Plane Stress Linear Elastic

[ZAARAOUI999]

Hello Mr. Andreas, I have tested (using Felupe) the Plane Stress Linear Elastic branch of the Matadi module as shown in the pictures below, but I still can’t understand what do you really mean by Hyperelastic Linear Elastic, is it a composite of two different materials (H + LE)?
The test is uniaxial with clamped=True and a ramp from 0 to 50.
Thank you in advance.

[adtzlr]

No, it's just the classical linear elastic material formulation (small-strain linear elasticity; strain tensor as symmetric part of the displacement gradient). Matadi hyperelastic materials are defined on a strain energy function and thus, the small-strain formulation is derived from a strain energy function. This is quite nonsense, but I used it for testing the gradients and hessians of the strain energy function.

https://github.com/adtzlr/matadi/blob/b63491a86926a37c1efcf80207c55974bc5468b2/matadi/models/_hyperelasticity_isotropic.py#L5-L7

P.S.: Plane stress is for 2D problems only (e.g. meshes with quads). I'm not really sure what you'd like to evaluate on 3d structures given above.

[ZAARAOUI999]

Thank you, I were misunderstanding it. So, the reason behind the use of 3D geometry instead of 2D geometry was that it didn't work with me, I mean that I have got an error from casadi when I worked with the second case (quad). But when I changed to the 3D case, it works with no problem. I'm just discovering the Matadi through Felupe. I like working with Felupe because it's easy to use and to understand, so I'm interested in every detail of it. It will become a super FEM tool in the future, thank you.

[adtzlr]

This could help (slightly modified code-block of README.md):

import felupe as fem
import matadi as mat

# create a hexahedron-region on a cube
region = fem.RegionQuad(fem.Rectangle(n=11))

# add a field container (with displacement field)
field = fem.FieldsMixed(region, n=1)

# apply a uniaxial elongation on the cube
boundaries = fem.dof.uniaxial(field, clamped=True)[0]

# define the constitutive material behaviour and create a solid body
# felupe only ships the linear elastic material formulation for plane stress
# for anything else, code it by yourself or use matadi
umat = fem.LinearElasticPlaneStress(E=1, nu=0.3)

# use `MaterialHyperelasticPlaneStressIncompressible` with any hyperelastic material model of matadi
# (the deformed thickness is evaluated based on the incompressibility constraint `det(F)=1`)
umat = mat.MaterialHyperelasticPlaneStressIncompressible(
    mat.models.neo_hooke, C10=0.5 # bulk-modulus not necessary
)

# use `MaterialHyperelasticPlaneStressLinearElastic` only with the linear_elastic material 
# (the deformed thickness is evaluated based on the Lamé constants)
umat = mat.MaterialHyperelasticPlaneStressLinearElastic(
    mat.models.linear_elastic, mu=1, lmbda=3
)
solid = fem.SolidBody(umat, field)

# prepare a step with substeps
move = fem.math.linsteps([0, 2, -0.4, 0], num=10)
step = fem.Step(
    items=[solid], 
    ramp={boundaries["move"]: move}, 
    boundaries=boundaries
)

# add the step to a job, evaluate all substeps and create a plot
job = fem.CharacteristicCurve(steps=[step], boundary=boundaries["move"])
job.evaluate(filename="result.xdmf")
fig, ax = job.plot(
    xlabel="Displacement $u$ in mm $\longrightarrow$",
    ylabel="Normal Force $F$ in N $\longrightarrow$",
)

[adtzlr]

Oh, the filename-argument in job.evaluate(filename="result.xdmf") was newly introduced in v5.2.0. For v5.1.0, simply run job.evaluate().

[ZAARAOUI999]

okey thank you, I'm already working with the v5.2.0