Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store

Elastic Behavior of Solids

Reviewed by:
ffImage
hightlight icon
highlight icon
highlight icon
share icon
copy icon
SearchIcon

What is Elasticity?

Elasticity is defined as an attribute of rigid bodies to restore their original shape. Consider a spring hanging at one end through a rod at the top and the other end of it is left free. If I stretch this free end, the spring starts vibrating back and forth. It means the potential energy stored inside it transforms into kinetic energy; the spring is in solid form, so there is a tiny space between the successive atoms. Due to the force of attraction between them, they try to come back to their lattice points. This is how an interatomic force of attraction comes into play. So soon the stage comes when restoring force acting in the opposite direction to the applied force brings the spring into its natural state. Hence, the condition in which the body rolls back to its initial form. Such a condition is elasticity.


Explain Elastic Behaviour of Solids

Solid is one of the three states of matter composed of many molecules or atoms arranged in a particular form. Here, each molecule is acted upon by the forces because of neighbouring molecules.  The solids take such a shape that each molecule finds itself in a position of stable equilibrium. The rigid bodies when stretched with an external force restore their original shape after the removal of this force. It means they are in an elastic limit. So, until the elastic limit, the body resists the changes. Therefore, we can say that the body is perfectly elastic. Thus, the elastic behaviour of solids can be explained very well by observing the microscopic nature of the solids. 


Elastic Behavior of Solids

When a solid body is deformed, the atoms or molecules inside it are displaced from their fixed points or lattice points (equilibrium positions) causing a change in interatomic and intermolecular distances. When this force is removed, the interatomic force tries to bring back the body into its original position. Thus, the body comes to its original shape.


Mechanical Properties of Solids

The restoring mechanism can be visualized through a model of a spring ball system.  Here, the ball represents atoms and spring represents the interatomic force of attraction between the balls or atoms. 


(Image will be added soon)


Initially, these atoms are in their respective lattice points as shown in Fig.2. When they are displaced from their points, the interatomic force of attraction brings the system to its original shape.


Deformation: The phenomenon of change in the shape of a body under the effect of applied force.


Deforming Force: The external force that is responsible for deformation in the shape of the system is called the deforming force.


Restoring Force: The opposite force that works in the way the frictional force does in a moving body. This force acts in the opposite direction, and it is a property of a body to come back to its original position after an external force is removed.


Physical and Chemical Properties of Solids

  • Solids are incompressible, which means that the constituent particles are placed close to each other, resulting in little space between the constituent particles.

  • Solids have a fixed mass, volume, and form, resulting in a compact arrangement of component particles.

  • Solids are inflexible. This is because there isn't enough space between the constituent particles, which causes it to be hard or fixed.

  • Molecules have a small intermolecular distance. As a result, the force between component particles (atoms, molecules, or ions) is extremely strong.

  • Particles in the system can only fluctuate about their mean locations.

  • The melting point of a solid is determined by the strength of the interactions between its constituents: stronger interactions result in a higher melting point.


Important Points on Elastic Behaviour of Solids


The attribute of a matter or a body under which a body regains its original configuration is called elasticity.  Let us understand this through an experiment:


On stretching a rubber band, we observe that there is a change in its shape and size. On releasing the band, the rubber regains its original length.


(Image will be added soon)


The force applied to the rubber band is the deforming force. Therefore, the force that restores the elongated body to its original shape, and size is called the restoring force.


What Causes this to Happen?

Depending on their atomic elasticity, solids are formed up of atoms (or molecules). They are surrounded by other atoms of the same type, which are kept in balance by interatomic forces. When a force is applied to the solid, these particles are displaced, causing it to distort. When the deforming force is eliminated, the atoms revert to their previous state of equilibrium due to interatomic interactions. Because no substance is fully elastic, elasticity is an idealization.


Applications of Elastic Behavior of Materials

Elastic materials are those materials that can be used in places where the long-term usage of such material is required. The applications of elastic materials are outlined below:


  • Used in the construction of bridges, beams, columns, pillars: while constructing these materials, in-depth knowledge of the strength of the materials used in the construction is of prime importance.

  • Construction of cranes: Cranes are used to lift the loads. Therefore, great care is taken into consideration that the extension of the rope does not exceed the elastic limit of the rope.

  • In engineering, it is of utmost importance to know the elastic behaviour of materials being used.

  • The bridges are designed in such a way that they don’t get deformed or break under a load of heavy traffic, or due to the force of strongly blowing wind, and its weight.

  • Let’s consider a bar of length L and breadth d. Let Y be the young's modulus of the material of the bar. When a load ‘W’ is attached at its middle point, the depression δ produced at its middle point is given by,

                         δ = Wl3/4Ybd3

  • The metallic parts of the machinery are designed in such a way that when they are subjected to stress beyond the elastic limit, they will get permanently deformed.


Factors Affecting Elasticity

Effect of Stress: Even within the elastic limit, we know that when a solid is exposed to a high number of cycles of stresses, it loses its elastic characteristic. As a result, the material's operating stress should be kept lower than the ultimate tensile strength and the safety factor.


Effects of Temperature: Temperature affects the elastic properties of materials. Elasticity rises with lower temperatures and decreases with higher temperatures.


Effect Nature of Crystals: The flexibility of the crystals also relies on whether they are single crystals or polycrystals. The elasticity of a single crystal is higher, whereas the elasticity of a polycrystal is lower.


Effect of Annealing: Annealing is a procedure that involves heating a material to a very high temperature and then cooling it slowly. Typically, this technique is used to improve the material's softness and ductility. However, annealing a material causes the production of big crystal grains, which lowers the material's elastic properties.


Effect of Impurities: The presence of impurities causes variations in the materials' elastic properties. The type of impurity introduced to it determines how much elasticity it gains or loses.


Differences Between Elasticity and Plasticity

  • Elasticity is the quality of a solid material that allows it to restore its form once external stress is removed. Plasticity is the characteristic of a solid substance that allows it to keep its distorted shape even when the external load is removed.

  • The amount of elastic deformation is minimal. The amount of plastic distortion is substantial.

  • The amount of external force necessary to bend a solid elastically is relatively tiny. Plastic deformation needs a greater amount of force.

  • Within this elastic zone, Hooke's Law of Elasticity applies. If the material is plastically distorted, Hooke's Law does not apply.

  • Within this elastic area, most solid materials exhibit linear stress-strain behaviour. In the plastic zone, the stress-strain curve is non-linear.

  • Although atoms of the material are displaced from their original lattice location during elastic deformation, they return to their original position once external stress is eliminated. As a result, atoms are momentarily displaced. Plastic deformation causes solid atoms to be permanently displaced from their original lattice location. They maintain their new location even when the external stress is removed.

  • Elastic deformation takes place before plastic deformation. Only after it has been elastically deformed does it undergo plastic deformation.


The Similarity Between Elasticity and Plasticity

  • Both are the qualities of Solid.

  • Both forms of deformations can occur as a result of any sort of loading (normal, shear, or mixed).

  • Depending on the application, both elastic and plastic deformations might be advantageous.

  • Only when the material has been elastically deformed can plastic deformation begin. As a result, plastic deformation is impossible without elastic deformation.

FAQs on Elastic Behavior of Solids

1. What is meant by the elastic behavior of solids in the context of CBSE Class 11 Physics?

The elastic behavior of solids refers to the property of a solid to return to its original shape and size after the external force causing deformation is removed, provided the deformation does not exceed the elastic limit. This ability is due to the restoring forces acting at the atomic or molecular level within the material.

2. How does Hooke’s Law help in understanding elasticity?

Hooke’s Law states that within the elastic limit, the extension or deformation of a solid is directly proportional to the applied load or force. Mathematically, Stress ∝ Strain or Stress = E × Strain, where E is the modulus of elasticity. This relationship explains how materials behave under various forces in engineering and physics problems.

3. What are the practical applications of elastic materials in daily life and engineering?

Elastic materials are used in many applications where recovery of shape is important. Key examples include:

  • Construction of bridges, beams, and columns to withstand loads without permanent deformation.
  • Manufacturing of springs, ropes, and shock absorbers due to their ability to restore original form.
  • Engineering designs that rely on predictable elastic responses for safety and durability.

4. Why is steel considered more elastic than rubber?

Steel is more elastic than rubber because it can return to its original shape faster and with less permanent deformation when the applied stress is removed. The modulus of elasticity for steel is higher, making its elastic behavior more prominent for the same amount of strain.

5. What is the difference between elasticity and plasticity in solids?

Elasticity is the property of a material to regain its original configuration after removing external stress, while plasticity is the ability of a substance to undergo permanent deformation. Elastic deformation is reversible and occurs before plastic deformation. In plastic deformation, atoms are permanently displaced from their original position.

6. How do factors like temperature, impurities, and crystal structure affect the elastic properties of solids?

The elasticity of solids can be influenced by:

  • Temperature: Lower temperatures increase elasticity while higher temperatures reduce it.
  • Impurities: The presence and type of impurities can either increase or decrease elasticity.
  • Crystal Structure: Single crystals are generally more elastic than polycrystalline materials due to their uniform atomic arrangement.

7. What is the elastic limit and why is it important in the study of solids?

The elastic limit is the maximum stress a material can endure and still return to its original shape once the force is removed. If the applied force exceeds this limit, the material will undergo permanent deformation. Knowing the elastic limit is crucial for safe engineering design and material selection.

8. How do stress and strain relate to each other in elastic deformation?

During elastic deformation, stress (force per unit area) is directly proportional to strain (relative deformation) up to the elastic limit. This linear relationship is the basis of Hooke's Law and helps in predicting how a material will respond to external loads.

9. In what way does the atomic structure of a solid affect its elastic behavior?

The elastic behavior of a solid depends significantly on its atomic or molecular structure. Strong intermolecular or interatomic forces and a closely packed arrangement contribute to higher elasticity, as particles can only move slightly from their equilibrium positions before returning under the influence of restoring forces.

10. What are common misconceptions about the elastic behavior of solids?

One common misconception is that materials like rubber are more elastic than steel because they stretch more. However, elasticity actually measures how well a material returns to its original shape, and steel is more elastic as per the definition. Another misconception is that all deformation is reversible, but only changes within the elastic limit are reversible.