lecture 3

b80c4a71 · Rostislav Chudoba · 38ab1bfa · b80c4a71 · b80c4a71 · b80c4a71
Commit b80c4a71 authored 3 years ago by Rostislav Chudoba
--- a/index.ipynb
+++ b/index.ipynb
@@ -140,7 +140,7 @@
    "### 1.3 Interactive computational environment\n",
    "\n",
    "To demonstrate the theory on examples that can be interactively modified, let us consider an elementary case of mixture rule to determine the effective stiffness of an elastic composite </br>\n",
-    "[**Mixture rule**: example elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)"
+    "[**Mixture rule**: example elastic mixture rule](pull_out/1_1_elastic_stiffness_of_the_composite.ipynb)"
   ]
  },
  {

 %% Cell type:markdown id: tags:

 # **Brittle-Matrix Composite Structures**

 Institute of Structural Concrete; @author: Rostislav Chudoba, Abedulgader Baktheer

 %% Cell type:markdown id: tags:

 ## Expedition investigating the BMCS landscape

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 | |   |   |   |
 |-|-|-------|------|
 | ![image-15.png](attachment:image-15.png) | ![image-4.png](fig/reinforcement.png)  | ![image-2.png](fig/bond.png) | ![image.png](fig/matrix.png) |
 | ![image-14.png](attachment:image-14.png) | [![image-6.png](fig/pullout.png)](pull_out/pull_out.ipynb) | ![image-7.png](fig/crack_bridge.png)| [![image-8.png](fig/mkappa.png)](mkappa/mkappa.ipynb) |
 | ![image-13.png](attachment:image-13.png)  | [![image-9.png](fig/tension.png)](pull_out/fragmentation.ipynb) | [![image-10.png](fig/bending.png)](bending/bending_3pt.ipynb) | ![image-11.png](fig/compression.png) |

 %% Cell type:markdown id: tags:

 ## Guided tours provided through BMCS landscape

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 | No. | Title |
 |- | - |
 | **Tour 1:** | Mixture rule (effective composite stiffness) |
 | **Tour 2:** | Constant bond (friction, pull-out, crack-bridge, multiple cracking) |
 | **Tour 3:** | Nonlinear bond (hardening, softening -> failure modes: anchorage, cracing) |
 | **Tour 4:** | Plastic bond behavior (irreversibility ->  energy dissipation) |
 | **Tour 5:** | Damage bond behavior (2D sheet debonding) |
 | **Tour 6:** | Concrete cracking and yielding (bended cross section) |
 | **Tour 7:** | Beam deflection - comparison wth EC2 and Model Code |

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 ## Tools used in the BMCS

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 | Engine and wheels | Further information |
 |-- |---|
 | Jupyter notebooks |   |
 | OpenWebApps |   |
 | Elementary syntax of Python language |  |
 | Plotting tools | `matplotlib`  |
 | Computer Algebra System | `sympy`  |

 %% Cell type:markdown id: tags:

 ## Knowledge and skills developed during the BMCS expedition

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 * Understand nonlinear material behavior, stress-redistribution, objectivity of material laws
 * Develop a basic understanding of damage, plasticity, fracture
 * Formulate simplified analytical models capturing material and structural behavior
 * Compare self-developed analytical models with general finite-element models
 * Distinguish model verification, calibration, validation and parametric studies

 %% Cell type:markdown id: tags:

 ## **Tour 1**: Introduction

 ### 1.1 A roadmap through the BMCS landscape
 ### 1.2 Introduction to Jupyter Web Apps and notebooks
 Not only static slides and videos but also the possibility to interactively put your fingers on the theory in terms of prepared interactive applications is used throughout the course. Basic information how to
 use the `jupyter` notebooks are summarized here:</br>
 [**Web Apps:** first steps](link)

 ### 1.3 Interactive computational environment

 To demonstrate the theory on examples that can be interactively modified, let us consider an elementary case of mixture rule to determine the effective stiffness of an elastic composite </br>
-[**Mixture rule**: example elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)
+[**Mixture rule**: example elastic mixture rule](pull_out/1_1_elastic_stiffness_of_the_composite.ipynb)

 %% Cell type:markdown id: tags:

 ## **Tour 2:** Constant bond - pull-out, crack bridge, fragmentation

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 ### 2.1 - Pull-out from rigid matrix - test setup and theory

 Using the analytical solution of the pullout problem assuming constant bond-slip law, elastic fiber and rigid matrix, we first explore the fundamental relations between the measured pull-out curve of a steel-rebar from the concrete matrix:</br>
 [**Pull-out:** analytical constant-bond model](pull_out/2_1_1_PO_observation.ipynb)

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 ### 2.2 - Classification of pullout configurations with constant bond stress

 Include further configurations of a pull-out to show the differences in their behavior, learning the correspondence between the shape of the pull-out curve and the distribution of slip, shear, fiber and matrix strain and stresses depending on a particular configuration, i.e. elastic matrix, short fiber, short matrix and  clamped fiber:</br>
 [**Pull-out:** extended analytical constant-bond models - short / long / elastic / clamped](pull_out/2_2_1_PO_configuration_explorer.ipynb)

 %% Cell type:markdown id: tags:

 ### 2.3 - Multiple cracking - fragmentation

 The crack-bridging action of a fiber within a composite loaded in tension is a key to understanding the behavior of brittle-matrix composites. By putting crack bridges in a series, we can directly simulate a tensile test and predict the test response in terms of the stress-strain and crack spacing curves. This helps us to study and understand the relation between reinforcement ratio, bond strength, matrix strenth and the tensile response of the composite:
 </br>
 [**Multiple cracking:** tensile response of a composite](pull_out/fragmentation.ipynb)

 %% Cell type:markdown id: tags:

 ## **Tour 3:** Non-linear bond-slip law

 ### 3.1 - Pull-out with softening and hardening bond behavior

 The shape of the bond-slip law is distinguished into hardening and softening leading to a completely different pull-out behavior. A numerical model of the pull-out test is used to visualize the debonding process</br>
 [**Pull-out**: with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb)

 ### 3.2 - Anchorage failure mechanisms

 With the developed understanding, we address the questions related to design rules: What is the necessary bond length to avoid (or to guarantee)  a fiber pull-out (fiber rupture). At which distance can we expect a matrix crack to appear?</br>
 [**Anchorage**: pull-out, fiber rupture, matrix crack](pull_out/)

 supportive material [EXTRA - Newton iterative scheme](extras/newton_method.ipynb), [EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb))

 %% Cell type:markdown id: tags:

 ## **Tour 4:** Unloading and reloading

 ### 4.1 - Reversible and irreversible behavior

 Non-linear behavior can be described by nonlinear functions as we did so far. However,
 this description cannot capture the irreversible changes within the material structure.
 To demonstrate this, let us revisit the pull-out test and unload.</br>

 - 4.1 [Unloading with multi-linear bond-slip law](bmcs_course/4_1_PO_multilinear_unloading.ipynb)
 - 4.2 [Basic concept of plasticity, ideal and isotropic hardening](bmcs_course/4_2_BS_EP_SH_I_A.ipynb)
 - 4.3 [Basic concept of plasticity, kinematic hardening](bmcs_course/4_3_BS_EP_SH_IK_A.ipynb)
 - 4.4 [EXTRA - Generalization of the algorithm using vectors](bmcs_course/4_4_BS_EP_SH_IK_N.ipynb)

 %% Cell type:markdown id: tags:

 ## **Tour 5**
 - 5.1 [Damage initiation, damage evolution, 2D bond behavior](bmcs_course/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb)
 - 5.2 [Pull out simulation using damage model](bmcs_course/5_2_PO_DM_FRP_N.ipynb)

 %% Cell type:markdown id: tags:

 ## **Tour 6**

 - 6.1 Crack propagation

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 ## **Tour 7**

 - 7.1 Beam bending

 %% Cell type:code id: tags:

 ``` python
 ```

--- a/pull_out/1_1_elastic_stiffness_of_the_composite.ipynb
+++ b/pull_out/1_1_elastic_stiffness_of_the_composite.ipynb
--- a/pull_out/fragmentation.ipynb
+++ b/pull_out/fragmentation.ipynb
--- a/pull_out/pmcm.py
+++ b/pull_out/pmcm.py
@@ -79,7 +79,7 @@ class CBMConstantBond(bu.Model):
    def _get_A_m(self):
        return self.A_c - self.A_f

-    E_c = tr.Property(depends_on='state_changed')
+    E_c = tr.Property(bu.Float, depends_on='state_changed')
    @tr.cached_property
    def _get_E_c(self):
        return self.E_m * (1 - self.v_f) + self.E_f * self.v_f  # [MPa] mixture rule
@@ -105,6 +105,7 @@ class CBMConstantBond(bu.Model):
    ipw_view = bu.View(
        bu.Item('E_m'),
        bu.Item('E_f'),
+        bu.Item('E_c', readonly=True),
        bu.Item('tau'),
        bu.Item('A_c'),
        bu.Item('A_f'),