A cube polymer matrix is subjected to elastic deformation in compression by 10 N applied force. The cube is deformed by 20% of its original shape. The cube side has a length of 1 m. If you assume that the polymer has the intrinsic properties of rubber, find the storage shear modulus of the polymer matrix. Poisson's ratio for rubber = .50.
To find the storage shear modulus of the polymer matrix, we can use the following formula:
G' = (2 * F * (1 - ν)) / (A * δ)
Where:
G' is the storage shear modulus
F is the applied force
ν is the Poisson's ratio
A is the area of the face of the cube
δ is the deformation of the cube
To calculate the area of the face of the cube, we can use the formula:
A = (side length)^2
Given:
F = 10 N (applied force)
ν = 0.50 (Poisson's ratio)
side length = 1 m (length of the cube side)
δ = 20% (deformation in percentage)
First, let's calculate the deformation in meters:
δ = (20/100) * 1 m = 0.2 m
Next, let's calculate the area of the face of the cube:
A = (1 m)^2 = 1 m^2
Now, we can substitute the values into the formula to find the storage shear modulus:
G' = (2 * 10 N * (1 - 0.50)) / (1 m^2 * 0.2 m)
= (2 * 10 N * 0.50) / (1 m^2 * 0.2 m)
= 20 N / (0.2 m^3)
= 100 N/m^3
Therefore, the storage shear modulus of the polymer matrix is 100 N/m^3.