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# How are Compression Modulus and Tensile Modulus related to Lame` constants?

Hello everyone

I have a material with a compression modulus and tensile modulus along with Poisson's ratio. Are compression modulus and tensile modulus related to the Lame` constants? Or does this material fall under 'cubic symmetry' which needs three elastic constants? In that case, how are they related to the elastic coefficients (C12, C44 or C11)?

I need to incorporate these material properties in ABAQUS. How do I model this material in ABAQUS?

Any lead on this problem is appreciated. Thanks a lot.

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Nikhil

## Hello Nikhil, You should

Hello Nikhil,

You should check this:

http://en.wikiversity.org/wiki/Introduction_to_Elasticity/Constitutive_r...

Gives a nice consize summary. On the end of the page is a table with the formulas of Lame constants, shear modulus, etc. to calculate from one each other.

Andras

## Compressive and tensile modulus

Dear Nikhil,

Compressive and tensile modulus are not related by Lamé constants. The difference between both modulus is not related to material symmetry conditions, but with material behaviour. For instance, a unidirectional composite has different modulus when the fibre is oriented at 0º, but tensile and compressive modulus are the same when the fibre is oriented at 90º.

Otherwise, tensile and compressive modulus are related to flexural modulus. If your model works in flexure, in my opinion the best way is to use the flexural modulus. Related information:

http://www.aer.bris.ac.uk/comptest2004/proceedings/posters/comptest_59.pdf

Determination of tensile and compressive moduli by flexural tests

Polymer Testing, Volume 25, Issue 6, September 2006, Pages 766-771

F. Mujika, N. Carbajal, A. Arrese, I. Mondragon

Regards.

Faustino Mujika

## Definition of Tangent modulus, Secant modulus, and Chord modulus

Cheers Mujika.

The paper is very helpful for my present research .

Very clear explanation about the relation of compressive and tensile modulus.

As a reference, the definitions of tangent modulus, secant modulus, and chord modulus are given here:

http://www.makeitfrom.com/info/?about=Flexural_Modulus

By the way, what is the difference between tangent modulus and flexural modulus in flexural testing?

## Flexural modulus

Dear Enyang,

Flexural modulus is the one obtained by flexural tests. It can be tangent, secant or chord modulus as explained int the web pages that you refer.

The following references could be interesting for you. As you can see, the modulus used for calculation in both casesre are chord modulus.

On the difference between flexural moduli obtained by three-point and four-point bending tests

Polymer Testing, Volume 25, Issue 2, April 2006, Pages 214-220

F. Mujika

On the effect of shear and local deformation in three-point bending tests

Polymer Testing, Volume 26, Issue 7, October 2007, Pages 869-877

F. Mujika

Regards.

Faustino Mujika

## Great reference

Dear Faustino,

Many thanks for the references.

Recently, I am trying to summarize an empirical equation based on the experimental results of polymeric foams.

Your papers are very helpful in understanding the 3 modulus terms.

Best regards,

Enyang WANG