VM234

VM234
Cyclic Loading of a Rubber Block

Overview

Reference:	G. A. Holzapfel, "On Large Strain Viscoelasticity: Continuum Formulation and Finite Element Applications to Elastomeric Structures", International Journal for Numerical Methods in Engineering, Vol. 39, 1996, pp. 3903-3926.
Analysis Type(s):	Static Structural Analysis (ANTYPE = 4)
Element Type(s):	3D 8-Node Structural Solid Elements (SOLID185)
Input Listing:	vm234.dat

Test Case

A cube of rubber is subjected to a sinusoidal displacement controlled load with a mean value of zero (completely reversed). The load amplitude is constant within a full cycle (4 seconds) and increases with each successive cycle. For the first period A = 0.01 and it increases by 0.01 each cycle until the fourth when A = 0.04. At t = 16 seconds the load is removed and the residual stresses are permitted to relax.

Figure 391: Rubber Block Model

Material Properties

Geometric Properties

τ₁ = 0.40 sec

τ₂ = 0.20 sec

β₁ = β₂ = 1

L = 0.1 m

A = 0.01

Analysis Assumptions and Modeling Notes

The analysis was performed using a single SOLID185 element. The rubber was simulated with an Ogden material model. The load was applied using a looping application of the displacement boundary condition. The plot displays the Cauchy stress evolution over the specified time periods. The accumulated stress relaxes after the load is removed at t = 16 seconds. The accumulated stress at t = 16 seconds and the relaxed stress state at t = 20 seconds are the verified results for this test.

Figure 392: Stress Evolution Over Time

Results Comparison

	Target	Mechanical APDL	Ratio
Cauchy Stress (N/m²) t = 16 sec	6.013E5	5.993889E5	0.997
Cauchy Stress (N/m²) t = 20 sec	0.0	17.7	0.000