- #1

Trying2Learn

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- Summary
- Where does it come from?

Earlier today, I posted a question about the strain energy function.

I am happy with the answer (I love this group).

But the answer opened up a deeper question.

Many elasticity textbook posit the existence of a strain energy function:

And they make an additional assumption about its properties

Where does this come from? Who formulated it? I have always accepted it, but now I am questioning it.

Indeed, these two assumptions lead me down the path (along with further assumptions about the symmetries of the stress and strain tensors and related issues, and material property symmetries) to Young's Modulus and Poisson's Ratio. Thus, as statements, the "jive" with mechanical engineering results.

Are the assumptions above a case of

Or is there any validity or justification of such assumptions, other than that they work? Is there any rational justification for such an assumption (independent of where it leads us)?

I am happy with the answer (I love this group).

But the answer opened up a deeper question.

Many elasticity textbook posit the existence of a strain energy function:

And they make an additional assumption about its properties

Where does this come from? Who formulated it? I have always accepted it, but now I am questioning it.

Indeed, these two assumptions lead me down the path (along with further assumptions about the symmetries of the stress and strain tensors and related issues, and material property symmetries) to Young's Modulus and Poisson's Ratio. Thus, as statements, the "jive" with mechanical engineering results.

Are the assumptions above a case of

*post hoc ergo propter hoc*?Or is there any validity or justification of such assumptions, other than that they work? Is there any rational justification for such an assumption (independent of where it leads us)?