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

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

.. _sphx_glr_examples_umats_EPKCP.py:


Plasticity with Isotropic and Kinematic 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 14-39

This plasticity model combines both isotropic and kinematic hardening with a
power-law isotropic hardening and linear kinematic hardening.

Seven 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 parameter :math:`k`
6. The isotropic hardening exponent :math:`m`
7. The kinematic hardening modulus :math:`k_X`

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} & = \frac{2}{3} k_X \dot{\varepsilon}^{\textrm{p}}_{ij} \\
  \Phi & =\overline{\sigma - X}-\sigma_{Y}-kp^m\leq 0

where :math:`X_{ij}` is the kinematic hardening (back stress) tensor resulting from
linear kinematic hardening, and the isotropic hardening follows a power-law
evolution :math:`kp^m`.

.. GENERATED FROM PYTHON SOURCE LINES 39-80

.. code-block:: Python


    umat_name = "EPKCP"  # 5 character code for combined isotropic-kinematic hardening
    nstatev = 14  # Number of internal variables

    # Material parameters
    E = 67538.0  # Young's modulus (MPa)
    nu = 0.349  # Poisson ratio
    alpha = 1.0e-6  # Thermal expansion coefficient
    sigma_Y = 300.0  # Initial yield stress (MPa)
    k = 1500.0  # Isotropic hardening parameter
    m = 0.3  # Isotropic hardening exponent
    k_X = 2000.0  # Kinematic hardening modulus

    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, k, m, k_X])

    path_data = "data"
    path_results = "results"
    pathfile = "EPKCP_path.txt"
    outputfile = "results_EPKCP.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 81-85

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

We plot the stress-strain curve showing both isotropic and kinematic hardening.

.. GENERATED FROM PYTHON SOURCE LINES 85-122

.. code-block:: Python


    outputfile_macro = os.path.join(path_results, "results_EPKCP_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
    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="EPKCP 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_EPKCP_001.png
   :alt: EPKCP
   :srcset: /examples/umats/images/sphx_glr_EPKCP_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.266 seconds)


.. _sphx_glr_download_examples_umats_EPKCP.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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