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# **Brittle-Matrix Composite Structures** # **Brittle-Matrix Composite Structures**
Institute of Structural Concrete; @author: Rostislav Chudoba, Abedulgader Baktheer Institute of Structural Concrete; @author: Rostislav Chudoba, Abedulgader Baktheer
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## Expedition investigating the BMCS landscape ## 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-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-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)](tension/fragmentation.ipynb) | [![image-10.png](fig/bending.png)](bending/bending_3pt.ipynb) | ![image-11.png](fig/compression.png) | | ![image-13.png](attachment:image-13.png) | [![image-9.png](fig/tension.png)](tension/fragmentation.ipynb) | [![image-10.png](fig/bending.png)](bending/bending_3pt.ipynb) | ![image-11.png](fig/compression.png) |
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## Guided tours provided through BMCS landscape ## Guided tours provided through BMCS landscape
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| No. | Title | | No. | Title |
|- | - | |- | - |
| **Tour 1:** | Mixture rule (effective composite stiffness) | | **Tour 1:** | Mixture rule (effective composite stiffness) |
| **Tour 2:** | Constant bond (friction, pull-out, crack-bridge, multiple cracking) | | **Tour 2:** | Constant bond (friction, pull-out, crack-bridge, multiple cracking) |
| **Tour 3:** | Nonlinear bond (hardening, softening -> failure modes: anchorage, cracing) | | **Tour 3:** | Nonlinear bond (hardening, softening -> failure modes: anchorage, cracing) |
| **Tour 4:** | Plastic bond behavior (irreversibility -> energy dissipation) | | **Tour 4:** | Plastic bond behavior (irreversibility -> energy dissipation) |
| **Tour 5:** | Damage bond behavior (2D sheet debonding) | | **Tour 5:** | Damage bond behavior (2D sheet debonding) |
| **Tour 6:** | Concrete cracking and yielding (bended cross section) | | **Tour 6:** | Concrete cracking and yielding (bended cross section) |
| **Tour 7:** | Beam deflection - comparison wth EC2 and Model Code | | **Tour 7:** | Beam deflection - comparison wth EC2 and Model Code |
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## Tools used in the BMCS ## Tools used in the BMCS
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| Engine and wheels | Further information | | Engine and wheels | Further information |
|-- |---| |-- |---|
| Jupyter notebooks | | | Jupyter notebooks | |
| OpenWebApps | | | OpenWebApps | |
| Elementary syntax of Python language | | | Elementary syntax of Python language | |
| Plotting tools | `matplotlib` | | Plotting tools | `matplotlib` |
| Computer Algebra System | `sympy` | | Computer Algebra System | `sympy` |
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## Knowledge and skills developed during the BMCS expedition ## Knowledge and skills developed during the BMCS expedition
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* Understand nonlinear material behavior, stress-redistribution, objectivity of material laws * Understand nonlinear material behavior, stress-redistribution, objectivity of material laws
* Develop a basic understanding of damage, plasticity, fracture * Develop a basic understanding of damage, plasticity, fracture
* Formulate simplified analytical models capturing material and structural behavior * Formulate simplified analytical models capturing material and structural behavior
* Compare self-developed analytical models with general finite-element models * Compare self-developed analytical models with general finite-element models
* Distinguish model verification, calibration, validation and parametric studies * Distinguish model verification, calibration, validation and parametric studies
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## Tour 1 ## Tour 1
- 1.1 A roadmap through the BMCS landscape - 1.1 A roadmap through the BMCS landscape
- 1.2 Introduction to Jupyter Web Apps and notebooks (mathematics and mechanics support) - 1.2 Introduction to Jupyter Web Apps and notebooks (mathematics and mechanics support)
- 1.3 [Example Elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb) - 1.3 [Example Elastic mixture rule](bmcs_course/1_1_elastic_stiffness_of_the_composite.ipynb)
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## Tour 2 ## Tour 2
### Material and cross-section ### Material and cross-section
- 2.1 [Pull-out of long fiber from rigid matrix](bmcs_course/2_1_PO_LF_LM_RG.ipynb) - 2.1 [Pull-out of long fiber from rigid matrix](bmcs_course/2_1_PO_LF_LM_RG.ipynb)
- 2.2 [Pull-out of long fiber from long elastic matrix](bmcs_course/2_2_PO_LF_LM_EL.ipynb) - 2.2 [Pull-out of long fiber from long elastic matrix](bmcs_course/2_2_PO_LF_LM_EL.ipynb)
- 2.3 [Pull-out of short fiber from rigid matrix](bmcs_course/2_3_PO_SF_M_RG.ipynb) - 2.3 [Pull-out of short fiber from rigid matrix](bmcs_course/2_3_PO_SF_M_RG.ipynb)
- 2.4 [Crack-bridge behavior] - 2.4 [Crack-bridge behavior]
### Cross section and structure ### Cross section and structure
- 2.6 [Anchorage] - 2.6 [Anchorage]
- 2.7 [Multiple cracking] - 2.7 [Multiple cracking]
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## Tour 3 ## Tour 3
- 3.1 [Pull-out with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb) - 3.1 [Pull-out with softening and hardening](bmcs_course/3_1_PO_LF_LM_EL_FE_CB.ipynb)
- 3.2 [EXTRA - Newton iterative scheme](extras/newton_method.ipynb) - 3.2 [EXTRA - Newton iterative scheme](extras/newton_method.ipynb)
- 3.2 [EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb) - 3.2 [EXTRA - Nonlinear finite-element solver for 1d pullout](extras/pullout1d.ipynb)
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## Tour 4 ## Tour 4
- 4.1 [Unloading with multi-linear bond-slip law](bmcs_course/4_1_PO_multilinear_unloading.ipynb) - 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) - 4.2 [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) - 4.3 [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) - 4.4 [EXTRA - Generalization of the algorithm using vectors](bmcs_course/4_4_BS_EP_SH_IK_N.ipynb)
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## Tour 5 ## Tour 5
- 5.1 [Damage initiation, damage evolution, 2D bond behavior](bmcs_course/5_1_Introspect_Damage_Evolution_Damage_initiation.ipynb) - 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) - 5.2 [Pull out simulation using damage model](bmcs_course/5_2_PO_DM_FRP_N.ipynb)
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## Tour 6 ## Tour 6
- 6.1 Crack propagation - 6.1 Crack propagation
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## Tour 7 ## Tour 7
- 7.1 Beam bending - 7.1 Beam bending
......
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