{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Example 2.3: PO-ESF-RSM\n",
    "Pull-out of a short fiber from short matrix "
   ]
  },
  {
   "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 $x < 0$. The fiber is assumed to have an infinite length for $x < -L_\\mathrm{b}$. This means that the length of the bond zone $L_\\mathrm{b}$ remains constant - this fiber will never be pulled out."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The meaning of the variables defining the idealization is summarized in the table"
   ]
  },
  {
   "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"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "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": "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}', nonnegative = True )\n",
    "E_m, A_m = sp.symbols(r'E_\\mathrm{m}, A_\\mathrm{m}', nonnegative = True )\n",
    "tau, p = sp.symbols(r'\\bar{\\tau}, p', nonnegative = True)\n",
    "P, w = sp.symbols('P, w')\n",
    "x, a, L_b = sp.symbols('x, a, L_b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "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)\n",
    "sp_vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Reuse the pullout equation\n",
    "As long as the debonding did not reach the end of the fiber, everything remains the sam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "Pw_pull = sp.sqrt(2*w*tau*E_f*A_f*p)\n",
    "Pw_pull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introduce finite embedded length\n",
    "What happens if the debonded  length $a$ reaches the end of the bond zone $x = -L_\\mathrm{b}$?\n",
    "With reference to the blue subplot above, we see that this point corresponds to a maximum possible shear flow area over the bond zone. Thus, the maximum force that can be transfered through the bond is \n",
    "\\begin{align}\n",
    " P_\\max = \\int_{x = -L_\\mathrm{b}}^{x=} p \\tau(x) \\; \\mathrm{d}x = p \\bar{\\tau} L_\\mathrm{b}\n",
    "\\end{align}\n",
    "The corresponding pullout displacement can be obtained by solving the equation\n",
    "\\begin{align}\n",
    "P_\\max = p \\bar{\\tau} L_\\mathrm{b} = P_\\mathrm{pull}(w) \\implies w\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "P_max = p * tau * L_b\n",
    "w_argmax = sp.solve(P_max - Pw_pull, w)[0]\n",
    "w_argmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introduce finite fiber length\n",
    "What happens when the fiber has a length $L_\\mathrm{f} < L_\\mathrm{b}$? The debonding phase with ascending pull-out curve remains the same as in the previous example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "Pw_up_pull = Pw_pull"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Once $a = L_\\mathrm{b}$ the bond zone starts to shorten. \n",
    "The amount of shortening is equal to the slip at the unloaded end. Let us denote the diminishing effective length of the bond zone in the second phase  \n",
    "\\begin{align}\n",
    "  b = -L_\\mathrm{b} + u_\\mathrm{f}(-L_b)\n",
    "\\end{align}\n",
    "\\begin{align}\n",
    " P_{\\mathrm{down}} = p \\bar{\\tau} b\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "b, P_down = sp.symbols(r'b, P_\\mathrm{down}')"
   ]
  },
  {
   "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",
    "The strain at $x = b$ must be zero and the displacement must be equal to $L_\\mathrm{b} - b$. The strain profile of the pulled out fiber with the instantaneous length $b$ is linear with $\\varepsilon(b) = 0$. Thus the elongation of of the fibuer equals\n",
    "\\begin{align}\n",
    "\\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b\n",
    "\\end{align}\n",
    "The current pull-out displacement is thus a sum of the slip \n",
    "at the free end and the fiber elongation of the zone $b$\n",
    "\\begin{align}\n",
    " w = u_\\mathrm{f}(-L_\\mathrm{b}) - \\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b   \n",
    "\\end{align}\n",
    "After substituting\n",
    "\\begin{align}\n",
    "w = L_\\mathrm{b} + b - \\frac{1}{2} \\varepsilon_\\mathrm{f}(0) b\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sig_0_down = P_down / A_f\n",
    "eps_0_down = 1 / E_f * sig_0_down\n",
    "eps_0_down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "w_down =  (L_b + b) - sp.Rational(1,2) * eps_0_down * b\n",
    "w_down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "Pw_down_pull, Pw_down_push = sp.solve(w_down.subs(b, -P_down / p / tau) -w, P_down)\n",
    "Pw_down_pull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "Pw_short = sp.Piecewise((0, w <= 0),\n",
    "                        (Pw_up_pull, w <= w_argmax),\n",
    "                        (Pw_down_pull, w < L_b),\n",
    "                        (0, True)\n",
    "                       )\n",
    "Pw_short"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp.simplify(Pw_down_pull.args[1].args[3].args[0].subs(w,w_argmax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "get_Pw_short = sp.lambdify(sp_vars, Pw_short)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "w_range = np.linspace(0,2,5000)\n",
    "params = {w: w_range, A_f:1.8, E_f:2, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
    "param_vals = tuple(params[map_py2sp[py_var]] for py_var in py_vars)\n",
    "fix, ax = plt.subplots(1,1, figsize=(8,2))\n",
    "ax.plot(w_range, get_Pw_short(*param_vals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Postprocessing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "w_L_b_a = L_b - Pw_down_pull / p / tau\n",
    "w_L_b = sp.Piecewise((0, w <= w_argmax),\n",
    "                     (w_L_b_a, (w > w_argmax) & (w <= L_b)),\n",
    "                     (w, True)) \n",
    "w_L_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "aw_pull_elastic = - (Pw_short / p / tau)\n",
    "aw_pull_elastic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "aw_up = -Pw_up_pull/p/tau\n",
    "bw_down = -Pw_down_pull/p/tau\n",
    "sig_f_x = sp.Piecewise(\n",
    "    (0, ((w <= w_argmax) & (x <= aw_up)) ),\n",
    "    (-Pw_up_pull/A_f/aw_up*(x-aw_up), ((w <= w_argmax) & (x > aw_up)) ),\n",
    "    (0, ((w > w_argmax) & (x <= bw_down)) ),\n",
    "    (-Pw_down_pull/A_f/bw_down*(x-bw_down), ((w > w_argmax) & (x > bw_down)) ),\n",
    ")\n",
    "sp.simplify(sig_f_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sp_vars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "get_sig_f_x = sp.lambdify((x,) + sp_vars, sig_f_x)\n",
    "get_aw_up = sp.lambdify(sp_vars, aw_up)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.warnings.filterwarnings('ignore', category=np.VisibleDeprecationWarning)                 \n",
    "w_range = np.linspace(0,2,50)\n",
    "x_range = np.linspace(-1,0,100)\n",
    "params = {w: 0.4, A_f:1, E_f:2, A_m:1, E_m:4, tau:1, p:1, L_b:1}\n",
    "param_vals = tuple(params[map_py2sp[py_var]] for py_var in py_vars)\n",
    "get_sig_f_x(0, *param_vals), get_aw_up(*param_vals)\n",
    "fix, ax = plt.subplots(1,1, figsize=(8,2))\n",
    "ax.plot(x_range, get_sig_f_x(x_range, *param_vals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# ds = 0.2\n",
    "po_paper = PullOutAModel(models=[PO_SF_M_RG], py_vars=list(py_vars), map_py2sp=map_py2sp, w=.1, A_f=np.pi*(ds/2)**2, E_f=200000, L_b=9.75, p=np.pi*ds, tau=6.56)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "po_paper.interact_geometry()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Task: use the parameters of the test to fit the response\n",
    "Assume the length of the bond zone $L_b = 6.5m$ and $L_b = 9.75$, $E_\\mathrm{f}=200000$ MPa and the diameter $d = 0.2$ mm. Identify the bond stress $\\bar{\\tau}$ rendering the pullout curve with the maximum force $P_\\max$ = 49 N and final pullout displacement with zero force of 10 mm. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import bmcs_pullout_ui as poui\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "import traits.api as tr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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