Added fragile becomes supercompressible study

studies/fragile_becomes_supercompressible/3d_domain.yaml

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+domain:
+ young_modulus:
+ type: constant
+ value: 3500.0
+ n_longerons:
+ type: constant
+ value: 3
+ bottom_diameter:
+ type: constant
+ value: 100.0
+ ratio_top_diameter:
+ type: float
+ low: 0.0
+ high: 0.8
+ ratio_pitch:
+ type: float
+ low: 0.25
+ high: 1.50
+ ratio_d:
+ type: float
+ low: 0.004
+ high: 0.073
+ ratio_shear_modulus:
+ type: constant
+ value: 0.3677
+ circular:
+ type: constant
+ value: true
+ imperfection:
+ type: float
+ low: 0.0
+ high: 1.0

studies/fragile_becomes_supercompressible/7d_domain.yaml

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+domain:
+ young_modulus:
+ type: constant
+ value: 3500.0
+ n_longerons:
+ type: constant
+ value: 3
+ bottom_diameter:
+ type: constant
+ value: 100.0
+ ratio_top_diameter:
+ type: float
+ low: 0.0
+ high: 0.8
+ ratio_pitch:
+ type: float
+ low: 0.25
+ high: 1.50
+ ratio_shear_modulus:
+ type: float
+ low: 0.035
+ high: 0.45
+ ratio_area:
+ type: float
+ low: 0.0000117
+ high: 0.0041
+ ratio_Ixx:
+ type: float
+ low: 0.00000000001128
+ high: 0.0000014
+ ratio_Iyy:
+ type: float
+ low: 0.00000000001128
+ high: 0.0000014
+ ratio_J:
+ type: float
+ low: 0.00000000001353
+ high: 0.00000777
+ circular:
+ type: constant
+ value: false
+ imperfection:
+ type: float
+ low: 0.0
+ high: 1.0

studies/fragile_becomes_supercompressible/README.md

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+# Fragile becomes supercompressible
+
+<div style="display: flex;">
+ <img src="./img/undeformed.png" style="width: 20%;" alt="Image 1">
+ <img src="./img/fifty.png" style="width: 20%;" alt="Image 2">
+ <img src="./img/ninety.png" style="width: 20%;" alt="Image 3">
+</div>
+
+<br>
+
+This study is based on the work of [Bessa et al. (2019)](https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201904845) and aims to reproduce the results of the paper using the `f3dasm` package.
+## Summary
+
+For years, creating new materials has been a time consuming effort that requires significant resources because we have followed a trial-and-error design process. Now, a new paradigm is emerging where machine learning is used to design new materials and structures with unprecedented properties. Using this data-driven process, a new super-compressible meta-material was discovered despite being made of a fragile polymer.
+
+The above figure shows the newly developed meta-material prototype that was designed with the above-mentioned computational data-driven approach and where experiments were used for validation, not discovery. This enabled the design and additive manufacturing of a lightweight, recoverable and super-compressible meta-material achieving more than 90% compressive strain when using a brittle base material that breaks at around 4% strain. Within minutes, the machine learning model was used to optimize designs for different choices of base material, length-scales and manufacturing process. Current results show that super-compressibility is possible for optimized designs reaching stresses on the order of 1 kPa using brittle polymers, or stresses on the order of 20 MPa using carbon like materials.
+
+#### Design of experiments
+
+The supercompressible meta-material is parameterized by 5 geometric parameters and 2 material parameters. The geometry is defined by the top and bottom diameters, $D_1$ and $D_2$, the height $P$ and the cross-section parameters of the vertical longerons: the cross-sectional area $A$, moments of inertial $I_x$ and $I_y$, and torsional constant $J$. The isotropic material is defined by its elastic constants: Young's modulus $E$ and shear modulus $G$.
+
+<center>
+<img src="./img/supercompressible_metamaterial.png" alt="drawing" width=60%/>
+</center>
+
+<br>
+
+Due to the principle of superposition both the geometric and material parameters can be scaled by one of its dimensions/properties (here $D_1$ and $E$). Therefore, the variables that you will find in the dataset are:
+
+$$
+\frac{D_1-D_2}{D_1},\ \frac{P}{D_1},\ \frac{I_x}{D_1^4},\ \frac{I_y}{D_1^4},\ \frac{J}{D_1^4},\ \frac{A}{D_1^2}, \frac{G}{E}
+$$
+
+| expression | parameter name |
+| ----------- | --------------- |
+| $\frac{D_1-D_2}{D_1}$ | `ratio_top_diameter`
+|$\frac{P}{D_1}$| `ratio_pitch`
+|$\frac{I_x}{D_1^4}$| `ratio_Ixx`
+|$\frac{I_y}{D_1^4}$| `ratio_Iyy`
+|$\frac{J}{D_1^4}$| `ratio_J`
+|$\frac{A}{D_1^2}$| `ratio_area`
+|$\frac{G}{E}$| `ratio_shear_modulus`
+
+This is a 7-dimensional problem and learning the response surface may require a significant amount of training points[^1]. Therefore, you will also consider a simpler version of the problem in 3 dimensions, defined by constraining the longerons' cross-section to be circular with diameter $d$, and choosing a particular material, leading to the following 3 features:
+
+$$
+\frac{d}{D_1}, \frac{D_2-D_1}{D_1},\ \frac{P}{D_1}
+$$
+
+| expression | parameter name |
+| ----------- | --------------- |
+$\frac{D_1-D_2}{D_1}$| `ratio_top_diameter`
+$\frac{P}{D_1}$ |`ratio_pitch`
+$\frac{d}{D_1}$ |`ratio_d`
+
+[^1]: Remember the "curse of dimensionality"!
+
+
+
+
+
+
+## Contents of this folder
+
+| File/Folder | Description |
+|-------------|-------------|
+| `main.py` | Main script to run the experiment |
+| `config.yaml` | Configuration file for the experiment |
+| `README.md` | Explanation of this experiment |
+| `img/` | Folder with images used in this file |
+| `pbsjob.sh` | TORQUE job file to run the experiment in a cluster |
+| `outputs/` | Folder with the results of running this experiment |
+
+> The `outputs/` folder is created when the experiment has been run for the first time.
+
+## Usage
+
+### Before running the experiment
+
+1. Install the `abaqus2py` package. See [here](https://github.com/bessagroup/abaqus2py) for instructions.
+2. Change the `config.yaml` file to your liking. See [here](#explanation-of-configyaml-parameters) for an explanation of the parameters.
+
+### Running the experiment on your local machine
+
+1. Navigate to this folder and run `python main.py`
+
+### Running the experiment on a TORQUE cluster
+
+1. Make sure you have an `conda` environment named `f3dasm_env` with the packages installed in the first step
+2. Navigate to this folder and submit the job with i.e. 2 nodes: `qsub pbsjob.sh -t 0-2`
+
+
+## Results
+
+Results are stored in a newly created `outputs` folder, with a subdirectory
+indicating the current date (e.g. `2023-11-06`).
+
+* When running on a local machine, the output will be saved in a directory indicating the current time (e.g. `13-50-14`).
+* When running on a cluster, the output will be saved in a directory indicating the current job ID (e.g. `538734.hpc06.hpc`).
+
+The following subdirectories are created:
+
+* `experiment_data`: Contains the input, output, domain and jobs to construct the [`f3dasm.ExperimentData`](https://f3dasm.readthedocs.io/en/latest/rst_doc_files/classes/design/experimentdata.html) object.
+* `.hydra`: Contains the `config.yaml` file used to run the experiment.
+* `lin_buckle` and `riks`: Contain the ABAQUS simulation results for the linear buckling and Riks analysis, respectively.
+
+
+Lastly, a log file `main.log` is created.
+
+The folder structure is as follows:
+
+```
+outputs/
+└── 2023-11-06/
+ └── 13-50-14/
+ ├── .hydra/
+ ├── experiment_data/
+ │ ├── domain.pkl
+ │ ├── input.csv
+ │ ├── output.csv
+ │ └── jobs.pkl
+ ├── lin_buckle/
+ │ ├── 0/
+ │ ├── 1/
+ │ └── 2/
+ ├── riks/
+ │ ├── 0/
+ │ ├── 1/
+ │ └── 2/
+ ├── loads/
+ │ ├── 0.npy
+ │ ├── 1.npy
+ │ └── 2.npy
+ ├── max_disps/
+ │ ├── 0.ny
+ │ ├── 1.npy
+ │ └── 2.npy
+ └── main.log
+```
+
+## Explanation of `config.yaml` parameters
+
+There are two different configurations for this experiment:
+ - The full 7-dimensional problem as defined in the paper
+- The 3-dimensional problem, defined by constraining the longerons' cross-section to be circular with diameter $d$ and choosing a fixed material.
+
+### Common problem domain
+
+#### young_modulus
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| value | `float` | Young's modulus value |
+
+#### n_longerons
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| value | `float` | Number of longerons in the design |
+
+#### bottom_diameter ($D_2$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| value | `float` | Bottom diameter of the design |
+
+#### ratio_top_diameter ($\frac{D_1-D_2}{D_1}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of top diamater ratio |
+| high | `float` | Upper bound of top diamater ratio |
+
+#### ratio_pitch ($\frac{P}{D_1}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of the pitch ratio |
+| high | `float` | Upper bound of the pitch ratio |
+
+### 3 dimensional problem domain
+
+
+#### ratio_d ($\frac{d}{D_1}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of longerons cross-section |
+| high | `float` | Upper bound of longerons cross-section |
+
+#### ratio_shear_modulus ($\frac{G}{E}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| value | `float` | Lower bound of shear modulus ratio |
+
+### 7 dimensional problem domain
+
+#### ratio_area ($\frac{A}{D_1^2}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of the area ratio |
+| high | `float` | Upper bound of the area ratio |
+
+#### ratio_Ixx ($\frac{I_x}{D_1^4}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of the $I_{xx}$ ratio |
+| high | `float` | Upper bound of the $I_{xx}$ ratio |
+
+#### ratio_Iyy ($\frac{I_y}{D_1^4}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of the $I_{yy}$ ratio |
+| high | `float` | Upper bound of the $I_{yy}$ ratio |
+
+#### ratio_J ($\frac{J}{D_1^4}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of the $J$ ratio |
+| high | `float` | Upper bound of the $J$ ratio |
+
+#### ratio_shear_modulus ($\frac{G}{E}$)
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| low | `float` | Lower bound of shear modulus ratio |
+| high | `float` | Upper bound of shear modulus ratio |
+
+
+#### circular
+| Name | Type | Description |
+|------------|----------|----------------------------|
+| value | `bool` | If the design is simplified or not |
+
+...
+
+### Experiment Data
+#### from Sampling
+| Name | Type | Description |
+|--------------|--------|------------------------|
+| sampler | `str` | Sampler name |
+| seed | `int` | Seed value |
+| n_samples | `int` | Number of samples |
+| domain | `f3dasm.Domain` | `f3dasm` Domain object ([reference](https://f3dasm.readthedocs.io/en/latest/rst_doc_files/classes/design/domain.html)) |
+
+### mode
+| Name | Type | Description |
+|-------|--------|-------------|
+| mode | string | Evaluation mode of `f3dasm` ([reference](https://f3dasm.readthedocs.io/en/latest/rst_doc_files/classes/datageneration/datagenerator.html#)) |
+
+
+### hpc
+| Name | Type | Description |
+|--------|------|--------------|
+| jobid[^2] | `int` | Job ID of the array-job, automatically overwritten by scheduler bash script |
+
+[^2]: When running on a local machine, this value will be left as the default: -1.
+
+### imperfection
+
+| Name | Type | Description |
+|--------------|--------|------------------------|
+| mean | `float` | Mean value of lognormal distribution |
+| std | `float` | Standard deviation value of lognormal distribution |
+
+### scripts
+
+| Name | Type | Description |
+|--------------|--------|------------------------|
+| lin_buckle_pre | `str` | Absolute path of linear buckling script |
+| lin_buckle_post | `str` | Absolute path of linear buckling post-processing script |
+| riks_pre | `str` | Absolute path of RIKS analysis script |
+| riks_post | `str` | Absolute path of RIKS analysis post-processing script |
+
+
+### Logging
+| Name | Type | Description |
+|-----------|------|-----------------|
+| log_level | `int` | Log level value ([see `logging` module for more info](https://docs.python.org/3/library/logging.html#logging-levels)) |

studies/fragile_becomes_supercompressible/config.yaml

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+defaults:
+ - 7d_domain
+ - override hydra/job_logging: custom
+
+experimentdata:
+ from_file: ./example_design
+
+ # from_sampling:
+ # sampler: latin
+ # seed: 42
+ # n_samples: 3
+ # domain: ${domain}
+
+mode: sequential
+
+hpc:
+ jobid: -1
+
+imperfection:
+ mean: -2.705021452041446
+ sigma: 0.293560379208524
+ domain:
+ imperfection:
+ type: float
+ low: 0.0
+ high: 1.0
+
+scripts:
+ lin_buckle_pre: ./scripts/supercompressible_lin_buckle.py
+ lin_buckle_post: ./scripts/supercompressible_lin_buckle_pp.py
+ riks_pre: ./scripts/supercompressible_riks.py
+ riks_post: ./scripts/supercompressible_riks_pp.py
+
+
+log_level: 20

studies/fragile_becomes_supercompressible/example_design/experiment_data/input.csv

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+,bottom_diameter,circular,imperfection,n_longerons,ratio_Ixx,ratio_Iyy,ratio_J,ratio_area,ratio_pitch,ratio_shear_modulus,ratio_top_diameter,young_modulus
+0,100,0,0.2,3,0.0000001697758,0.0000003717950,1e-06,0.003624,0.75,0.367714286,0.4,3500.0

studies/fragile_becomes_supercompressible/example_design/experiment_data/output.csv

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+""
+0