Update composite.rst

docs/howto/composite.rst

@@ -1,95 +1,104 @@
 Composite Regions with Solid Bodies
 -----------------------------------
 
-This section demonstrates how to set up a problem with two regions, each associated to a seperated solid body.
+This section demonstrates how to set up a problem with two regions, each associated to a
+seperated solid body. Different element formulations are used for the solid bodies.
 
 ..  pyvista-plot::
     :context:
 
     import felupe as fem
-    import numpy as np
 
-    m = fem.Rectangle(n=21)
+    inner = fem.Rectangle(a=(-1, -1), b=(1, 1), n=(5, 5)).triangulate()
+
+    lower = fem.Rectangle(a=(-3, -3), b=(3, -1), n=(13, 5))
+    upper = fem.Rectangle(a=(-3, 1), b=(3, 3), n=(13, 5))
+    left = fem.Rectangle(a=(-3, -1), b=(-1, 1), n=(5, 5))
+    right = fem.Rectangle(a=(1, -1), b=(3, 1), n=(5, 5))
+
+    outer = fem.MeshContainer([lower, upper, left, right], merge=True).stack()
+
+    container = fem.MeshContainer([inner, outer], merge=True)
+
 
+A top-level (vertex) field, which contains all the unknowns, is required for the
+definition of the boundary conditions as well as for the evaluation of the job.
 
-In a second step, sub-meshes are created.
+..  note::
+    Ensure to init the mesh container with ``merge=True``, otherwise the points-array of
+    the container will be empty.
 
 ..  pyvista-plot::
     :context:
 
-    # take some points from the inside for the fiber-reinforced area
-    eps = 1e-3
-    mask = np.arange(m.npoints)[np.logical_and.reduce([
-        m.points[:, 0] >= 0.3,
-        m.points[:, 0] <= 0.7 + eps,
-        m.points[:, 1] >= 0.3,
-        m.points[:, 1] <= 0.7 + eps,
-    ])]
-
-    # copies of the mesh
-    mesh = [m.copy(), m.copy()]
-
-    # create sub-meshes (fiber, matrix)
-    mesh[0].update(cells=m.cells[ np.all(np.isin(m.cells, mask), axis=1)])
-    mesh[1].update(cells=m.cells[~np.all(np.isin(m.cells, mask), axis=1)])
+    container = fem.MeshContainer([inner, outer], merge=True)
+    field = fem.Field.from_mesh_container(container).as_container()
 
-This is followed by the creation of a global region/field and two sub-regions/sub-fields.
+The sub-meshes are available in the global mesh container, on which the sub-fields are
+created.
 
 ..  pyvista-plot::
     :context:
-
-    # a global and two sub-regions
-    region = fem.RegionQuad(m)
-    regions = [fem.RegionQuad(me) for me in mesh]
-
-    # a global and two sub-fields
-    field = fem.FieldContainer([fem.FieldPlaneStrain(region, dim=2)])
+
+    regions = [
+        fem.RegionTriangle(container.meshes[0]),
+        fem.RegionQuad(container.meshes[1]),
+    ]
     fields = [
         fem.FieldContainer([fem.FieldPlaneStrain(regions[0], dim=2)]),
         fem.FieldContainer([fem.FieldPlaneStrain(regions[1], dim=2)]),
     ]
 
-The displacement boundaries are created on the total field.
+The displacement boundaries are created on the top-level field.
 
 ..  pyvista-plot::
     :context:
 
     boundaries = dict(
-        fixed=fem.Boundary(field[0], fx=0),
-        move=fem.Boundary(field[0], fx=1),
+        fixed=fem.Boundary(field[0], fx=field.region.mesh.x.min()),
+        move=fem.Boundary(field[0], fx=field.region.mesh.x.max()),
     )
 
 
-The rubber is associated to a Neo-Hookean material formulation whereas the steel is modeled by a linear elastic material formulation. Due to the large rotation, its large-strain formulation is required. For each material a solid body is created.
+The rubber is associated to a Neo-Hookean material formulation whereas the steel is
+modeled by a linear elastic material formulation. Due to the large rotation, its
+large-strain formulation is required. For each material a solid body is created.
 
 ..  pyvista-plot::
     :context:
 
     # two material model formulations
-    neo_hooke = fem.NeoHooke(mu=1, bulk=1)
     linear_elastic = fem.LinearElasticLargeStrain(E=100, nu=0.3)
+    neo_hooke = fem.NeoHooke(mu=1, bulk=1)
 
     # the solid bodies
     fiber = fem.SolidBody(umat=linear_elastic, field=fields[0])
     matrix = fem.SolidBody(umat=neo_hooke, field=fields[1])
 
 
-A step is created and further added to a job. The global field must be passed to the ``x0`` argument during the evaluation of the job. Internally, all field values are linked automatically, i.e. they share their ``values`` attribute.
+A step is created and further added to a job. The global field must be passed as the
+``x0`` argument during the evaluation of the job. Internally, all field values are
+linked automatically, i.e. they share their ``values`` array.
 
 ..  pyvista-plot::
     :context:
     :force_static:
 
     # prepare a step with substeps
-    move = fem.math.linsteps([0, 0.5], num=10)
+    move = fem.math.linsteps([0, 3], num=10)
     step = fem.Step(
         items=[matrix, fiber],
         ramp={boundaries["move"]: move}, 
-        boundaries=boundaries
+        boundaries=boundaries,
     )
 
     # take care of the x0-argument
     job = fem.Job(steps=[step])
     job.evaluate(x0=field)
 
-    field.plot("Principal Values of Logarithmic Strain").show()
+    plotter = fields[0].plot(
+        "Principal Values of Logarithmic Strain", show_undeformed=False
+    )
+    fields[1].plot(
+        "Principal Values of Logarithmic Strain", show_undeformed=False, plotter=plotter
+    ).show()