... material:¹

The summation convention is used. Any repeated index is summed over all possible values, i.e., $x_i x_i$ implies $x_1 x_1 + x_2 x_2 + x_3 x_3$.

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...#tex2html_wrap_inline2595#
²

While some materials do have a negative Poisson's ratio, like some cellular materials (see a nice review of this by Roderick Lakes, Science, 235, 1038-1040 (1987)), they are unusual. Our considerations do not imply that materials that have $E < 0$ and $\nu < -1$ or $E < 0$ and $\nu > 1/2$, but I have never heard of one that exists.

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