The image above represents shear modulus of rubber.

To compute for shear modulus of rubber, three essential parameters are needed and these parameters are **Density of Network Cross Links (N), Boltzmann’s Constant (K _{B}) **and

**Temperature (T).**

The formula for calculating shear modulus of rubber:

G = NK_{B}T

Where:

G = Shear Modulus of Rubber

N = Density of Network Cross Links

K_{B} = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the shear modulus of rubber when the density of network cross links is 21, the boltzmann’s constant is 1.38064852E-23 and the temperature is 10.

This implies that;

N = Density of Network Cross Links = 21

K_{B} = Boltzmann’s Constant = 1.38064852E-23

T = Temperature = 10

G = NK_{B}T

G = (21)(1.38064852e-23)(10)

G = 2.89

Therefore, the **shear modulus of rubber **is **2.89e-23 Pa.**

**Calculating the Density of Network Cross Links when the Shear Modulus of Rubber, Boltzmann’s Constant and the Temperature is Given.**

N = ^{G} / _{K}_{B}T

Where;

N = Density of Network Cross Links

G = Shear Modulus of Rubber

K_{B} = Boltzmann’s Constant

T = Temperature

Let’s solve an example;

Find the density of network cross links when the shear modulus of rubber is 14, the boltzmann’s constant is 1.380e-23 and temperature is 4.

This implies that;

G = Shear Modulus of Rubber = 14

K_{B} = Boltzmann’s Constant = 1.380e-23

T = Temperature = 4

N = ^{G} / _{K}_{B}T

N = ^{14} / _{1.380e-23 x 4}

N = ^{14} / _{5.52e-23}

N = 2.54e-23

Therefore, the **network cross links **is **2.54e-23.**

Continue reading How to Calculate and Solve for Shear Modulus of Rubber | Fracture Mechanics