The purpose of this example is to introduce how to use typical visco-elastic material
to simulate creep and stress relaxation tests.
Stress relaxation is the phenomena of how polymers relieve stress under constant
strain, and creep is the phenomena of how polymers or metal move slowly or deform
permanently under constant stresses. This simulates the creep and relaxation
processes over a short period of time in quasi-static. Use visco-elastic material
law /MAT/LAW40 to simulate the creep and stress relaxation. Figure 1.
A foam sample with dimension: Radius 10 mm and high 15 mm.
For stress relaxation test: The foam sample has been compressed until a
given strain and kept in this state.
For creep test: The foam sample has been tensile under constant force.
Figure 2. Problem Description
Units: mm, s, Mg, N, MPa
To describe the phenomenon stress relaxation and creep, use viscous material law
/MAT/LAW40 with the following characteristics of foam:
Material Properties
Initial density
2e-9 [Mg/mm3]
Bulk modulus
66.67
Long time shear modulus Ginf
10
Shear modulus G1
90
Decay constant
1 = 0.01 [1/ms]
2 = 0.05 [1/ms]
1 = 1 [1/ms] for compare
Model Method
Figure 3. Stress Relaxation Test under Constant Displacement and Creep Test
under Constant Force
For stress relaxation test: The foam sample has been compressed under constant
displacement (/IMPDISP).
For creep test: The foam sample has been tensile under constant force
(/CLOAD).
Results
The stress relaxation test shows stress relieve under constant displacement with
different relaxation parameters (Decay constant, defined as the inverse of relaxation time
) and shows a different stress relive tendency. Figure 4. Figure 5. Stress Relieved with Different Decay Constant
in Stress Relaxation Test under Constant
Displacement
The creep test shows deformation increased under constant force and
with different relaxation parameter it shows a different deformation increase tendency. Figure 6. Figure 7. Sample Deformed with Decay Constant
in Creep Test under Constant Force
In LAW40 shear modulus is reduced with time and tends to G∞ after an
infinite period of time. The softening speed is determined by relaxation parameter
. Higher relaxation parameter means quick
softening.(1)
with
The general case of viscous materials represents time-dependent in elastic behavior.
Creep is time-depended deformation and stress relaxation is a time-depended decrease
in stress. Viscous material can describe these two phenomenons. In Radioss, the following material laws describe
viscous:
Ogden/Mooney-Rivlin with Prony viscosity (Hyperelastic materials)
/MAT/LAW62
Ogden (Hyperelastic materials)
/MAT/LAW70
Visco-elastic tabulated (solids)
/MAT/LAW77
Visco-elastic tabulated with porosity and air flow
Visco-elastic Plastic Law
/MAT/LAW33
Visco-elastic plastic (solids) and user-defined yield function
/MAT/LAW52
Gurson, visco-elasto-plastic porous metals, and strain rate dependent
/MAT/LAW66
Semi-analytical plastic model. Yield surface built from curves in tension,
compression and shear + /VISC/PRONY
The creep compliance and the relaxation modulus are often modeled by combinations of springs and
dashpots. The two typical simple schematic model of visco-elastic material are
Maxwell model and Kelvin-Voigt model. The Maxwell model represents the material
relaxation, but it is only accurate for secondary creep (creep with slow decrease in
creep strain rate) as the viscous strains after unloading are not taken into
account. The plasticity can be introduced in the models by using a plastic spring.
Based on the Maxwell and Kelvin-Voigt models adding other springs could get a
generalized model. The Maxwell and Kelvin-Voigt models are appropriate for ideal
stress relaxation and creep behaviors. Although, they are not adequate for most of
physical materials. A generalization of these laws, like LAW34, LAW35 and LAW40 are
a better choice, which can describe deviatory behavior of material. Figure 8. Maxwell Model Figure 9. Kelvin_Voigt Model
with 
