r"""
Run a Job
---------

.. topic:: Learn how to apply boundary conditions in a ramped manner within a **Step**
   and run a **Job**.

   * create a **Step** with ramped boundary conditions

   * run a **Job** and export a XDMF time-series file

This tutorial once again covers the essential high-level parts of creating and solving
problems with FElupe. This time, however, the external displacements are applied in a
ramped manner. The prescribed displacements of a cube under non-homogenous
:func:`uniaxial loading <felupe.dof.uniaxial>` will be controlled within a
:class:`step <felupe.Step>`. The
:class:`Ogden-Roxburgh <felupe.OgdenRoxburgh>` pseudo-elastic Mullins softening model is
combined with an isotropic hyperelastic :class:`Neo-Hookean <felupe.NeoHooke>` material
formulation, which is further applied on a
:class:`nearly incompressible solid body <felupe.SolidBodyNearlyIncompressible>` for a
realistic analysis of rubber-like materials. Note that the bulk modulus is now an
argument of the (nearly) incompressible solid body instead of the constitutive
Neo-Hookean material definition.
"""

import felupe as fem

mesh = fem.Cube(n=6)
region = fem.RegionHexahedron(mesh=mesh)
field = fem.FieldContainer([fem.Field(region=region, dim=3)])

boundaries = fem.dof.uniaxial(field, clamped=True, return_loadcase=False)

umat = fem.OgdenRoxburgh(material=fem.NeoHooke(mu=1), r=3, m=1, beta=0)
body = fem.SolidBodyNearlyIncompressible(umat=umat, field=field, bulk=5000)

# %%
# The ramped prescribed displacements for 12 substeps are created with
# :func:`~felupe.math.linsteps`. A :class:`~felupe.Step` is created with a list of items
# to be considered (here, one single solid body) and a dict of ramped boundary
# conditions along with the prescribed values.
move = fem.math.linsteps([0, 2, 1.5], num=[8, 4])
uniaxial = fem.Step(
    items=[body], ramp={boundaries["move"]: move}, boundaries=boundaries
)

# %%
# This step is now added to a :class:`~felupe.Job`. The results are exported after each
# completed and successful substep as a time-series XDMF-file. A
# :class:`~felupe.CharacteristicCurve`-job logs the displacement and sum of reaction
# forces on a given boundary condition.
job = fem.CharacteristicCurve(steps=[uniaxial], boundary=boundaries["move"])
job.evaluate(filename="result.xdmf")

field.plot("Principal Values of Logarithmic Strain").show()

# %%
# The sum of the reaction force in direction :math:`x` on the boundary condition
# ``"move"`` is plotted as a function of the displacement :math:`u` on the boundary
# condition ``"move"`` .
fig, ax = job.plot(
    xlabel=r"Displacement $u$ in mm $\longrightarrow$",
    ylabel=r"Normal Force $F$ in N $\longrightarrow$",
)