A cylindrical rod subjected to a tensile strain within the elastic limit undergoes a volume change. If the volume strain is equal to half the tensile strain, then the Poisson’s ratio of the rod is___________________?

Question

Accepted Answer

0. Volume strain ($
u_v$) is related to axial strain ($	ext{strain}_a$) and Poisson's ratio ($
u$) by $
u_v = -	ext{strain}_a (1 - 2
u)$. If $
u_v = 0.5 	imes 	ext{strain}_a$, then $0.5 = -	ext{strain}_a (1 - 2
u) / 	ext{strain}_a$, leading to $0.5 = -(1 - 2
u)$, so $
u = 0$.