Usage in FElupe

[adtzlr]

This is a little tutorial how to use matADi in FElupe. Let's set up a simple example - stretch of a clamped hyperelastic cube.

We'll start with the definition of our material.

from matadi import MaterialHyperelastic
from matadi.models import neo_hooke

umat = MaterialHyperelastic(neo_hooke, C10=0.5, bulk=2.0)

We set up a simple displacement-based problem starting with a mesh and a region, on which we create our vector-valued displacement-field, finally added to a field container. A numeric solid body applies the constitutive material formulation on the field.

import felupe as fem

region = fem.RegionHexahedron(mesh=fem.Cube(n=5))
displacement = fem.Field(region, dim=3)
field = fem.FieldContainer([displacement])
body = fem.SolidBody(umat, field)

This will be followed by the definition of the displacement boundaries.

bounds = {
    "left": fem.Boundary(displacement, fx=0, skip=(0, 0, 0)),
    "right": fem.Boundary(displacement, fx=1, skip=(1, 0, 0)),
    "move": fem.Boundary(displacement, fx=1, skip=(0, 1, 1), value=0.5),
}

dof0, dof1 = fem.dof.partition(field, bounds)
ext0 = fem.dof.apply(field, bounds, dof0)

A newton-rhapson procedure is used to obtain equilibrium. Finally the model is saved as VTK file.

res = fem.newtonrhapson(items=[body], dof0=dof0, dof1=dof1, ext0=ext0)
fem.save(region, field, filename="result.vtk")

The ouput of this script shows that the final solution is valid.

Newton-Rhapson solver
=====================

| # | norm(fun) |  norm(dx) |
|---|-----------|-----------|
| 1 | 3.087e-01 | 3.481e+00 |
| 2 | 2.482e-02 | 1.306e-01 |
| 3 | 1.468e-04 | 9.209e-03 |
| 4 | 4.814e-09 | 4.990e-05 |

Solution converged in 4 iterations within 0.197 seconds.

[adtzlr]

Note: The above script has been adopted and works with FElupe (beta) >= 0.1.1

Note: The above script has been adopted and works with FElupe (beta) >= 0.1.3

Note: The above script has been adopted and works with FElupe (beta) >= 0.1.6

Note: The above script has been adopted and works with FElupe >= 4.0.0

Note: The above script has been adopted and works with FElupe >= 6.0.0