Question

A cube of 10 mm length is compressed in the x direction and constrained from expanding in the x and y directions. the cube has the properties e = 100 gpa and ν=0.3. determine the effective modulus (gpa), which we'll define as the ratio of stress in the z direction to strain in the z direction.

Answer 1

The effective modulus for the given cube under compression can be found using Young's Modulus and Poisson's Ratio.

Step-by-step explanation:

Given that the cube is compressed in the x direction and constrained from expanding in the x and y directions, we can consider the cube's deformation in the z direction. The effective modulus, which is the ratio of stress in the z direction to strain in the z direction, can be determined using the formula:

Effective Modulus = Young's Modulus / (1 - Poisson's Ratio)

Young's Modulus (E) is given as 100 GPa and Poisson's Ratio (ν) is given as 0.3. Plugging these values into the formula, we get:

Effective Modulus = 100 GPa / (1 - 0.3) = 142.86 GPa