Temperature dependent materials

5

I experimented a little bit with temperature dependent materials and I got results which I do not understand. Maybe someone can help me.

Its a simple beam, fixed on one side and a force on the other side. All three cases have the same mesh and boundary conditions. The idea was to manipulate the youngs modulus with a temperature inital condition.

  1. I defined one material and one solid section as shown below, no temperature definition
    *Material, Name=Material-1
    *Elastic
    20000, 0.3
    *Solid section, Elset=Solid_Part-1, Material=Material-1

Maximum Displacement: 8.74e-4 mm what is really close at the analytical value (8.8e-4 mm)

  1. Temperature dependent Material with the same youngs modulus
    *Material, Name=Material-1
    *ELASTIC
    20000.0,0.3, 0
    20000.0,0.3, 300
    *INITIAL CONDITIONS,TYPE=TEMPERATURE
    1,150
    2,150
    3,150
    and so on (for all nodes definded)

Maximum Displacement: 8.74e-4 mm what I have expected

  1. Temperature dependent Material with the different youngs modulus
    *Material, Name=Material-1
    *ELASTIC
    30000.0,0.3, 0
    10000.0,0.3, 300
    *INITIAL CONDITIONS,TYPE=TEMPERATURE
    1,150
    2,150
    3,150
    and so on (for all nodes defined)

Maximum Displacement: 6.81e-4 mm

  1. Temperature dependent Material with the different youngs modulus but I changed the temperature boundaries
    *Material, Name=Material-1
    *ELASTIC
    30000.0,0.3, 300
    10000.0,0.3, 0
    *INITIAL CONDITIONS,TYPE=TEMPERATURE
    1,150
    2,150
    3,150
    and so on (for all nodes defined)

Maximum Displacement: 5.83e-4 mm

I have two questions:
-Why are the results of case 3 and 2 different? I think there should be a linear interpolation thus the resulting youngs modulus should be 20000 (or is there a influence because of the basis functions and interpolation at the integration points)
A analytical calculation shows, that calculix uses a young modulus of 26000 for the beam. Why 26000 and not 20000? I would suppose 150 K would lead to a young modulus of 20000 because of my definition
-Why is there a difference between case 3 and 4? I just changed the sign of the gradient of the temperature definition. I think its due to the fact, that calculix does not use the middle of the defined temperature gradient, but why is this the case?