An Introduction to Dynamic Modulus

A material undergoes various changes when it is placed under an external force. The dynamic modulus of material gives the value of the ratio between stress and strain experienced by the material. Dynamic modulus is of three kinds. Modulus of elasticity is defined as the straight-lined slope given by the stress-strain curve. This slope gives the elastic property of the material. Dynamic young’s modulus provides us with the property of a material by calculating the stress and strain values. The following article explains the dynamic modulus and dynamic modulus of elasticity. 

Dynamic Modulus

Dynamic modulus is a parameter widely used in structural engineering problems. The dynamic modulus is defined as the ratio between the stress and strain in certain conditions. Therefore, the dynamic modulus gives the elastic properties of various materials, thus the modulus of elasticity. Dynamic modulus of elasticity is of three kinds, 

• Dynamic young’s modulus
• Rigidity modulus
• Bulk modulus

Stress

When the deforming force is applied to an object, the object deforms. In order to bring the object back to the original shape and size, there will be an opposing force generated inside the object.

This restoring force will be equal in magnitude and opposite in direction to the applied deforming force. The measure of this restoring force generated per unit area of the material is called stress. It is usually represented by “σ.”

Strain

Strain is the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body. It is usually depicted by “ε.” 

Modulus of Elasticity

Dynamic modulus of elasticity, also simply known as the modulus of elasticity, is a measurement of the elastic properties of various materials. It is given by calculating the ratio between the stress and strain values of a material. The dynamic modulus of elasticity is generally observed by a graph between the different stress and strain values; this graph presents various material properties of the subject.

The dynamic modulus of elasticity is defined as the slope given by the graph. The portion of the stress and strain curve that covers a straight line is called the dynamic modulus of elasticity. 

For two different stress and strain points, the dynamic modulus of elasticity is given by,

Dynamic modulus of elasticity = [σ2 – σ1] / [ε2-ε1]

Different parts in a Stress-Strain Curve

A material undergoing stress and strain also undergoes various changes; these changes can be easily depicted by understanding the stress-strain curve,

The following are the different parts of a stress-strain curve:

• Proportional Limit

It is the part in the stress-strain curve in which the material properties follow the principle of Hooke’s law. According to this law, the stress and strain in the material remain in proportion. The proportionality constant derived by the ratio of stress and strain is known as the dynamic young’s modulus.

• Elastic Limit

In the graph up until this point, the material does not lose its elastic property; thus, it always retains its original shape when the external force is removed.

• Yield Point

This is defined as that point in a stress-strain curve from which the material starts to exhibit plastic properties. When an external force is applied, it does not come to its original shape and keeps deforming.

• Ultimate Stress Point

This is the point in a stress-strain curve immediately before the failure; it defines the ultimate load a material can take before failing.

• Breaking Point

At this point, the material breaks completely.

Dynamic young’s modulus

Dynamic young’s modulus is a property of a material that tells us how the body behaves under stress and strain. Therefore, the young’s modulus gives us information about how easily a material stretches under the influence of stress and strain. The dynamic young’s modulus is represented by E; it follows the principle of Hooke’s law.

Consider that a material with an area A is undergoing stress (σ), and strain (ε) under the influence of an external force F, the dynamic young’s modulus of elasticity is given by,

E = σ / ε,

We know that stress is given by, 

σ = F/A,

And, ε = dl/l

Where dl/l is the small deformation in the shape of the material.

Thus,

E = σ / ε = (F/A) / (dl/l).

By calculating the value of dynamic young’s modulus, we can determine if the material is of brittle, tensile, elastic, or plastic properties.

Conclusion

The dynamic modulus is defined as the ratio between the stress and strain experienced by the material. Depending upon the different properties of the material, the dynamic modulus is divided into three kinds. The dynamic modulus of elasticity is determined by observing the stress-strain curve; it is obtained by observing the straight-lined slope of the graph. The principle of Hooke’s law calculates the dynamic young’s modulus; according to this law, the values of stress and strain in material experiencing an external force remain in a direct proportion.