.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_interpolated_tip_area.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_interpolated_tip_area.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_interpolated_tip_area.py:


Interpolated Tip Area Function
==============================

This example uses a tabulated contact-depth/contact-area calibration curve as
an interpolated tip area function and compares it with analytical references.

.. GENERATED FROM PYTHON SOURCE LINES 8-15

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.interpolate import interp1d

    from micromechanics.indentation import Tip








.. GENERATED FROM PYTHON SOURCE LINES 16-19

Some calibrations are available as measured points rather than polynomial
prefactors. Here we create such a table by perturbing the perfect Berkovich
area with a shallow-depth rounding term.

.. GENERATED FROM PYTHON SOURCE LINES 19-25

.. code-block:: Python


    calibration_depth = np.linspace(0.02, 0.8, 18)
    perfect_reference = Tip("perfect")
    measured_area = perfect_reference.areaFunction(calibration_depth.copy())
    measured_area *= 1.0 + 0.18*np.exp(-calibration_depth/0.16)








.. GENERATED FROM PYTHON SOURCE LINES 26-28

``Tip`` accepts an interpolation function for ``Ac = f(hc)``. The interpolation
can then be used anywhere a regular tip area function is expected.

.. GENERATED FROM PYTHON SOURCE LINES 28-33

.. code-block:: Python


    interpolated_area = interp1d(calibration_depth, measured_area, fill_value="extrapolate")
    interpolated_tip = Tip(interpFunction=interpolated_area)
    spherical_tip = Tip(shape=[3.0, 70.3, "sphere"])








.. GENERATED FROM PYTHON SOURCE LINES 34-37

Compare the interpolated calibration with the perfect Berkovich and spherical
references. Differences at shallow depth are especially important because
small contact-depth errors strongly affect hardness.

.. GENERATED FROM PYTHON SOURCE LINES 37-52

.. code-block:: Python


    contact_depth = np.linspace(0.02, 0.8, 120)
    area_interpolated = interpolated_tip.areaFunction(contact_depth.copy())
    area_perfect = perfect_reference.areaFunction(contact_depth.copy())
    area_sphere = spherical_tip.areaFunction(contact_depth.copy())

    fig, ax = plt.subplots()
    ax.plot(calibration_depth, measured_area, "o", label="calibration points")
    ax.plot(contact_depth, area_interpolated, label="interpolated tip")
    ax.plot(contact_depth, area_perfect, "--", label="perfect Berkovich")
    ax.plot(contact_depth, area_sphere, ":", label="spherical tip")
    ax.set_xlabel(r"contact depth [$\mathrm{\mu m}$]")
    ax.set_ylabel(r"projected contact area [$\mathrm{\mu m^2}$]")
    ax.legend()




.. image-sg:: /auto_examples/images/sphx_glr_plot_interpolated_tip_area_001.png
   :alt: plot interpolated tip area
   :srcset: /auto_examples/images/sphx_glr_plot_interpolated_tip_area_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7fda32b2f250>



.. GENERATED FROM PYTHON SOURCE LINES 53-55

The representation confirms that this tip is driven by an interpolation
function instead of polynomial prefactors.

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: Python


    print(interpolated_tip)




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

 .. code-block:: none

    compliance: 0.0;   with interpolation function with 18 points





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

   **Total running time of the script:** (0 minutes 0.071 seconds)


.. _sphx_glr_download_auto_examples_plot_interpolated_tip_area.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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