1. Model: Thermally Induced Creep

2. Introduction This model computes the stress history over a long time for a material that exhibits creep behavior. The model is taken from NAFEMS Understanding Non- Linear Finite Analysis Through Illustrative Benchmarks. The displacement and stress levels are compared with the values given in the reference.

3. Geometry The geometry is a hollow sphere with an inner radius of 200 mm and an outer radius of 500 mm. The problem is axisymmetric. In order to follow the original example, a 10 degree sector is modeled.

4. Material Isotropic material with E=10 GPa, =0.25. Secondary Creep Data: with A=3.0E-6 (t in hours,  in MPa), =5.5, and:

5. Loads An internal pressure of 30 MPa is applied. The load will grow from zero to its full value in the first 0.1 seconds of the analysis. A temperature field with the distribution T=333(1+100/r).

6. Results The correspondence of the COMSOL Multiphysics simulation and the NAFEMS results is good in all respects. A COMSOL Multiphysics plot visualizing the effective stress at 10 8 hours is shown below.

7. Results The shows the evolution of displacement with time. The upper curve represents the inner radius, and the lower curve the outer radius.

8. Results The variation of the effective stress with time at the inner, middle and outer radius. Significant changes in the stress state occurs already at t=10 4, that is at one millionth of the total analysis time. In the final state the stresses are completely redistributed. The creep process is much faster at the inside due to the temperature variation, so the stresses tend to relax there.