Elasticity: Definition, Formula, & Examples | Lucent for GK - UPSC PDF Download

What is Elasticity?

Elasticity refers to the property of a material or object to withstand distorting influences and regain its original size and shape once the external force is removed. Unlike plasticity, where deformation is retained, elastic materials have the ability to bounce back. Understanding elasticity is essential, particularly for those preparing for the GATE exam, as it plays a significant role in materials science.

Exploring the Nature of Elasticity

The physical mechanisms behind elastic behavior can vary depending on the material. For instance, metals exhibit elastic behavior due to changes in the atomic lattice when forces are applied and released. On the other hand, the stretching of polymer chains creates elasticity in rubber and other polymers. These distinctions highlight the diverse nature of elasticity in different materials.

Stress: The Internal Forces at Play

When external forces are applied to a body, internal restorative forces come into play. Stress is defined as the force per unit area when a force is uniformly distributed over a surface. It acts in the opposite direction to the external force and is a crucial factor in understanding elasticity.

Types of Stress

Stress can be classified into three main categories, each with its unique characteristics:

• Longitudinal Stress: Longitudinal stress occurs when the stress is normal to the body's surface area and causes a change in length. This type of stress can be further divided into two subcategories: tensile stress, which causes stretching, and compressive stress, which leads to material compression.
• Volume Stress or Bulk Stress: Volume stress, also known as bulk stress, occurs when a deforming force acts in all dimensions, resulting in a change in the body's volume.
• Shear Stress or Tangential Stress: Shear stress arises when the applied force is tangential or parallel to the body's surface, causing a shift or twist in the object's shape.

Strain: Measuring Deformation:

When a body is subjected to stress, it undergoes deformation. Strain is the fractional change in the dimensions of a body caused by external stress. It is defined as the ratio of the change in dimension to the original dimension. Strain is a dimensionless quantity and holds great significance in the GATE ME syllabus.

Types of Strain

Strain can be categorized into three main types, each describing a particular aspect of deformation:

• Longitudinal Strain: Longitudinal strain occurs when stress causes a change in length beyond the body's elastic limit. It refers to the strain or deformation experienced by the body.
• Volume Strain: Volumetric strain represents the change in volume relative to the initial volume caused by external deformation-producing forces. It is commonly denoted by the symbol EV.
• Shearing Strain: Shearing strain occurs when the applied force alters the shape of the body. It is defined as the displacement ratio of a layer to its distance from a fixed layer.

Stress-Strain Curve: Exploring Material Behavior

Studying the mechanical properties of solids necessitates an understanding of their elastic characteristics. The stress-strain curve provides valuable insights into these properties. This curve illustrates the relationship between stress and strain for a material subjected to varying loads.

• Proportional Limit: The stress-strain curve exhibits Hooke's Law, where stress and strain are proportionate within the proportional limit. The proportionality constant is known as Young's modulus.
• Elastic Limit: The elastic limit represents the point at which the material returns to its original position after the removal of the applied load. Beyond this limit, plastic deformation occurs, and the material fails to regain its original shape.
• Yield Point: The yield point marks the onset of plastic deformation, leading to permanent changes in the material's shape. It consists of upper and lower yield points.
• Ultimate Stress Point: The ultimate stress point indicates the maximum stress a material can withstand before failure occurs.
• Fracture or Breaking Point: The fracture or breaking point represents the stress-strain curve's endpoint, where the material fails.
• Elastic Hysteresis: Elastic hysteresis refers to the energy lost as heat during loading and unloading cycles. It represents the difference between the strain energy required to achieve a particular stress and the elastic energy of the material.

Young's Modulus of Elasticity

Young's modulus, also known as the modulus of elasticity, measures a material's ability to tolerate compression or elongation relative to its length. It quantifies the stress required to induce a unit of strain. The pascal (Pa) serves as the SI unit for this modulus, and it plays a crucial role in understanding a material's behavior under stress.

Hooke's Law: The Law of Elasticity

Hooke's Law establishes a proportional relationship between stress and strain for minor deformations. This law applies to a wide range of materials within their elastic range. While steel typically exhibits linear-elastic behavior, other materials like aluminum adhere to Hooke's law only within a portion of their elastic range.

• Hooke's Law Definition: Hooke's Law states that the strain of a substance is directly proportional to the applied stress within its elastic limit. This law illustrates how elastic materials return to their original state after being stretched or compressed.
• Hooke's Law Formula: Hooke's Law can be mathematically expressed within the proportional limit as σ = Eε, where σ represents stress, E is the modulus of elasticity or Young's modulus, and ε stands for strain.

Examples of Elastic Materials

Elasticity finds practical applications in various fields. Here are some examples of elastic materials:

• Bungee Jumping
• Elastic Waistbands
• Rubber Bands
• Resistance Bands
• Spring Toys
• Spring Mattresses
• Trampolines
• Bows