VM268

VM268
Mullins Effect on a Rubber Tube Model Subjected to Tension Loading

Overview

Reference:

R.W.Ogden, et al., "A Pseudo-elastic Model for the Mullins Effect in Filled Rubber", Royal Society of London Proceedings Series A., (1989), pg: 2861-2877.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2D 4 node structural solid (PLANE182)

Input Listing:

vm268.dat

Test Case

An axisymmetric rubber plate made of Neo-Hookean material is modeled with radius R and height H. The model is subjected to cyclic displacement loading on the top surface. The axial stress obtained at different load steps is compared against reference solution.

Figure 466: Problem sketch

Material Properties

Geometric Properties

Displacement Loading

Neo-Hookean Constants:

µ = 8 MPa

Ogden-Roxburgh Mullins Constants:

r=2.104

m=30.45

β=0.2

R=0.5m

H=1m

One cycle of loading

Step 1: λ=1.5

Step 2: λ=2.0

Step 3: λ=3.0

Step 4: λ=2.0

Step 5: λ=1.5

Step 6: λ=1.0

Analysis Assumptions and Modeling Notes

The rubber tube is modeled using axisymmetric PLANE182 elements. Modified Ogden-Roxburgh Mullins effect was applied to model stress softening of hyper elastic material during unloading stage. Symmetric boundary conditions are applied to the model and the axial stress for element 1 obtained at different stretch is compared with reference solution.

Figure 467: Variation of axial stresses with stretch λ in one loading cycle

Results Comparison

Stretch λ	Axial stress (Pa)
Stretch λ	Target	Mechanical APDL	Ratio
1.5	12.666	12.666	1.000
2.0	28.000	28.000	1.000
3.0	69.333	69.333	1.000
2.0	20.819	20.822	1.000
1.5	8.660	8.670	1.001
1.0	0.000	0.000	1.000