Question

a material has poisons ratio 0.5 if a uniform rod of it suffers a longitudinal strain of 3 ×10^-3 i 20 what will be percentage increase in volume

Answer 1

$poisson \: ratio = \mu = 0.5$

$longitudinal \: strain = \epsilon_x = 3 \times {10}^{ - 3}$

$lateral \: strains = \epsilon_y \: and \: \epsilon_z \\ \epsilon_y = \epsilon_z = - \mu \times \epsilon_x \\ = - 0.5 \times 3 \times {10}^{ - 3} \\ = - 1.5 \times {10}^{ - 3}$

$volumetric \: strain = \epsilon_x + \epsilon_y + \epsilon_z \\ \\ \epsilon_v = 3 \times {10}^{ - 3} - 1.5 \times {10}^{ - 3} - 1.5 \times {10}^{ - 3} \\ \\ \epsilon_v = 0$

Since there is no volumetric strain, volume change is 0.