How to Calculate and Solve for Modulus of Elasticity of Composites Lower Bound | Composites

August 3, 2022 Loveth Idoko

Last Updated on May 28, 2024

The modulus of elasticity of composites lower bound is illustrated by the image below. To calculate modulus of elasticity of composites lower bound, four essential parameters are needed and these parameters are Modulus of Elasticity of the Matrix (E_m), Modulus of Elasticity of the Particle (E_p), Volume Fraction of the Matrix (V_m) and Volume Fraction of the Particle (V_p).

The formula for calculating modulus of elasticity of composites lower bound:

E_c(l) = ^E_mE_p/_{VmEp + VpEm}

Where:

E_c(u) = Modulus of Elasticity of Composites Lower Bound
E_m =Modulus of Elasticity of the Matrix
And then, E_p = Modulus of Elasticity of the Particle
V_m = Volume Fractions of the Matrix
V_p = Volume Fractions of the Particle

Let’s solve an example;
Find the modulus of elasticity of composites lower bound when the modulus of elasticity of the matrix is 2, the modulus of elasticity of the particle is 6, the volume fractions of the matrix is 8 and the volume fractions of the particle is 4.

This implies that;

E_m =Modulus of Elasticity of the Matrix = 2
E_p = Modulus of Elasticity of the Particle = 6
V_m = Volume Fractions of the Matrix = 8
V_p = Volume Fractions of the Particle = 4

E_c(l) = ^E_mE_p/_{VmEp + VpEm}
E_c(l) = ⁽²⁾⁽⁶⁾/_{(8)(6) + (4)(2)}
So, E_c(l) = ⁽¹²⁾/_{(48) + (8)}
E_c(l) = ⁽¹²⁾/₍₅₆₎
E_c(l) = 0.214

Therefore, the modulus of elasticity of composites lower bound is 0.214 Pa.

How to Calculate the Modulus of Elasticity of Composites Lower Bound With Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the modulus of elasticity of composites lower bound.

To get the answer and workings of the modulus of elasticity of composites lower bound using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Composites under Materials and Metallurgical

Now, Click on Modulus of Elasticity of Composites Lower Bound under Composites

The screenshot below displays the page or activity to enter your values, to get the answer for the modulus of elasticity of composites lower bound according to the respective parameter which is the Modulus of Elasticity of the Matrix (E_m), Modulus of Elasticity of the Particle (E_p), Volume Fraction of the Matrix (V_m) and Volume Fraction of the Particle (V_p).

Now, enter the values appropriately and accordingly for the parameters as required by the Modulus of Elasticity of the Matrix (E_m) is 2, Modulus of Elasticity of the Particle (E_p) is 6, Volume Fraction of the Matrix (V_m) is 8 and Volume Fraction of the Particle (V_p) is 4.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia can calculate the modulus of elasticity of composites lower bound and presents the formula, workings and steps too.