Relaxation and Creep Test Data

L8.20

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Relaxation Test Data

• Consider a simple shear relaxation test

• Here

g

₀is the instantaneous (short-time) applied shear strain, and



(t)is the measured shear stress response.

• Note: Be careful that the short-time duration of the prescribed strain is consistent with the time scale of your linear elastic or hyperelastic material definition.

L8.21

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Relaxation Test Data (cont'd)

• The measured shear stress response is data pairs of (shear stress, time)



₀,

time

₀



₁,

time

₁



₂,

time

₂



₃,

time

₃

…

• Because this is linear viscoelasticity only one curve may be used. If your material is not exactly linear in its viscoelastic response, then test at an applied strain that is close to your component analysis strain level of interest.

L8.22

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Relaxation Test Data (cont'd)

• Test data processing for use in Abaqus:

• Simply normalize all the measured stress values by



₀:



₀/



₀,time₀

and input this data using the *SHEAR TEST DATAsuboption of

*VISCOELASTIC, TIME=RELAXATION TEST DATA.

L8.23

Modeling Rubber and Viscoelasticity with Abaqus

• Example 1: Relaxation Test Data Usage

*MATERIAL,NAME=

*ELASTIC, MODULI= or *HYPERLEASTIC, MODULI=

... (data lines)

*VISCOELASTIC, TIME=RELAXATION TEST DATA, {ERRTOL = 0.01, NMAX = 13}

*SHEAR TEST DATA, SHRINF = 0.5 1.0000, 0.0001

0.9695, 0.001 0.9417, 0.002

...

*VOLUMETRIC TEST DATA, VOLINF = 0.5 1.0000, 0.0001

0.9695, 0.001 0.9417, 0.002

...

Relaxation and Creep Test Data

p G

i i

g



pairs of and

p K

i i

k



pairs of and

nonlinear least squares fits

L8.24

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 1: Relaxation Test Data Usage (cont'd)

• Volumetric relaxation test data is optional; many solid materials exhibit insignificant volumetric relaxation behavior.

• Separate fits are performed on the shear and volumetric parts and combined into one set of Prony series parameters.

• SHRINF is the normalized shear stress (modulus) as time → 1; if a value for this parameter is specified it will act as a further constraint to enforce

• VOLINF is the normalized pressure (modulus) as time → 1; if a value for this parameter is specified it will act as a further constraint to enforce

1

L8.25

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 2: Relaxation Test Data Usage (combined test data)

• If both the shear and volumetric relaxation tests are performed and the same time intervals are used in each, then the normalized experimental data can be specified using a single keyword: *COMBINED TEST DATA

L8.26

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 2: Relaxation Test Data Usage (combined test data, cont'd)

*MATERIAL,NAME=

*ELASTIC, MODULI= or

*HYPERLEASTIC, MODULI= or

*HYPERFOAM ... (data lines)

*VISCOELASTIC, TIME=RELAXATION TEST DATA, {ERRTOL = 0.01, NMAX = 13}

*COMBINED TEST DATA,

SHRINF = 0.5, VOLINF = 0.5 0.99256, 0.99256, 0.1

0.98525, 0.98525, 0.2 0.97805, 0.97805, 0.3 ...

p p

i i i

g k



groups of , , and

single curve fit

L8.27

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Creep Test Data

• Consider a simple shear creep test

• Here



₀is the instantaneous (short-time) applied shear stress, and

g

(t)is the measured shear strain response.

• Note: Be careful that the short-time duration of the prescribed stress is consistent with the time scale of your linear elastic or hyperelastic material definition.

L8.28

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Creep Test Data (cont'd)

• The measured shear strain response is data pairs of (shear strain, time)

g

₀,

time

₀

g

₁,

time

₁

g

₂,

time

₂

g

₃,

time

₃

…

• Because this is linear viscoelasticity only one curve may be used. If your material is not exactly linear in its viscoelastic response then test at an applied stress that is close to your component analysis stress level of interest.

L8.29

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Creep Test Data (cont'd)

• Test data processing for use in Abaqus:

• Simply normalize all the measured strain values by

g

₀ :

g

₀/

g

₀,

time

₀

g

₁/

g

₀,

time

₁

g

₂/

g

₀,

time

₂

g

₃/

g

₀,

time

₃

…

and input this data using the *SHEAR TEST DATAsuboption of

*VISCOELASTIC, TIME=CREEP TEST DATA.

L8.30

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 3: Creep Test Data Usage

*MATERIAL, NAME=

*ELASTIC, MODULI= OR

*HYPERLEASTIC, MODULI=

... (data lines)

*VISCOELASTIC, TIME=CREEP TEST DATA, {ERRTOL=0.01, NMAX=13}

*SHEAR TEST DATA, SHRINF=2 1.00747, 0.1

1.01487, 0.2

...

1.99619, 100.0

*VOLUMETRIC TEST DATA, VOLINF=2 1.00747, 0.1

pairs of and

p K

i i

k



pairs of and

nonlinear least squares fits

L8.31

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 3: Creep Test Data Usage (cont'd)

• Volumetric creep test data is optional; many solid materials exhibit insignificant volumetric creep/relaxation behavior.

• Separate fits are performed on the shear and volumetric parts and combined into one set of Prony series parameters.

• SHRINF is the normalized shear strain (compliance) as time → 1; if a value for this parameter is specified it will act as a further constraint to enforce

• VOLINF is the normalized volume strain (compliance) as time → 1; if a value for this parameter is specified it will act as a further constraint to enforce

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 4: Creep Test Data Usage (combined test data)

• If both the shear and volumetric creep tests are performed and the same time intervals are used in each, then the normalized experimental data can be specified using a single keyword: *COMBINED TEST DATA

L8.33

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Example 4: Creep Test Data Usage (combined test data, cont'd)

*MATERIAL, NAME=

*ELASTIC,MODULI= or

*HYPERLEASTIC,MODULI= or

*HYPERFOAM ... (data lines)

*VISCOELASTIC, TIME = CREEP TEST DATA, {ERRTOL = 0.01, NMAX = 13}

*COMBINED TEST DATA, SHRINF = 2, VOLINF = 2 1.00747, 1.00747, 0.1 1.01487, 1.01487, 0.2 ...

1.99619, 1.99619, 100.0

p p

i i i

g k



groups of , , and

single curve fit

L8.34

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• Prony Series Curve Fit Notes

• The proper number of terms in the Prony series should be used

• Too few terms will yield a poor fit.

• Too many terms may cause ill-conditioning

• Typically you need about the same number of Prony terms as you have decades of time data.

• The ERRTOLparameter on the *VISCOELASTIC option controls the accuracy of the fit, and thus the number of terms generated.

• It is the allowable average RMS error in the least squares fit.

• The default value is

0.01

.

L8.35

Modeling Rubber and Viscoelasticity with Abaqus

Relaxation and Creep Test Data

• The NMAXparameter on the *VISCOELASTICoption controls specifies the maximum number of terms in the Prony series.

• Fit is performed from N1 toNNMAXuntil convergence is achieved for the lowest N with respect to ERRTOL .

• Visually check your fit using unit-cube type analyses.

In document Modeling+Rubber+and+Viscoelasticity+with+Abaqus- (Page 188-196)