Examples of Elastic Behaviour of Solids

When the forces that caused the deformation are eliminated, elasticity refers to the ability of a distorted material body to return to its original shape and size. Elastic behaviour (or response) is a term used to describe a body that has this flexibility. Most solid materials exhibit elastic behaviour to some degree.

Still, the size of the force and the resulting deformation within which elastic recovery is possible for any specific material is limited. This post will look at several examples of solids’ elastic behaviour.

What is Elasticity?

Elasticity is a body property that allows an object to restore its original orientation after being subjected to an external force. A solid is a hard entity in the cosmos that exists in one of three states of matter. When it applies to this item, an external force changes its physical orientation and structure.

As a result, the object’s length, volume, or shape has changed. We call it elastic when a thing retains its previous form and dimensions after removing external acting forces. Let’s look at what elasticity is, its use, and Hooke’s law says about it.

What Do You Understand by the Elastic Behaviour of Materials?

When we stretch a slingshot, it deforms owing to the imposed strain. Still, it returns to its original shape when we stop applying the force, known as elasticity, which means that the body resists any permanent alteration when stress is used. When pressure is removed from the body, it returns to its former shape and size.

Let’s imagine you’ve chosen a thin steel rod for your bent. Bending a little should stop the application of force. As a result, the rod does not revert to its previous state. The elastic and plastic can notice the material behaviour properties of the materials, which can be explained using Hooke’s law. Elasticity refers to a body’s ability to resist any lasting alteration when applied to stress.

Different materials exhibit varying degrees of elasticity. Therefore, it is critical to investigate a material’s elastic behaviour. In the building of diverse structures such as bridges, columns, pillars, and beams, most engineering design requires an understanding of the elastic behaviour of materials.

Examples of Elasticity-Hooke’s law

Consider a beam supported at both ends and subject to a load W at its midway. The shaft length is l, the breadth is b, and the thickness is a. When a weight is applied at its halfway point, the object bends in the manner indicated. The upper surface is crushed, while the lower surface stretches during the operation. Due to the load, the beam will sag or deflect.

If the breadth b is bigger and the length is smaller, the shaft bends less for a given force. It is because the load-induced deflection of the beam is inversely proportional to the cube of the width and directly proportional to the cube of the beam’s length. However, increasing the width, b, increases the risk of the beam bending unless the weight is positioned correctly.

Buckling is the term for this bending. As a result, asymmetric loading can cause the beam to buckle, which is common in bridges that carry differentially dispersed traffic at different periods. As a result, the cross-section of the shaft selects to be an I-shape to avoid this. This shape provides a large load-bearing surface and enough depth to prevent bending.

It is written as

δ=Wl³/4bd3γ

Where,

δ is the sag.

Y is Young’s modulus of elasticity.

Using the above equation, we can easily deduce that the material’s Young’s modulus of elasticity must be high to limit the amount of bending for a given load. The depth d must be addressed since sag is inversely proportional to the cube of depth. However, as the depth increases, the likelihood of bending increases, known as buckling. As a result, a compromise between the various cross-sectional shapes is reached.

The elastic limit varies greatly depending on the solid evaluation; for example, a steel bar or wire may only be stretched by roughly 1% of its original length, whereas strips of certain rubberlike materials can be extended by up to 1,000%. On the other hand, steel is significantly stronger than rubber because the tensile force necessary to achieve maximum elastic extension in rubber is far lower (by a factor of roughly 0.01) than that required in steel. Many solids in tension have flexible characteristics that fall between these two extremes.

Steel and rubber have different macroscopic elastic characteristics due to their microscopic structures. Steel and other metals have flexibility due to short-range interatomic forces that keep the atoms in regular patterns when the material is not stressed. Under stress can disrupt atomic bonding at minor deformations.

 On the other hand, rubber-like materials and other polymers are made up of long-chain molecules that uncoil as the material is stretched and rebound during elastic recovery. The macroscopic reaction of the material is the focus of the mathematical theory of elasticity and its application to engineering mechanics, not the underlying mechanism that creates it.

The elastic response of materials like steel and bone in a simple tension test is typified by a linear relationship between the tensile stress (tension or stretching force per unit area of cross-section of the material) and the extension ratio (difference between extended and initial lengths divided by the initial length), e.

Another way is proportional to e; this is represented as = Ee, where E, the proportionality constant, is Young’s modulus. The value of E varies depending on the substance; the ratio of steel and rubber values is around 100,000. The equation σ = Ee is known as Hooke’s law and is an example of a constitutive rule.

It expresses the material’s nature (or constitution) in macroscopic proportions. Hooke’s rule is primarily applicable to one-dimensional deformations. Still, it can be extended to more general (three-dimensional) deformations by adding linearly linked stresses and strains (generalisations of and e) to account for shearing, twisting, and volume changes.

The resulting generalised Hooke’s law, which underpins the linear theory of elasticity, accurately describes the elastic characteristics of all materials, as long as the deformations correspond to extensions of less than 5%. This theory is frequently used to analyse engineering constructions and seismic disturbances.

In principle, the elastic limit differs from the proportional limit, which signifies the end of the type of elastic behaviour described by Hooke’s law, namely, that in which the stress is proportional to the strain (relative deformation) or that in which the load is proportional to the displacement.

For some elastic materials, the elastic limit roughly coincides with the proportional limit, making the two difficult to differentiate at times; nevertheless, for other materials, a zone of non-proportional elasticity occurs between the two.

The linear theory of elasticity is insufficient to describe significant deformations in rubber or soft human tissue like skin. Except for very tiny deformations, the elastic response of these materials is nonlinear. It may be expressed by the constitutive law σ = f (e), where f (e) is a mathematical function of e that depends on the material and approximates E(e) when e is very small.

In contrast to the situation in linear theory, nonlinearity indicates that the graph of plot versus e is not a straight line. The energy, W(e), stored in the material under the action of the stress σ represents the area under the graph of σ = f (e). It can be converted into many types of energy, such as kinetic energy.

By comparing the theoretical relationship between and e with the results of experimental tension testing in which and e are measured, the stored-energy function W(e) can be derived. To quantify the elastic response of any solid in tension can use a stored energy function in this way.

The development of certain forms of strain-energy parts from the findings of experiments involving three-dimensional deformations, generalising the one-dimensional case described above, is an important aspect of the theory of elasticity.

In situations where a direct experimental test is not possible, strain-energy functions can be used to anticipate the material’s behaviour. They can be used to develop components for engineering structures in particular.

For example, rubber is utilised in bridge bearings and engine mountings, where its elastic qualities are critical for vibration absorption. Steel beams, plates, and shells are used in various constructions because of their flexible flexibility. In addition, the skin’s elasticity plays a significant role in the effectiveness of skin grafting procedures.

Problems relating to such applications are solved using the mathematical framework of elasticity theory. The material qualities involved in the strain-energy function significantly impact the results anticipated by mathematics, and a wide range of intriguing events can be described, which allows them to withstand high pressures without causing material damage or failure.

The skin’s elasticity plays a significant role in the effectiveness of skin grafting procedures. Problems relating to such applications are solved using the mathematical framework of elasticity theory. The material qualities involved in the strain-energy function significantly impact mathematics’s anticipated results and can describe a wide range of intriguing events.

Conclusion

As no material is perfectly elastic, the concept of elasticity is an idealisation. If you use a hair tie to groom yourself, you may have seen that its size tends to distort over time. It may snap after a certain point. It is because the hair tie loses its elastic properties over time. When deforming pressures are released, a flexible body returns to its original shape and dimensions. A plastic body can’t bear its previous condition and size after being deformed by tiny forces. When deforming pressures are removed, elasticity refers to a body’s ability to return to its last shape and size. It demonstrates a resistance to change.