.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_unloading_stiffness_fit.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_unloading_stiffness_fit.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_unloading_stiffness_fit.py:


Unloading Stiffness Fit
=======================

This example shows how the unloading part of a force-depth curve is fitted to
obtain the contact stiffness used by the Oliver-Pharr method.

.. GENERATED FROM PYTHON SOURCE LINES 8-15

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from micromechanics.indentation import Indentation
    from micromechanics.indentation.definitions import Method








.. GENERATED FROM PYTHON SOURCE LINES 16-20

Build a compact synthetic load-unload experiment. The loading segment rises
linearly, while the unloading segment follows a power law with a known residual
depth. The synthetic data makes it easy to see which part of the curve is used
for the stiffness fit.

.. GENERATED FROM PYTHON SOURCE LINES 20-29

.. code-block:: Python


    loading_depth = np.linspace(0.0, 1.0, 24)
    loading_force = np.linspace(0.0, 5.0, 24)
    unloading_depth = np.linspace(1.0, 0.25, 36)
    unloading_force = 5.0*((unloading_depth-0.1)/(1.0-0.1))**1.5

    depth = np.r_[loading_depth, unloading_depth]
    force = np.r_[loading_force, unloading_force]








.. GENERATED FROM PYTHON SOURCE LINES 30-33

``iLHU`` stores the load-hold-unload indices as
``[load start, load end, unload start, unload end]``. Real instrument files
populate this during loading or with ``identifyLoadHoldUnload``.

.. GENERATED FROM PYTHON SOURCE LINES 33-40

.. code-block:: Python


    indentation = Indentation("")
    indentation.method = Method.ISO
    indentation.setRawData(depth, force, np.arange(len(depth), dtype=float))
    indentation.iLHU = [[0, len(loading_depth)-1, len(loading_depth), len(depth)-1]]
    indentation.output["verbose"] = 3





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    *WARNING*: Poisson Ratio different than in file. 0.3 0.18
    Open Agilent file: /home/runner/work/micromechanics/micromechanics/micromechanics/indentation/data/Example.xls




.. GENERATED FROM PYTHON SOURCE LINES 41-43

The fitting routine returns the stiffness, a mask marking the evaluated point,
the unloading-fit mask, the optimized power-law parameters, and a success flag.

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: Python


    stiffness, valid, mask, opt, powerlaw_fit = indentation.stiffnessFromUnloading(force, depth, plot=True)
    print(f"Fitted unloading stiffness: {stiffness[0]:.2f} mN/um")
    print(f"Power-law fit succeeded: {powerlaw_fit[0]}")




.. image-sg:: /auto_examples/images/sphx_glr_plot_unloading_stiffness_fit_001.png
   :alt: plot unloading stiffness fit
   :srcset: /auto_examples/images/sphx_glr_plot_unloading_stiffness_fit_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Number of unloading segments:1  Method:1
    Initial fitting values B,hf,m 6.755229140733971 0.21344081076517907 1.2589254117941673
      Bounds (array([0. , 0. , 0.8]), array([        inf,  0.67857143, 10.        ]))
      Optimal values B,hf,m 5.856069741415784 0.1000000000415452 1.4999999999144056
    Fitted unloading stiffness: 8.33 mN/um
    Power-law fit succeeded: True




.. GENERATED FROM PYTHON SOURCE LINES 49-51

The red dashed line in the figure is the tangent stiffness. This is the slope
that later enters the Oliver-Pharr contact-depth and modulus calculation.

.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: Python


    plt.plot(depth[valid], force[valid], "ro", label="stiffness point")
    plt.plot(depth[mask], force[mask], "C0o", fillstyle="none", label="fit domain")
    plt.legend()



.. image-sg:: /auto_examples/images/sphx_glr_plot_unloading_stiffness_fit_002.png
   :alt: plot unloading stiffness fit
   :srcset: /auto_examples/images/sphx_glr_plot_unloading_stiffness_fit_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7fda2e4dc550>




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.188 seconds)


.. _sphx_glr_download_auto_examples_plot_unloading_stiffness_fit.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_unloading_stiffness_fit.ipynb <plot_unloading_stiffness_fit.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_unloading_stiffness_fit.py <plot_unloading_stiffness_fit.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_unloading_stiffness_fit.zip <plot_unloading_stiffness_fit.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_