# SED

## differentiation of Strain energy Function

Dear,
I am having problem to find "Cauchy stress(σ) " and " Spatial elastic Tensor (c)" from the "strain energy function (ψ)" using 2nd Piola Kirchhoff stress ( S) of transversely isotropic hyper-elastic material. as per the Mechanics the

## Exponential model W (strain energy density function)- Zero stress zero strain condition

Hi,

I am new here and have a very basic question on the Strain Energy Density (SED) function of exponential model.

This is the exponential model SED form : W=a(e(b(I1-3))-1)

Now we have certain postulates such as that

1.W=0 when there is no deformation and

2. stress=0 when strain =0.

When there is no deformation I1=3 and hence W=0, which is correct.

However, when we take the 1st derivative of W with respect to I1 to get our stress and then substitute I1=3 we don't get stress=0.

## Tensile testing curve and fracture toughness relation

Hello everyone,
I am studying fracture of polymer composites.
I had a question I want to relate fracture toughness of composite to the composite stress-strain curve found from simple tensin test(on samples with no notch or pre-existing crack), can anyone give me a hint , how to do it? 