# Temperature dependent materials

**URL:** <https://calculix.discourse.group/t/temperature-dependent-materials/120>\
**Category:** Uncategorized\
**Created:** [August 12, 2020, 8:36am UTC](https://calculix.discourse.group/t/temperature-dependent-materials/120 "2020-08-12T08:36:49Z")\
**Posts on this page:** 1\
**Showing post:** 5

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**Author:** ![patrick](https://avatars.discourse-cdn.com/v4/letter/p/b2d939/32.png) [@patrick](https://calculix.discourse.group/u/patrick)\
**Post date:** [August 26, 2020, 2:04pm UTC](https://calculix.discourse.group/t/temperature-dependent-materials/120/5 "2020-08-26T14:04:05Z")

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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?

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