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If I'm not mistaken, a Young's modulus $E$ can theoretically take on any positive value without bound. Physically, I interpret this as though a solid can have any arbitrary "stiffness" (within the limits of its linear stress-strain region, of course). On the other hand, the range of possible Poisson's ratios is constrained to $[-1,0.5]$ for stable, isotropic, linearly elastic materials. I'm not quite sure how to interpret this physically. Why must the Poisson's ratio necessarily be constrained?

Řídící
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Paul
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A Poisson ratio larger than 1/2 would correspond to a material that has its volume expand when compressed. A Poisson ratio less than -1 would correspond to a material that when compressed in a given direction, shrinks more in transverse direction than in the given direction.

In practice, most materials have a Poisson ratio in the range of 0 to 0.5, meaning that when compressed in any direction, the material 1) shrinks in volume and 2) expands in lateral directions. (And when elongated in any direction, the material increases in volume, and shrinks in lateral directions.)

Johannes
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    This is incorrect. Any material with a poisson's ratio between -1 and 0 will exhibit the behavior you described, which is typical of an auxetic material. The bounds on the Poisson's ratio are due to the fact that the elastic energy of a material must be positive for a non-zero deformation. I just answered a question that addresses these constraints in a rigorous manner. http://physics.stackexchange.com/q/99077/ – Tyler Olsen Feb 21 '14 at 19:57