Elastic Modulus: Definition, Values, and Examples

Elastic modulus, also known as Young's modulus, is a fundamental property of materials that measures their stiffness or resistance to elastic deformation under stress. This property is essential in engineering and materials science, as it determines a material's ability to support loads and maintain its shape. Elastic modulus is expressed as a force per unit area with units of pascals (Pa) or pounds per square inch (psi). Elastic modulus is determined by calculating the slope of the elastic portion of the stress-strain curve. The elastic modulus is different for different materials. Stiffer materials have a higher elastic modulus.

This article provides an overview of the elastic modulus, its measurement, units, and examples of materials with varying values.

What Is Elastic Modulus?

Elastic modulus can be defined as a material’s ability to resist elastic deformation when stress is applied to it. It is a measure of a material’s rigidity or stiffness. The modulus of elasticity, in terms of the stress-strain curve, is the slope of the stress-strain curve in the region of elastic 

behavior, where stress is linearly proportional to strain. Other names for elastic modulus include Young's modulus, modulus of elasticity, modulus of elasticity in tension, or tensile modulus. For more information, see our guide on Flexular Modulus.

Figure 1 is an example of Young’s Modulus of Elasticity (Y) graph:

What Is the SI Unit of Elastic Modulus?

The modulus of elasticity is measured in Pascal (Pa), the same unit used for stress. MPa and GPa are usually used to express the modulus of elasticity because of the large magnitude of typical values. 

What Is an Example of Elastic Modulus?

Steel is a common material used in construction due to its strength and durability. Its high elastic modulus of 200-210 GPa means that it is able to resist deformation and maintain its shape under stress, making it ideal for use in structures such as buildings and bridges. This property allows the steel to bear heavy loads without bending or breaking, ensuring the safety and stability of the structure. In addition, steel's high elastic modulus makes it an excellent choice for use in machine parts and tools, where stiffness and resistance to bending are essential factors. Its stiffness allows the machines to create precise parts by not having its flexibility participate in variability. However, steel's high elastic modulus also means that it is a relatively brittle material and can be prone to cracking under certain conditions. It is recommended to consider the specific application and potential stresses that steel will be subjected to in order to ensure its safe and effective use.

What Are the Elastic Modulus Values?

The elastic moduli for some common materials are listed in Table 1 below:

How Are the Values of Elastic Modulus Expressed?

The value of elastic modulus is typically expressed in units of pressure or stress, such as pounds per square inch (psi) or pascals (Pa). It is a measure of a material's stiffness or resistance to elastic deformation under stress.

There are different types of elastic modulus depending on the type of stress being applied. The most commonly used elastic modulus is Young's modulus. Young’s modulus measures the ratio of stress to strain when stress is applied perpendicular to the material's cross-sectional area.

The formula for Young's modulus is:

Other types of elastic modulus include the bulk modulus and the shear modulus. The bulk modulus measures the resistance to compression, and the shear modulus measures the resistance to deformation under shear stress.

What Material Has the Highest Elastic Modulus?

Diamond has the highest known elastic modulus,  ~1220 GPa, and is also considered to be the hardest known material. This is considerably higher than all types of plastics and metals. The elastic modulus of most plastics typically ranges from 1 to 10 GPa (gigapascals). 

In contrast, the elastic modulus of metals is generally much higher than that of plastics. The elastic modulus of metals can vary widely depending on the specific material and its composition. Most metals have elastic moduli in the range of 50 to 400 GPa. It's important to note that these are general ranges. The elastic modulus of a specific material can vary depending on factors such as: temperature, strain rate, and the presence of defects or impurities. 

What Does a Large Elastic Modulus Value Indicate?

A large elastic modulus indicates that a material is very stiff. Calculating elastic deflections involves using the elastic modulus, a crucial design parameter. The stiffer the material is, or the smaller the elastic strain that arises from the application of a given stress, the greater the modulus. 

What Does a Small Elastic Modulus Value Indicate?

A small elastic modulus indicates that it does not take much force to induce a considerable amount of elastic strain in a material. It is flexible, not stiff. It will easily deform elastically if any sort of compression or tensile stress is applied. Rubber is an example of such a material, with a very low elastic modulus of 0.05 GPa.

What Is the Elastic Modulus Symbol?

The symbol for elastic modulus is E. It is equal to the stress applied to a material in the elastic strain region, divided by the strain experienced by that material. Elastic modulus is measured in Pa or psi.

How Is Elastic Modulus Determined?

The elastic modulus of a material is determined by generating a stress-strain curve for the material. The slope of the straight-line (linear elastic) portion of the curve is then calculated. First, the material is stretched by a machine that measures the force used and the change in length that results from that force and plots these values on a stress-strain curve. The stress-strain curve will have a linear portion at the beginning. The elastic modulus is determined by calculating the slope of this portion of the curve.

What Is the Elastic Modulus Equation?

The equation for elastic modulus is:

The equation for elastic modulus is simply the ratio of the stress applied to a material, to the strain resulting from that stress.

What Is the Difference Between Elastic Modulus and Shear Modulus?

Elastic modulus measures a material’s ability to resist being deformed when tensile stress is applied to it, whereas shear modulus measures a material’s ability to resist being deformed when shear stress is applied. The main difference between the two moduli is the type of stress applied to the test specimen.

Summary

This article presented elastic modulus, explained what it is, and discussed its importance and how to calculate it. To learn more about elastic modulus, contact a Xometry representative.

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