What is the primary difference between elastic and plastic deformation?

Elastic deformation is a temporary change in shape or size that a material undergoes when subjected to an external force, and it fully recovers its original dimensions once the force is removed. This recovery is due to internal restoring forces. Plastic deformation, on the other hand, is a permanent change in shape or size. Even after the external force is removed, the material does not return to its original state, indicating that the internal structure has been permanently altered, often through the movement of dislocations within the material's crystal lattice.

Why does a material have different elastic moduli (Young's, Bulk, Shear)?

A material exhibits different elastic moduli because it responds differently to various types of deforming forces. Young's modulus quantifies resistance to stretching or compression along a single axis. Bulk modulus measures resistance to uniform volume change (compression from all sides). Shear modulus quantifies resistance to twisting or shearing, where layers slide past each other. Each modulus describes the material's stiffness under a specific mode of deformation, reflecting the anisotropic nature of interatomic bonds and lattice structures when subjected to different force orientations.

Can a material be perfectly elastic?

In an ideal theoretical sense, a perfectly elastic material would instantly and completely return to its original shape after any deformation, no matter how large, without any energy loss. However, no real-world material is perfectly elastic. All materials exhibit some degree of plastic deformation or energy dissipation (e.g., as heat) during the deformation and recovery cycle. For practical purposes, materials like steel are considered highly elastic within their elastic limits, meaning they closely approximate ideal elastic behaviour under typical working conditions.

What is the significance of the stress-strain curve's yield point?

The yield point on a stress-strain curve is highly significant as it marks the transition from elastic to plastic behaviour. Below the yield point, the material will return to its original shape upon unloading. Beyond the yield point, permanent deformation occurs. For engineers, the yield strength (stress at the yield point) is a critical design parameter, as it represents the maximum stress a component can withstand without undergoing permanent changes in shape, which is often undesirable in structural applications.

How does temperature affect the elastic properties of a solid?

Temperature generally has a significant effect on the elastic properties of solids. As temperature increases, the kinetic energy of atoms within the material increases, leading to larger atomic vibrations and weaker effective interatomic bonds. This typically results in a decrease in elastic moduli (e.g., Young's modulus, Bulk modulus, Shear modulus) and a reduction in the material's yield strength. In essence, materials tend to become less stiff and more ductile at higher temperatures, making them easier to deform plastically.

Elastic Behaviour of Solids

Physics

NEET UG

Version 1Updated 23 Mar 2026

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The elastic behaviour of solids refers to their intrinsic property to regain their original shape and size after the removal of deforming forces. This phenomenon is governed by the internal restoring forces that arise within the material when it is subjected to external stresses. These restoring forces oppose the deformation and attempt to bring the material back to its equilibrium configuration. …

Quick Summary

Elastic behaviour describes a solid's ability to regain its original shape and size after deforming forces are removed. This property arises from internal restoring forces within the material's atomic structure.

Stress is the internal restoring force per unit area ( $N/m^2$ ), categorized as normal (tensile/compressive), tangential (shear), or volumetric. Strain is the dimensionless ratio of change in dimension to original dimension, also categorized as longitudinal, shear, or volumetric.

Hooke's Law states that for small deformations, stress is directly proportional to strain. The constant of proportionality is the modulus of elasticity. Key moduli include Young's Modulus (Y) for longitudinal deformation, Bulk Modulus (B) for volumetric deformation, and **Shear Modulus (G or $eta$ )** for shear deformation.

**Poisson's Ratio ( $u$ ) describes the ratio of lateral to longitudinal strain. The stress-strain curve** illustrates a material's response to increasing stress, showing the proportional limit, elastic limit, yield point, ultimate tensile strength, and fracture point, distinguishing between elastic and plastic regions.

Work done in deforming an elastic material is stored as elastic potential energy, with energy density given by $\frac{1}{2} \text{Stress} \times \text{Strain}$ .

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Key Concepts

Stress: The Internal Resistance

Stress is not just the external force, but the *internal* restoring force that the material develops per unit…

Strain: The Measure of Deformation

Strain quantifies how much a material has deformed relative to its original size or shape. It's a ratio,…

Hooke's Law and Elastic Moduli

Hooke's Law is the cornerstone of linear elasticity, stating that within the elastic limit, stress is…

Stress ($sigma$) — Force per unit area.

\sigma = F/A

. Unit: Pa or

N/m^2

Strain ($epsilon$) — Change in dimension / Original dimension. Dimensionless.

Hooke's Law —

\sigma = E \times \epsilon

(within elastic limit).

Young's Modulus (Y) —

Y = \frac{\text{Normal Stress}}{\text{Longitudinal Strain}} = \frac{FL}{A\Delta L}

Bulk Modulus (B) —

B = \frac{\text{Volumetric Stress}}{\text{Volumetric Strain}} = -\frac{PV}{\Delta V}

Shear Modulus (G or $eta$) —

G = \frac{\text{Tangential Stress}}{\text{Shear Strain}} = \frac{F_{\parallel}}{A\theta}

**Poisson's Ratio ($

u $)**:$ \nu = -\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$. Dimensionless.

Elastic Potential Energy (U) —

U = \frac{1}{2}F\Delta L = \frac{1}{2} \frac{YA}{L} (\Delta L)^2

Energy Density (u) —

u = \frac{1}{2} \text{Stress} \times \text{Strain} = \frac{1}{2} Y (\text{Strain})^2 = \frac{1}{2} \frac{(\text{Stress})^2}{Y}

Stress-Strain Curve — Proportional limit, Elastic limit, Yield point, Ultimate Tensile Strength, Fracture point.

Stress Strain Hooke's Young Bulk Shear Poisson Energy

Stress: Force/Area Strain: Change/Original Hooke's: Stress $\propto$ Strain Young: Length change Bulk: Volume change Shear: Shape change Poisson: Lateral/Longitudinal Energy: $\frac{1}{2}F\Delta L$