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According to my current understanding, if a non compressible solid cube is subjected to a uniaxial compressing force, it will essentially be flattened - it will get shorter along the axis that is being compressed, but longer on the other two axes to conserve volume.

The shortening on the compressed axis is pretty clearly caused by normal stress, but what about the lengthening on the other axes? Is that caused normal stress or shear stress?

Is it possible for a force to create normal stress that is perpendicular to the direction of the force?

Person
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  • Maybe I'm missing something, but how can a non compressible solid cube get "flattened"? – Bob D Mar 07 '22 at 14:39

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If forces flatten the cube along the x axis and gets shorter, that is normal stress. If forces make the y and z axes get longer, that is also normal stress.

Shear stress would be if forces push two parallel faces of the cube so they slide parallel to each other.

mmesser314
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Lateral expansion/contraction is a so-called Poisson effect. Yes, it's induced by normal axial stress (and not by shear stress). But this doesn't imply that a normal stress is acting laterally. The lateral strain arises from the material geometry as altered by the normal strain. Most materials shrink laterally when stretched axially; some, with special internal structure, expand.

(Now, if you constrained the lateral or Poisson strain, then a lateral normal stress state would arise. But the lateral stress is typically taken as zero for an elongated geometry in the absence of lateral constraints.)

Does this get at what you're asking about?

Chemomechanics
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