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

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

.. _sphx_glr_auto_examples_plot_tip_area_models.py:


Tip Area Models
===============

This example compares projected contact area for a perfect Berkovich tip, an
ISO-style calibrated area function, and a spherical tip.

.. GENERATED FROM PYTHON SOURCE LINES 8-14

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from micromechanics.indentation import Tip








.. GENERATED FROM PYTHON SOURCE LINES 15-18

The projected contact area is evaluated as a function of contact depth. All
depths passed to ``areaFunction`` are in micrometers, while the calibrated
prefactors are stored in the unit convention used by the indentation package.

.. GENERATED FROM PYTHON SOURCE LINES 18-21

.. code-block:: Python


    contact_depth = np.linspace(0.01, 0.8, 120)








.. GENERATED FROM PYTHON SOURCE LINES 22-25

A perfect Berkovich tip is the usual analytical reference. The ISO-style tip
uses a polynomial area function, and the spherical model is useful for blunt
tips or rounded apex behavior at shallow depth.

.. GENERATED FROM PYTHON SOURCE LINES 25-30

.. code-block:: Python


    perfect = Tip("perfect")
    iso = Tip(shape=[24.5, 420.0, -30.0])
    sphere = Tip(shape=[3.0, 70.3, "sphere"])








.. GENERATED FROM PYTHON SOURCE LINES 31-34

Larger area at a given depth means the same load would produce a lower
hardness. Comparing area functions is therefore a direct way to inspect how a
tip calibration changes the mechanical result.

.. GENERATED FROM PYTHON SOURCE LINES 34-47

.. code-block:: Python


    area_perfect = perfect.areaFunction(contact_depth.copy())
    area_iso = iso.areaFunction(contact_depth.copy())
    area_sphere = sphere.areaFunction(contact_depth.copy())

    fig, ax = plt.subplots()
    ax.plot(contact_depth, area_perfect, label="perfect Berkovich")
    ax.plot(contact_depth, area_iso, label="ISO area function")
    ax.plot(contact_depth, area_sphere, label="spherical cap")
    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_tip_area_models_001.png
   :alt: plot tip area models
   :srcset: /auto_examples/images/sphx_glr_plot_tip_area_models_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7fda32b07c50>



.. GENERATED FROM PYTHON SOURCE LINES 48-49

The inverse area function maps a measured contact area back to contact depth.

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: Python


    known_area = perfect.areaFunction(np.array([0.35]))
    recovered_depth = perfect.areaFunctionInverse(known_area)
    print(f"Use initial depth 0.35um and recovered depth for the perfect tip: {recovered_depth[0]:.3f} um")




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

 .. code-block:: none

    Use initial depth 0.35um and recovered depth for the perfect tip: 0.350 um





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

   **Total running time of the script:** (0 minutes 0.068 seconds)


.. _sphx_glr_download_auto_examples_plot_tip_area_models.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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