Update README.md

README.md

@@ -6,7 +6,7 @@
  Hyperelastic formulations using an algorithmic differentiation with hyper-dual numbers in Python.
 </p>
 
-[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.8224136.svg)](https://doi.org/10.5281/zenodo.8224136) [![Generic badge](https://img.shields.io/badge/pypi-v0.0.3-<COLOR>.svg)](https://pypi.org/project/hypermat/)
+[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.8224136.svg)](https://doi.org/10.5281/zenodo.8224136) [![Generic badge](https://img.shields.io/badge/pypi-v0.0.4-<COLOR>.svg)](https://pypi.org/project/hypermat/)
 
 
 HyperMAT is based on the definitions of the second Piola-Kirchhoff stress $\large S$ and the material tangent modulus $\large \hat{C}$ given below:
@@ -45,7 +45,54 @@ C = umat.hessian(F)
 > </picture><br>
 >
 > Only models in the form of series function based on invariants are supported.
+ 
+Sometimes a lucky engineer will have some tension or compression stress-strain test data, or simple shear test data. Processing and applying these data is a critical step to analyze the hyperelastic models. HyperMAT has a calibration module that can help to get the best fitted model parameters. Let's take a look on how things are going on:
 
+```python
+import os
+from hypermat import NeoHooke, Yeoh, read_file, to_dict, Uniaxial
+
+
+#Prepare material models
+umat1 = NeoHooke(C10=1.5,K=2000)
+umat2 = Yeoh(C10=0.5,C20=-0.01,C30=0.2, K=2000)
+
+#Prepare experimental data
+cdir = os.getcwd()
+dataset = read_file(cdir+'//_hypermat//_calibration//_data//_data_2.csv', delimiter=',', dtype=np.float64)
+data = to_dict(dataset[1:,:], ['time', 'strain', 'stress'])
+strain = data['strain']
+stress = data['stress']
+
+#Choose loading type (Uniaxial, Biaxial or Shear)
+test1 = Uniaxial(umat1, data)
+test2 = Uniaxial(umat2, data)
+
+#Plot experimental data
+test1.plot()
+
+#Fit parameters
+test1.fit_data([0,0],[20,2000],[True, False])
+test2.fit_data([0,-20,-20,0],[20,20,20,2000],[True,True,True, False])
+
+#Plot results
+test1.plot_model(c='r')
+test2.plot_model(c='g')
+```
+You should get something like that:
+
+<p align="center">
+ <img src="https://github.com/ZAARAOUI999/hypermat/assets/115699524/5513f0ef-733f-40c6-ad99-369814ae97ee">
+</p>
+
+```
+HyperMAT fitted parameters
+{'C10': 0.6624343754510106}
+{'C10': 0.5903745146776757, 'C20': -0.09056730756209555, 'C30': 0.3065185192428228}
+MCalibration fitted parameters
+{'C10': 0.623489155}
+{'C10': 0.585555703, 'C20': -0.0846386036, 'C30': 0.304613717}
+```
 <h2>License</h2>
 
 HyperMAT- Hyperelastic formulations using an algorithmic differentiation with hyper-dual numbers in Python, (C) 2023 Mohamed ZAARAOUI, Tunisia.