# Equivalent uniaxial tensile modulus from pure shear

Hello,

I am trying to model a thin-film, silicone rubber strain sensor. I am using a pure shear/planar test to obtain the material parameters for my thin film (around 5 micrometers thick) as this is the only way to get good enough force data with the load cell we have (the large sample width enables the force to be resister by the load cell without too much noise). As the device will be operating in a small strain region (5%) I will model the device as linearly elastic but I was wondering how I convert the Youngs modulus I obtain (i.e. by measuring the gradient) to the equivalent Youngs modulus for a uniaxial tensile test, which I assume the FEM software will expect as the input? I have have seen some literturature suggesting that one can use a 3/4 conversion factor (i.e. 4 times the shear modulus), is this correct?

Many thanks,

Araromi,

before converting you still need to figure out a way to determine/estimate Poissons modulus.

In linear elasticity the shear modulus and Youngs modulus are related via Poissons ratio, there are humpteen sources on the Web on the matter.

If you tested a thin strip you would record a force F, due to extension only (the specimen can contract along the vast majority of its length). In the pure shear geometry such lateral contracation is somewhat prevented, and this increases the stiffness of the specimen.

My advice is to use non-linear elasticity first, far more natural, and then linearise at small strains.

Search for pure shear, you will find plenty of sources that will help you express the deformation gradient for such deformation mode. Assume the material behaves as an incompressible Neo-Hookean solid (you will anyhow linearise later), use the deformation gradient you found to get the strains and finally to get your stress/load and all you need is to calibrate the material constant versus your experiments. There is then an easy relationship between the Neo-Hookean constant and Youngs modulus, Wikipedia will help you (you will find there easy to follow derivations using the Neo-Hookean model for simple extension: pure shear requires very little modifications).

Hope this helps

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