The modulus of elasticity of composites upper bound is illustrated by the image below.

To compute for modulus of elasticity of composites upper 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 upper bound:

E_{c(u)} = E_{m}V_{m} + E_{p}V_{p}

Where:

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound

E_{m} =Modulus of Elasticity of the Matrix

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 upper bound when the modulus of elasticity of the matrix is 4, the modulus of elasticity of the particle is 7, the volume fractions of the matrix is 2 and the volume fractions of the particle is 6.

This implies that;

E_{m} =Modulus of Elasticity of the Matrix = 4

E_{p} = Modulus of Elasticity of the Particle = 7

V_{m} = Volume Fractions of the Matrix = 2

V_{p} = Volume Fractions of the Particle = 6

E_{c(u)} = E_{m}V_{m} + E_{p}V_{p}

E_{c(u)} = (4)(2) + (7)(6)

E_{c(u)} = (8) + (42)

E_{c(u)} = 50

Therefore, the **modulus of elasticity of composites upper bound **is **50 Pa.**

**Calculating the Modulus of Elasticity of the Matrix when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Particle, the Volume Fraction of the Matrix and the Volume Fraction of the Particle is Given.**

E_{m} = ^{Ec(u) – EpVp} / _{Vm}

Where:

E_{m} =Modulus of Elasticity of the Matrix

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound

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 the matrix when the modulus of elasticity of composites upper bound is 40, the modulus of elasticity of the particle is 10, the volume fractions of the matrix is 5 and the volume fractions of the particle is 2.

This implies that;

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound = 40

E_{p} = Modulus of Elasticity of the Particle = 10

V_{m} = Volume Fractions of the Matrix = 5

V_{p} = Volume Fractions of the Particle = 2

E_{m} = ^{Ec(u) – EpVp} / _{Vm}

E_{m} = ^{40 – (10)(2)} / _{5}

E_{m} = ^{40 – 20} / _{5}

E_{m} = ^{20} / _{5}

E_{m} = 4

Therefore, the **modulus of elasticity of the matrix **is **4.**

**Calculating the Modulus of Elasticity of the Particle when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Particle, the Volume Fraction of the Matrix and the Volume Fraction of the Particle is Given.**

E_{p} = ^{Ec(u) – EmVm} / _{Vp}

Where:

E_{p} = Modulus of Elasticity of the Particle

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound

E_{m} =Modulus of Elasticity of the Matrix

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 the particle when the modulus of elasticity of composites upper bound is 50, the modulus of elasticity of the matrix is 4, the volume fractions of the matrix is 5 and the volume fractions of the particle is 10.

This implies that;

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound = 50

E_{m} =Modulus of Elasticity of the Matrix = 4

V_{m} = Volume Fractions of the Matrix = 5

V_{p} = Volume Fractions of the Particle = 10

E_{p} = ^{Ec(u) – EmVm} / _{Vp}

E_{p} = ^{50 – (4)(5)} / _{10}

E_{p} = ^{50 – 20} / _{10}

E_{p} = ^{30} / _{10}

E_{p} = 3

Therefore, the **modulus of elasticity of the particle **is **3.**

**Calculating the Volume Fraction of the Matrix when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Matrix, the Modulus of Elasticity of the Particle and the Volume Fraction of the Particle is Given.**

V_{m} = ^{Ec(u) – EpVp} / _{Em}

Where:

V_{m} = Volume Fractions of the Matrix

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound

E_{m} =Modulus of Elasticity of the Matrix

E_{p} = Modulus of Elasticity of the Particle

V_{p} = Volume Fractions of the Particle

Given an example;

Find the volume fractions of the matrix when the modulus of elasticity of composites upper bound is 30, the modulus of elasticity of the matrix is 3, the modulus of elasticity of the particle is 5 and the volume fractions of the particle is 3.

This implies that;

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound = 30

E_{m} =Modulus of Elasticity of the Matrix = 3

E_{p} = Modulus of Elasticity of the Particle = 5

V_{p} = Volume Fractions of the Particle = 3

V_{m} = ^{Ec(u) – EpVp} / _{Em}

V_{m} = ^{30 – (5)(3)} / _{3}

V_{m} = ^{30 – 15} / _{3}

V_{m} = ^{15} / _{3}

V_{m} = 5

Therefore, the **volume fraction of the matrix **is **5.**

**Calculating the Volume Fraction of the Particle when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Matrix, the Modulus of Elasticity of the Particle and the Volume Fraction of the Matrix is Given.**

V_{p} = ^{Ec(u) – EmVm} / _{Ep}

Where:

V_{p} = Volume Fractions of the Particle

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound

E_{m} =Modulus of Elasticity of the Matrix

E_{p} = Modulus of Elasticity of the Particle

V_{m} = Volume Fractions of the Matrix

Let’s solve an example;

Find the volume fractions of the particle when the modulus of elasticity of composites upper bound is 10, the modulus of elasticity of matrix is 2, the modulus of elasticity of the particle is 4 and the volume fraction of the matrix is 3.

This implies that;

E_{c(u)} = Modulus of Elasticity of Composites Upper Bound = 10

E_{m} =Modulus of Elasticity of the Matrix = 2

E_{p} = Modulus of Elasticity of the Particle = 4

V_{m} = Volume Fractions of the Matrix = 3

V_{p} = ^{Ec(u) – EmVm} / _{Ep}

V_{p} = ^{10 – (2)(3)} / _{4}

V_{p} = ^{10 – 6} / _{4}

V_{p} = ^{4} / _{4}

V_{p} = 1

Therefore, the **volume fractions of the particle **is **1.**

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

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

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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 Upper 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 upper 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

**4**,

**Modulus of Elasticity of the Particle (E**is

_{p})**7**,

**Volume Fraction of the Matrix (V**is

_{m})**2**and

**Volume Fraction of the Particle (V**is

_{p})**6**.

Finally, Click on Calculate

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