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

.. only:: html

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

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

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

.. _sphx_glr_examples_umats_EPCHA.py:


Plasticity with Chaboche Hardening Example
=============================================

.. GENERATED FROM PYTHON SOURCE LINES 5-13

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt
    from simcoon import simmit as sim
    import os

    plt.rcParams["figure.figsize"] = (18, 10)








.. GENERATED FROM PYTHON SOURCE LINES 14-43

The Chaboche plasticity model combines isotropic and kinematic hardening.
This model is particularly suited for cyclic loading applications where the
Bauschinger effect is important.

Ten parameters are required:

1. The Young modulus :math:`E`
2. The Poisson ratio :math:`\nu`
3. The coefficient of thermal expansion :math:`\alpha`
4. The initial yield stress :math:`\sigma_Y`
5. The isotropic hardening saturation value :math:`Q`
6. The isotropic hardening rate :math:`b`
7. The first kinematic hardening modulus :math:`C_1`
8. The first kinematic hardening rate :math:`D_1`
9. The second kinematic hardening modulus :math:`C_2`
10. The second kinematic hardening rate :math:`D_2`

The constitutive law is given by:

.. math::

  {\sigma}_{ij} & = L_{ijkl}\left({\varepsilon}^{\textrm{tot}}_{kl}-\alpha_{kl}\left(T-T^{\textrm{ref}}\right)-{\varepsilon}^{\textrm{p}}_{kl}\right) \\
  \dot{\varepsilon}^{\textrm{p}}_{ij} & =\dot{p}\Lambda_{ij}, \quad \Lambda_{ij}=\frac{3}{2}\frac{\sigma'_{ij} - X_{ij}}{\overline{\sigma} - X} \\
  \dot{X}_{ij} & = \sum_{k} \frac{2}{3} C_k \dot{\varepsilon}^{\textrm{p}}_{ij} - D_k X^{(k)}_{ij} \dot{p} \\
  \dot{R} & = b(Q - R)\dot{p} \\
  \Phi & =\overline{\sigma - X}-\sigma_{Y}-R\leq 0

where :math:`X_{ij}` is the kinematic hardening (back stress) tensor and :math:`R` is the
isotropic hardening variable.

.. GENERATED FROM PYTHON SOURCE LINES 43-87

.. code-block:: Python


    umat_name = "EPCHA"  # 5 character code for Chaboche plasticity
    nstatev = 33  # Number of internal variables

    # Material parameters
    E = 140000.0  # Young's modulus (MPa)
    nu = 0.3  # Poisson ratio
    alpha = 1.0e-6  # Thermal expansion coefficient
    sigma_Y = 62.859017  # Initial yield stress (MPa)
    Q = 416.004456  # Isotropic hardening saturation
    b = 4.788635  # Isotropic hardening rate
    C_1 = 30382.293921  # First kinematic hardening modulus
    D_1 = 172.425687  # First kinematic hardening rate
    C_2 = 195142.490843  # Second kinematic hardening modulus
    D_2 = 3012.614659  # Second kinematic hardening rate

    psi_rve = 0.0
    theta_rve = 0.0
    phi_rve = 0.0
    solver_type = 0
    corate_type = 1

    props = np.array([E, nu, alpha, sigma_Y, Q, b, C_1, D_1, C_2, D_2])

    path_data = "data"
    path_results = "results"
    pathfile = "EPCHA_path.txt"
    outputfile = "results_EPCHA.txt"

    sim.solver(
        umat_name,
        props,
        nstatev,
        psi_rve,
        theta_rve,
        phi_rve,
        solver_type,
        corate_type,
        path_data,
        path_results,
        pathfile,
        outputfile,
    )








.. GENERATED FROM PYTHON SOURCE LINES 88-93

Plotting the results
----------------------

We plot the stress-strain hysteresis loop which shows the cyclic behavior
including the Bauschinger effect from kinematic hardening.

.. GENERATED FROM PYTHON SOURCE LINES 93-130

.. code-block:: Python


    outputfile_macro = os.path.join(path_results, "results_EPCHA_global-0.txt")

    fig = plt.figure()

    e11, e22, e33, e12, e13, e23, s11, s22, s33, s12, s13, s23 = np.loadtxt(
        outputfile_macro,
        usecols=(8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19),
        unpack=True,
    )
    time, T, Q_out, r = np.loadtxt(outputfile_macro, usecols=(4, 5, 6, 7), unpack=True)
    Wm, Wm_r, Wm_ir, Wm_d = np.loadtxt(
        outputfile_macro, usecols=(20, 21, 22, 23), unpack=True
    )

    # First subplot: Stress vs Strain (hysteresis loop)
    ax1 = fig.add_subplot(1, 2, 1)
    plt.grid(True)
    plt.tick_params(axis="both", which="major", labelsize=15)
    plt.xlabel(r"Strain $\varepsilon_{11}$", size=15)
    plt.ylabel(r"Stress $\sigma_{11}$ (MPa)", size=15)
    plt.plot(e11, s11, c="blue", label="Chaboche model")
    plt.legend(loc="best")

    # Second subplot: Work terms vs Time
    ax2 = fig.add_subplot(1, 2, 2)
    plt.grid(True)
    plt.tick_params(axis="both", which="major", labelsize=15)
    plt.xlabel("time (s)", size=15)
    plt.ylabel(r"$W_m$", size=15)
    plt.plot(time, Wm, c="black", label=r"$W_m$")
    plt.plot(time, Wm_r, c="green", label=r"$W_m^r$")
    plt.plot(time, Wm_ir, c="blue", label=r"$W_m^{ir}$")
    plt.plot(time, Wm_d, c="red", label=r"$W_m^d$")
    plt.legend(loc="best")

    plt.show()



.. image-sg:: /examples/umats/images/sphx_glr_EPCHA_001.png
   :alt: EPCHA
   :srcset: /examples/umats/images/sphx_glr_EPCHA_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.172 seconds)


.. _sphx_glr_download_examples_umats_EPCHA.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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