Strain energy is a sort of potential energy that is stored in an object due to elastic deformation. When an object is deformed from its unstressed condition, the external work done on it is converted into (and regarded as equivalent to) the strain energy stored in it. Its unit is N-m, or Joules. The derivation of the strain energy formula, its units, equations, and so on are fully addressed in this article.
Table of Contents
Simple Definition of Strain Energy
Strain energy is the energy stored in a body due to deformation. Strain energy density and the area under the stress-strain curve towards the point of deformation are terms used to describe the strain energy per unit volume. The entire system returns to its initial form when the applied force is removed.
- The material should be loaded up to its elastomeric limit.
- The material should not be permanently deformed.
- The quantity of strain energy is proportional to the amount of load and the kind of load imposed.
Strain Energy Formula
Consider a rod of length L, and gradually apply a weight to either side of the rod. The rod deforms by a length (ΔL) as a result of the imposed load. As per definition, the energy stored in a body when force is applied to it to deform within the elastic limit is equal to the work done.
Strain energy (U) = Work done (W) = F x ΔL/2
Stress-Strain Form
- The force per unit area applied to a material is defined as its stress. The breaking stress, or ultimate tensile stress, is the greatest stress that a material can withstand before breaking.
- Strain is the ratio of extension to original length; it has no units because it is a ratio of two lengths measured in meters.
Stress = Force in Newtons/Area in meter square = F/A
Strain = Change in length/original length (no units, it’s a ratio) = ΔL /L
A stress-strain graph of a material’s deformation within the elastic limit is given as
U= Area under the curve = (1/2) Stress x Strain
U = 1/2 x (F/A) x (ΔL /L)
U = 1/2 x (F x ΔL)/L3
Where:
F is the applied force,
ΔL is the extension obtained at force F
A is the area of the cross-section of the object
L is the length of the object
With the knowledge of strain energy, we can calculate the total energy stored in an object (i.e., that given by the area under the force-extension graph) if we know the volume of the object.
Daily Life Examples of Strain Energy
Strain energy, also known as elastic potential energy, has several advantages in various fields of study and engineering, including:
- Material Science: Strain energy can be used to predict the mechanical behaviour of a material under stress or strain, allowing engineers to design materials and structures that are strong, durable, and resistant to failure.
- Structural Engineering: By understanding the strain energy stored in a structure, engineers can determine the load-bearing capacity of a structure and design it to withstand external loads and stresses.
- Robotics and Mechanics: Strain energy can be used to model and control the behaviour of robotic systems, including the design of actuators, sensors, and control systems.
- Biomechanics: Strain energy can be used to study the mechanical behaviour of biological tissues and organs, helping to improve the design of medical devices and treatments.
- Energy Storage: Strain energy can be used as a form of energy storage, for example in elastic springs or rubber bands, which can store energy when they are stretched and release it when they are compressed.
Overall, the concept of strain energy provides a useful tool for understanding and predicting the mechanical behaviour of materials and structures, enabling engineers to design and create more efficient and effective products and systems.
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Linear Acceleration
The Spring Constant & Spring Force Concept
Relativistic Kinetic Energy| Easy Explanation
Elasticity Definition
Elasticity is the quality of an object that allows it to return to its original shape once a deforming force is removed.
The modulus of elasticity is just the stress-strain ratio.
Elastic limit is the top limit of deforming force beyond which, if the deforming force is removed, the body totally regains its original shape and beyond which, if the deforming force is raised, the body loses its elasticity and becomes permanently deformed.
Summary
- Strain energy is a type of potential energy stored in an object due to elastic deformation.
- Its symbol is U and its unit is N-m or Joules.
- We can use the strain energy formula to calculate the total energy stored in an object.
Frequently Asked Questions
1. What is resilience?
The capacity of a material to endure elastic deformation without plastic deformation is referred to as its resilience. The modulus of resilience is the greatest amount of volume that material may elastically deform before being permanently distorted.
2. Define plastic deformation?
Plastic deformation is the permanent distortion that happens when tensile, compressive, bending, or torsion loads surpass the yield strength of a material, causing it to elongate, compress, buckle, bend, or twist.
3. Explain elastic deformation?
Elastic deformation is a temporary deformation of a material’s shape that is self-reversible once the force or load is removed. Elastic deformation occurs when a material’s shape is altered by applying a force within its elastic limit.
4. What is the Yield point?
In mechanical engineering, the yield point is the load at which a stretched solid material begins to flow or change shape permanently, divided by its original cross-sectional area; or the amount of stress in a solid at the commencement of permanent deformation.
5. What is strain energy and how it is different from resilence?
Strain energy is elastic, which means that when the stress is removed, the material tends to recover. Resilience is the feature of a material that allows it to hold energy without permanent distortion; the energy is released as soon as the load is removed, and thus the body does not deform permanently.
6. What is negative work?
Work can be negative if the applied force is in the opposite direction to the moving object’s displacement. Please refer to the full article “Can work be negative?”.
7. Displacement physics?
Displacement in physics is a vector with a length equal to the shortest distance between the initial and final positions of a moving object.
8. What is gravitational potential energy?
Gravitational potential energy (w) is the energy that an item has as a result of its location in a gravitational field. If the item is pushed straight up at a constant speed, the force (F) necessary to hoist it to the height (h) is equal to its weight (mg).
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Mechanical Energy Formula & Examples
Light Energy| Definition, and Properties
Thermal Energy Equation- Simple Overview
Body’s Preferred Source of Energy
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