{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BMCS applications\n",
    "Collection of notebooks accompanying the course on brittle-matrix composite structures.\n",
    "\n",
    "Institute of Structural Concrete\n",
    "@author: Rostislav Chudoba, Abedulgader Baktheer\n",
    "\n",
    "## Seminar work\n",
    " - [J0000 - How to set the pullout model parameters](bmcs_course/SeminarWorkHowTo.ipynb)\n",
    "\n",
    "## Rule of mixtures for elastic composites\n",
    " - [J0101 - Elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)\n",
    " \n",
    "# BOND\n",
    "\n",
    "## Constant bond-slip law\n",
    "\n",
    "- [J0201 - Pull-out of long fiber from rigid matrix](bmcs_course/2_1_PO_LF_LM_RG.ipynb)\n",
    "- [J0202 - Pull-out of long fiber from long elastic matrix](bmcs_course/2_2_PO_LF_LM_EL.ipynb)\n",
    "- [J0203 - Pull-out of short fiber from rigid matrix](bmcs_course/2_3_PO_SF_M_RG.ipynb)\n",
    "- [J0204 - Comparison of several models](bmcs_course/2_4_PO_comparison.ipynb)\n",
    "\n",
    "## Nonlinear bond-slip law\n",
    "- [J0301 - Pull-out with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb) \n",
    "- [J0302 - EXTRA - Newton iterative scheme](extras/newton_method.ipynb)\n",
    "- [J0303 - EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb)\n",
    "\n",
    "## Unloading, reloading and inelasticity\n",
    "\n",
    "- [J0401 - Unloading with multi-linear bond-slip law](bmcs_course/4_1_PO_multilinear_unloading.ipynb) (PO_BS_ML)\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)\n",
    "- [J0403 - Basic concept of plasticity, kinematic hardening](bmcs_course/4_3_BS_EP_SH_IK_A.ipynb) (BS_EP_SH_I_A)\n",
    "- [J0404 - EXTRA - Generalization of the algorithm using vectors](bmcs_course/4_4_BS_EP_SH_IK_N.ipynb) (BS_EP_SH_IK_N)\n",
    "\n",
    "## Inelasticity modeled as damage\n",
    "- [J0501 - Damage initiation, damage evolution, 2D bond behavior](bmcs_course/5_1_Introspect_Damage_Evolution_Damage_initiation)\n",
    "- [J0502 - Pull out simulation using damage model](bmcs_course/5_2_PO_DM_FRP_N.pynb)\n",
    "\n",
    "# CRACK\n",
    "\n",
    "## Energy dissipation\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import bmcs_utils.api"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Structural levels and the model components\n",
    "Stress redistribution processes - how do they affect the design principles?\n",
    " - ultimate limit state\n",
    " - serviceability limit state\n",
    " \n",
    " Minimialstic assumptions - nonlinear - multilinear stress-strain response of concrete, bond and brittle matrix "
   ]
  },
  {
   "attachments": {
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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![image.png](attachment:b1d481d2-04ed-458d-b196-5b2e2a13d7fa.png)](reference)[![image.png](attachment:18b01361-65d7-4834-bd05-a276832cfbad.png)](reference2)[![image.png](attachment:ca77b4ab-74c9-4d4c-9042-49f58e7ee1f2.png)](reference3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Types of material behavior "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - nonlinearity hardening / softening\n",
    " - damage / plasticity\n",
    " - energy dissipation / fracture energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unloading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stable crack growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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