# Are storage and loss modulus are intrinsic mechanical properties of the material?

Dear Sir,

I want to know that, Are storage and loss modulus are intrinsic mechanical properties of the material? If I have storage and loss modulus of a particular material then can i use it for FE analysis for any kind of shape of that material?

Hi,

I will take the freedom to tentatively answer.

The answer to your question is affirmative, storage and loss modulus are intrinsic property of the material, completely geometry-independent.

You could apply them to any geometry as long as you remain in the domain of linear viscoelasticity. Also, strorage modulsu (or loss modulus) are in a one-to-one relationship with the relaxation modulus, if the latter is preferred.

A possible source of issues lies in the range of frequencies used for their calibration. In other words, one has to be sure that a sufficient range of requencies is covered. Typically the fitting quality degrades badly at the end of the frequency range used for the calibration, and one has to ensure that values outside then range are not used during the numerical simulation. Areas where high strain rates occur are typically problematic (as these could be coupled to high frequencies).

Regards

Thanks Muzialis for the reply.

As you said, as long as I remain in linear viscoelasticity domain, I can use storage and loss modulus to any shape, But how to know whether the material has linear or non-linear viscoelastic characteristics. Is there any method to know it, by using or comparing storage and loss modulus curve in different loading conditions?

Also one more query -

In DMA testing, there is two option for testing. 1. In tensile mode and 2. In compression mode. As the storage and loss modulus are intrinsic property of the material, will the testing mode affect the result or shall I get same storage and loss modulus in both mode of testing.

{Just for Info -

I am using Abaqus for FE analysis.

Frequency range - 0.1 to 200Hz.

DMA machine - Metravib DMA50}

[QUOTE=Tarup_Chordia,13364]Thanks Muzialis for the reply.

As you said, as long as I remain in linear viscoelasticity domain, I can use storage and loss modulus to any shape, But how to know whether the material has linear or non-linear viscoelastic characteristics. Is there any method to know it, by using or comparing storage and loss modulus curve in different loading conditions?

Also one more query -

In DMA testing, there is two option for testing. 1. In tensile mode and 2. In compression mode. As the storage and loss modulus are intrinsic property of the material, will the testing mode affect the result or shall I get same storage and loss modulus in both mode of testing.

{Just for Info -

I am using Abaqus for FE analysis.

Frequency range - 0.1 to 200Hz.

DMA machine - Metravib DMA50}[/QUOTE]

Dear Tarup,

in reference to your first point about linear viscoelasticity, there are very easy ways to check if linear viscoelasticity can be applied to your case (every viscoelastic material can be deemed linearly viscoelastic if strains/rates are sufficiently small, so the whole matter is to understand if the strains involved by your applications exceed the limits). In the time domain, one can check that the relaxation modulus does not depend on the applied stress: one can perform relaxation/creep experiments at various initial strains/stress and verify that all the relaxation/creep curves collapse after they are normalised by the initial strain/stress (the relaxation modulus G(t) equals sigma(t)/strain_{initial}).

If the relaxation modulus does not depend on initial strain, and given that there is a one-to-one relationship between relaxation modulus and complex modulus, one concludes the complex modulus does not depend on strain amplitude.

So, one can perform frequency scans at increasing applied amplitude and check when the storage/loss modulus starts deviating from the values obtained in the scan at the lowest amplitude. In practice though the amplitude applicable in DMA machines is rather small, so the procedure is really not that useful. In the time domain it is easier to apply larger strains.

The second question is a little bit trickier. If one tested, for example, a linearly viscoelastic rod in tension and compression (provided it does not buckle), there would be no difference. But the complex modulus would not in generally coincide with the one obtained by testing a disk in confined compression, for example.

In the time domain,and 3D, it is common to distinguish between deviatoric and bulk relaxation response: this difference will translate to their dynamic counterparts.

It hence depends on what compression sample your DMA is capable of testing: it is generally true that deviatoric relxation is much faster than bulk one, but still the latter can be appreciable.

In practice I would start by considering the deformation modes prevalent in the application of interest and use the related mode for DMA testing.

Hope it helps

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