Mixed-field formulations with multiple solid bodies

[adtzlr]

Using mixed-field formulation solid bodies with multiple solid bodies is possible, but tricky. This is a working example which should be added to the How-To section.

import felupe as fem

# create three meshes and a merged container
meshes = [
    fem.Rectangle(n=(4, 10)),
    fem.Rectangle(n=(6, 10)).translate(1, axis=0),
    fem.Rectangle(n=(10, 10)).translate(2, axis=0),
]
container = fem.MeshContainer(meshes, merge=True)
ax = container.imshow()

# stack a top-level mesh, create a region and a field
# the dual-mesh must be created for the dual submesh(es) of the mixed-fields
# the offsets must match between the top-level mixed-field and the mixed sub-field
mesh = container.stack()
region = fem.RegionQuad(mesh)
field = fem.FieldsMixed(
    region,
    n=3,
    axisymmetric=True,
    mesh=fem.MeshContainer(meshes[1:], merge=True).stack().dual(points_per_cell=1),
)

# sub regions and first sub-field (displacements as single-field container)
regions = [fem.RegionQuad(m) for m in container.meshes]
field1 = fem.FieldContainer([fem.FieldPlaneStrain(regions[0], dim=2)])

# mixed sub-fields: the dual meshes must be created manually
# the number of points must be taken from the top-level mixed-field
# the offsets must match for the mixed-fields and their dual meshes
field2 = fem.FieldsMixed(
    regions[1],
    n=3,
    axisymmetric=True,
    offset=0,
    mesh=meshes[1].dual(
        points_per_cell=1,
        offset=0,  # first dual mesh, no offset
        npoints=field[1].region.mesh.npoints,  #  must match top-level dual-mesh
    ),
)
field3 = fem.FieldsMixed(
    regions[2],
    n=3,
    axisymmetric=True,
    offset=meshes[1].ncells,
    mesh=meshes[2].dual(
        points_per_cell=1,
        offset=meshes[1].ncells,  # second dual mesh, offset necessary
        npoints=field[1].region.mesh.npoints,  #  must match top-level dual-mesh
    ),
)
fields = [field1, field2, field3]

# load case
boundaries, loadcase = fem.dof.uniaxial(field, move=-0.8, clamped=True)

# constitutive material formulations and solid bodies
# a) (u)-formulation) on large-strain extended linear-elasticity
# b) (u-p-J)-formulation on large-strain extended linear-elasticity
# c) (u-p-J)-formulation for a nearly-incompressible hyperelastic material
umats = [
    fem.LinearElasticLargeStrain(E=10, nu=0.3),
    fem.ThreeFieldVariation(fem.LinearElasticLargeStrain(E=3, nu=0.3)),
    fem.NearlyIncompressible(fem.NeoHooke(mu=1), bulk=5000),
]
solids = [fem.SolidBody(umat, f) for umat, f in zip(umats, fields)]

# add the step to the job and pass the top-level field as x0-argument+
step = fem.Step(items=solids, boundaries=boundaries)
job = fem.Job([step]).evaluate(x0=field)
ax = field.imshow("Principal Values of Logarithmic Strain")