VM269

VM269
Deformation of Tube and Sphere Modeled with Neo-Hookean Material Model

Overview

Reference:Z. Yosibash, " Axisymmetric Pressure Boundary Loading for Finite Deformation Analysis Using p-FEM", Computer Methods in Applied Mechanics and Engineering, 196(2007): 1261-1277.
Analysis Type(s):Static analysis (ANTYPE = 0)
Element Type(s):
2D 4 node structural solid (PLANE182)
3D 8 node structural solid (SOLID185)
Input Listing:vm269.dat

Test Case

The tube is modeled with width W and height H and the sphere is modeled with inner radius r1 and outer radius r2. Both the models are made up of neo-hookean material. Stresses are computed at the outer edge nodes for both the models and compared with reference values.

Figure 468: Problem sketch

Problem sketch

Material PropertiesGeometric Properties Loading

Neo-Hookean Constants:

µ=1 Mpa

d=1e-3

Tube

W=1m

H=1m

Sphere

r1=0.01m

r2=0.03m

Deformation (u) in radial direction (R)

u = (A-1)*R, A=2

Analysis Assumptions and Modeling Notes

The tube is modeled with axisymmetric PLANE182 elements and 1/8 of sphere is modeled with SOLID185 elements. Displacements are constrained in all directions except for the radial ones. Deformation which is proportional to the radius is then applied along radial direction on all the nodes and static analysis with large deformation is performed to compute the stresses.

Results Comparison

  Target Mechanical APDLRatio
TubeS_RR 6000.0992 6000.0991 1.000
S_ZZ5999.8016 5999.8018 1.000
SphereS_RR14000.0000 14000.0000 1.000