therefore, we substitute the solution from step 1 using the method `.subs` that replaces `C` by the solution. Let us do this step separately"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "u_f.subs(C_subs).subs(D_subs) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Thus, only $D$ remained to be resolved. Then, we substituted $x = a$ using again the `.subs` method with the first argument specifying the variable to be substituted and the second argument the value to substitute. Finally, the `sp.solve` method is used to get the resolved integration constant $D$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compatibility condition requiring the continuity of slip\n",
    "Well, we could get rid of $D$ but a new unknown appeared in form of $a$. Thus, the continuity postulate did not solve the problem. Another condition must be found to get rid of parameter $a$. Still, there is a subtle difference. We can associate $a$ with clear meaning that represents the state of our pull-out problem. It is the **debonded length**. Knowing this, it is easier to find the last condition: can we say something about how does the displacement approach zero at the end of the debonded length? \n",
    "\n",
    "__Condition 3__: We postulate, that also the strain $\\varepsilon$ vanishes at the same distance $a$ as displacement reaches zero. i.e. $\\varepsilon_\\mathrm{f}(a) = 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "eqns_a = {eps_f.subs(C_subs).subs(D_subs).subs(x,a)}\n",
    "a_subs = sp.solve(eqns_a,a)\n",
    "a_subs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**sympy explanation:** The same methods of substitution and algebraic resolution were applied in the last step to resolve $a$\n",
    "\n",
    "Now all the unknown parameters are resolved. Lets put them all into a single dictionary called var_subs for convenience to avoid long substitution expressions to derive $u_\\mathrm{f}$, $\\varepsilon_\\mathrm{f}$ and $\\sigma_\\mathrm{f}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "var_subs = {**C_subs,**D_subs,**a_subs}\n",
    "var_subs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "With the known values of integration parameters we can resolve the sought displacement fields and plot it "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "u_f_x = u_f.subs(var_subs)\n",
    "u_f_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Visualization of results\n",
    "We have derived a symbolic expression. But how to efficiently quantify it?\n",
    "### Substitute for material parameters\n",
    "Substitute for all the material and geometry parameters and the load P the value 1 and plot the curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "data_f = {L_b:1, p:1, E_f:1, A_f:1, tau:1}\n",
    "u_f_x.subs(data_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let us now prepare this function for interactive visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "get_u_f_x = sp.lambdify((x, P), u_f_x.subs(data_f))\n",
    "x_range = np.linspace(-1, 0, 11)\n",
    "get_u_f_x(x_range, 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**`sympy` explanation:** The obtained expression `u_f_x` contains symbols. To plot a function, the symbolic expression must be transformed to a quantifiable procedure. This is what `sp.lambdify` is doing. Its first argument  specifies the input variables for the generated \"lambdified\" function. In our case, it is `x` and `P`. The second argument is the expression to be evaluated, i.e. our solution with substituted data parameters `u_f_x.subs(data_f)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "x_range = np.linspace(-2,0,100)\n",
    "u_f_x_range = get_u_f_x(x_range, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**`numpy` explanation:** To prepare an array of data we first generated an array `x_range` with 100 values in the range from (-2,0). Then the newly generated function `get_u_f_x` was called with these 100 values to get the corresponding value of displacement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**`matplotlib` explanation:** Let us plot the result using the matplotlib package. It is possible to invoke simply the method\n",
    "\n",
    "`plt.plot(x_range, u_f_range)`\n",
    "\n",
    "with the first argument specifying the data points along the horizontal and second argument along the vertical axis, respectively.\n",
    "\n",
    "But to prepare the later interaction with the model we directly use a more flexible plotting area with two subplots called `axes`. Such area is prepared using the function `plt.subplots(rows, cols)` which returns a figure and the `axes` for specified number of `rows` and `cols`. The returned `axes` objects can then be used to insert the data arrays as in the above `plt.plot` method. Below we construct a figure with two axes and plot into our displacement profile into the left diagram. We insert also a legend and fill the area between zero level and the data points with a value of opacity $0.2$. The second subplot axes is empty. It is prepared for the next diagram explained below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "fig, ax_u1 = plt.subplots(1,1, figsize=(6,3), tight_layout=True)\n",
    "ax_u1.plot(x_range, u_f_x_range, color='black');\n",
    "ax_u1.set_xlabel('x [mm]'); ax_u1.set_ylabel('$u$ [mm]')\n",
    "ax_u1.fill_between(x_range, u_f_x_range, color='black', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Range of validity\n",
    "The plot looks fine, but why do we get the displacement for $x < -1$? Let us recall that the debonded length was"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "a_subs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "so that $a = -1$. The range $x < a$ is beyond our applied model assumptions. We explicitly treated only the range $x \\in (a, 0)$. Thus for nicer postprocessing we have to set $u_f(x) = 0, \\; \\forall x < a$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This can be readily done using the piecewise covering the domain of $x$ piece by piece.\n",
    "\\begin{align}\n",
    "  u_\\mathrm{fa} & = \\left\\{\n",
    "  \\begin{array}{ll}\n",
    "  u_\\mathrm{f}(x) & \\iff x < 0 \\land x > a, \\; \\mathrm{where} \\; a = -\\frac{P}{p\\tau}, \\\\\n",
    "  0      & \\mathrm{otherwise}\n",
    "  \\end{array}\n",
    "  \\right.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "u_fa_x = sp.Piecewise((u_f_x, x > var_subs[a]),\n",
    "                      (0, x <= var_subs[a]))\n",
    "u_fa_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_u_fa_x = sp.lambdify((x, P), u_fa_x.subs(data_f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Plot the result in the right subplot `ax_u2` in the figure above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import ipywidgets as ipw\n",
    "u_fa_x_range = get_u_fa_x(x_range, 1)\n",
    "fig, (ax_u2) = plt.subplots(1,1, figsize=(6,3), tight_layout=True)\n",
    "line_u2, = ax_u2.plot(x_range, u_fa_x_range, color='black');\n",
    "ax_u2.set_xlabel('x [mm]'); ax_u2.set_ylabel('$u$ [mm]')\n",
    "def update(P):\n",
    "    line_u2.set_ydata(get_u_fa_x(x_range, P))\n",
    "ipw.interact(update, P=ipw.FloatSlider(min=0, max=1, step=0.05));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Evaluate strains and stresses\n",
    "With the known displacements at hand, we can directly calculate the strains as\n",
    "\\begin{align}\n",
    "\\varepsilon_\\mathrm{f} = \\frac{\\mathrm{d} u_\\mathrm{f}}{ \\mathrm{d} x}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "eps_f_x = sp.diff(u_fa_x,x)\n",
    "eps_f_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The stresses along the fiber are given as\n",
    "\\begin{align}\n",
    "\\sigma_\\mathrm{f} = \\frac{\\varepsilon_\\mathrm{f}}{ E_\\mathrm{f} }\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sig_f_x = E_f * eps_f_x\n",
    "sig_f_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The profile of shear stress along the bond zone is obtained as\n",
    "\\begin{align}\n",
    " \\tau = \\frac{\\mathrm{d} \\sigma}{\\mathrm{d} x}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "tau_x = sp.simplify(sig_f_x.diff(x) * A_f / p)\n",
    "tau_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot the strains and stresses\n",
    "Similarly to the callable function `get_u_fa_x` let us define the functions for the strains and stresses using the `sp.lambdify` generator "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "get_eps_f_x = sp.lambdify((x, P), eps_f_x.subs(data_f))\n",
    "get_sig_f_x = sp.lambdify((x, P), sig_f_x.subs(data_f))\n",
    "get_tau_x = sp.lambdify((x, P), tau_x.subs(data_f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To make the code for plotting shorter let us define a general procedure plotting and filling the curves and attaching the labels to a specified subplot in one call "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import bmcs_pullout_ui as poui"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from pull_out import PullOutAModel, CB_ELF_RLM_Symb\n",
    "po = PullOutAModel(symb_class=CB_ELF_RLM_Symb)\n",
    "po.interact()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Pull-out curve\n",
    "We have expressed the solution to find out what is the stress state within the bond zone $x \\in L_\\mathrm{b}$. However, to relate the test to the experimental observation we need to find the relation $P(w)$. Thus, we evaluate\n",
    "\\begin{align}\n",
    " w = u(x=0)\n",
    " = \\displaystyle \\frac{P^{2}}{2 A_\\mathrm{f} E_\\mathrm{f} p \\tau}\n",
    "\\end{align}\n",
    "Resolving this equation with respect to $P$ we obtain\n",
    "\\begin{align}\n",
    " P_{\\mathrm{push}, \\mathrm{pull}} = \\pm \\sqrt{ 2 A_\\mathrm{f} E_\\mathrm{f} p \\tau w }\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "**`sympy` explanation:** In parallel let us use again the `subs` and `solve` provided in `sympy` to define the `P_push` and `P_pull` variables in the running `jupyter` kernel. As `solve` searches for zero point of the supplied equation we must transform the above equation into"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "u_f_x.subs(x,0) - w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "and then send it to `sp.solve`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "Pw_pull = sp.solve(u_f_x.subs({x:0})-w, P)[0]\n",
    "Pw_pull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Note that the obtained $P(w)$ covers both the pull-out and push-in case. If we supply the parameters defined above with unit stiffness, area and perimeter we obtain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "data_f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "Pw_pull.subs(data_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot the pull-out curve\n",
    "The symbolic expression must be transformed into a quantifiable form using `sp.lambdify`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "get_Pw_pull = sp.lambdify(w, Pw_pull.subs(data_f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Plotting is done using the same methods as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "fig, ax_pull = plt.subplots(1,1, figsize=(7,4), tight_layout=True)\n",
    "w_range = np.linspace(0,2,50)\n",
    "ax_pull.plot(w_range, get_Pw_pull(w_range), \n",
    "                color='blue')\n",
    "ax_pull.set_xlabel(r'$w$ [mm]'); ax_pull.set_ylabel(r'$P$ [N]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Displacement at the unloaded end\n",
    "To see the difference between the displacement measured at $x = 0$ and $x = -L_\\mathrm{b}$ let us provide a callable function evaluating $u_\\mathrm{f}(x = -L_\\mathrm{b})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "py_vars = ('w', 'tau', 'p', 'L_b', 'A_f', 'A_m', 'E_f', 'E_m')\n",
    "map_py2sp = {py_var : globals()[py_var] for py_var in py_vars}\n",
    "sp_vars = tuple(map_py2sp[py_var] for py_var in py_vars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_L_b = u_fa_x.subs(x, -L_b).subs(P, Pw_pull)\n",
    "w_L_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "aw_pull = a_subs[a].subs(P, Pw_pull)\n",
    "aw_pull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Package the derived methods for later use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import traits.api as tr\n",
    "class PO_LF_LM_RG(tr.HasTraits):\n",
    "    get_Pw_pull = sp.lambdify(sp_vars, Pw_pull)\n",
    "    get_aw_pull = sp.lambdify(sp_vars, aw_pull)\n",
    "    get_w_L_b = sp.lambdify(sp_vars, w_L_b.subs(P, Pw_pull))\n",
    "    get_u_fa_x = sp.lambdify((x,) + sp_vars, u_fa_x.subs(P, Pw_pull))\n",
    "    get_u_ma_x = lambda x, *args: np.zeros_like(x)\n",
    "    get_eps_f_x = sp.lambdify((x,) + sp_vars, eps_f_x.subs(P, Pw_pull))\n",
    "    get_eps_m_x = lambda x, *args: np.zeros_like(x)\n",
    "    get_sig_f_x = sp.lambdify((x,) + sp_vars, sig_f_x.subs(P, Pw_pull))\n",
    "    get_sig_m_x = lambda x, *args: np.zeros_like(x)\n",
    "    get_tau_x = sp.lambdify((x,) + sp_vars, tau_x.subs(P, Pw_pull))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interactive exploration\n",
    "Now that we have finished the construction of the model we can track the process and explore the correspondence between the internal state and externally observed response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import bmcs_pullout_ui as poui\n",
    "po = poui.ModelInteract(\n",
    "    models=[PO_LF_LM_RG],\n",
    "    w_max = 1.0,\n",
    "    py_vars=list(py_vars),\n",
    "    map_py2sp=map_py2sp\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "po.interact_fields()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Let's learn from the model\n",
    "\n",
    "Exercise the relation between $P$ and $\\tau(x)$ and between $w$ and $\\varepsilon(x)$.\n",
    "\n",
    " 1. What is the meaning of the green area?\n",
    " 2. What is the meaning of the red area?\n",
    " 3. What is the meaning of the slope of the green curve?\n",
    " 4. Is it possible to reproduce the shown RILEM test response using this \"frictional\" model?\n",
    " 4. What is the role of debonded length $a$ in view of general non-linear simulation?\n",
    " 5. When does the pull-out fail?\n",
    " 5. What happends with $a$ upon unloading?"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Let's make a prediction\n",
    "What happens if we substitute the parameters from the RILEM pull-out test?\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "get_Pw_pull_args = sp.lambdify((w, A_f, E_f, tau, p, L_b), Pw_pull)\n",
    "ds16 = 16  \n",
    "ds28 = 28\n",
    "w_range = np.linspace(0, 0.12, 100)\n",
    "fig, ax = plt.subplots(1,1, figsize=(7,4), tight_layout=True)\n",
    "ax.plot(w_range, get_Pw_pull_args(w_range, np.pi*(ds16/2)**2, 210000, 2, p=np.pi*ds16, L_b=5*ds16 ), \n",
    "        color='blue', label='ds=16, L_b=5ds')\n",
    "ax.plot(w_range, get_Pw_pull_args(w_range, np.pi*(ds16/2)**2, 210000, 2, p=np.pi*ds16, L_b=10*ds16 ), \n",
    "        color='red', label='ds=16, L_b=10ds')\n",
    "ax.plot(w_range, get_Pw_pull_args(w_range, np.pi*(ds28/2)**2, 210000, 2, p=np.pi*ds28, L_b=3*ds28 ), \n",
    "        color='green', label='ds=28, L_b=3ds')\n",
    "ax.set_ylabel(r'P [N]'); ax.set_xlabel(r'w [mm]')\n",
    "fig.legend(loc=9);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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   "execution_count": null,
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   "execution_count": null,
   "metadata": {},
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
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  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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