Difference Between Strain Energy and Distortion Energy

The key difference between strain energy and distortion energy is that strain energy is related to the volumetric change in a system, whereas distortion energy is related to the change in the shape of a system.

The terms, strain energy and distortion energy are related to physical systems. We can define strain energy density at a point in a solid substance using two separate components: strain energy and distortion energy. Strain energy is related to the volumetric change of the system we are considering, while distortion energy is related to the change in shape.

CONTENTS

1. Overview and Key Difference
2. What is Strain Energy 
3. What is Distortion Energy
4. Side by Side Comparison – Strain Energy vs Distortion Energy in Tabular Form
5. Summary

What is Strain Energy?

Strain energy is the elastic potential energy a wire can gain during elongation with a stretching force. We can give the strain energy of linearly elastic materials as follows:

U = ½ Vσε

Where U is strain energy, σ is stress and ε is strain. When considering the molecular strain in molecules, we can observe the strain energy being released when the constituent atoms are allowed to rearrange themselves during a chemical reaction. Here, the external work done on an elastic substance that causes it to undergo distortion from its unstressed state transforms into strain energy. Strain energy is a type of potential energy. We can observe that strain energy that comes in the form of elastic deformation, is recoverable but in the form of mechanical work.

Figure 01: Stress vs Strain diagram for a Ductile Material

For example, cyclopropane has a heat of combustion that is very high (higher than propane) for each additional methyl unit (CH2 unit). Therefore, compounds having unusually large strain energies include tetrahedranes, propellanes, cubane-like clusters, fenestranes, and cyclophanes.

What is Distortion Energy?

Distortion energy is a type of energy that is responsible for the change in the shape of a substance. It is one of the two components of strain energy density, whereas the other energy type is strain energy. We can give this relationship as follows:

Ud = Uo – Uh

Where Ud is the strain energy density, Uo is the strain energy and Uh is the distortion energy. We can use this equation to derive the final condition for failure depending on Von-mise theory.

We can describe distortion energy as a quantity that describes the increase in the free energy density of a substance such as a liquid or a crystal. This free energy change occurs due to the distortions from the substance’s uniformly aligned configuration. This term is also known as the Franck free energy, named after the scientist Frederick Charles Frank.

What is the Difference Between Strain Energy and Distortion Energy?

There are two components of the strain energy density of a solid substance: strain energy and distortion energy. Strain energy is the elastic potential energy that a wire can gain during elongation with a stretching force while distortion energy is a type of energy that is responsible for the change in the shape of a substance. The key difference between strain energy and distortion energy is that strain energy is related to the volumetric change in a system, whereas distortion energy is related to the change in the shape of a system. Moreover, the equation for strain energy is U = ½ Vσε, where U is strain energy, σ is stress and ε is strain. Whereas, the equation for distortion energy is  Ud = Uo – Uh where Ud is the strain energy density.

The following infographic summarizes the differences between strain energy and distortion energy in tabular form.

Summary – Strain Energy vs Distortion Energy

There are two components of the strain energy density of a solid substance named strain energy and distortion energy. The key difference between strain energy and distortion energy is that strain energy is related to the volumetric change in a system whereas distortion energy is related to the change in the shape of a system.

Reference:

1. “Distortion Energy.” An Overview | ScienceDirect Topics, Available here.
2. “Strain Energy.” Wikipedia, Wikimedia Foundation, 25 Mar. 2021, Available here.

Image Courtesy:

1. “Stress strain ductile” By Nicoguaro – Own work (CC BY 4.0) via Commons Wikimedia

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