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

To compute for 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)} = ^{EmEp}/_{VmEp + VpEm}

Where:

E_{c(u)} = Modulus of Elasticity of Composites Lower 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 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)} = ^{EmEp}/_{VmEp + VpEm}

E_{c(l)} = ^{(2)(6)}/_{(8)(6) + (4)(2)}

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.**