What is the fundamental difference between stress and pressure?

While both stress and pressure are defined as force per unit area ($F/A$), their fundamental nature differs. Pressure is an external scalar quantity, always acting perpendicularly and inwards on a surface, typically associated with fluids. Stress, on the other hand, is an internal tensor quantity representing the restoring forces developed within a solid material due to deformation. Stress can be normal (perpendicular) or tangential (parallel) to the surface, and it reflects the material's internal resistance to change in shape or size. Volumetric stress is numerically equivalent to pressure, but general stress is a more comprehensive concept.

Why is strain a dimensionless quantity?

Strain is defined as the ratio of a change in dimension to the original dimension. For example, longitudinal strain is $Delta L / L$, volumetric strain is $Delta V / V$, and shear strain is $Delta x / h$ (or an angle in radians). In each case, the numerator and denominator have the same physical units (e.g., meters/meters, cubic meters/cubic meters). When identical units are divided, they cancel out, leaving strain as a pure number without any dimensions or units. This makes strain a relative measure of deformation.

Can a material experience stress without strain, or strain without stress?

In an ideal elastic material, stress and strain are intrinsically linked. According to Hooke's Law, within the elastic limit, stress is directly proportional to strain. Therefore, if there is no deformation (zero strain), there are no internal restoring forces, meaning zero stress. Conversely, if there are internal restoring forces (stress), there must be some deformation (strain). However, in real-world scenarios, residual stress can exist in materials even without external loads, and some materials might exhibit 'creep' (strain under constant stress over time) or 'stress relaxation' (stress decrease under constant strain over time), which are more advanced concepts beyond basic elasticity.

What is the significance of the 'elastic limit' in the context of stress and strain?

The elastic limit is a critical property of a material. It represents the maximum stress a material can withstand before it begins to undergo permanent or plastic deformation. If the applied stress is below the elastic limit, the material will fully regain its original shape and size once the deforming force is removed. If the stress exceeds this limit, the material will not return to its original state, retaining some permanent deformation. Understanding the elastic limit is vital for designing structures and components to ensure they operate safely without permanent damage.

How do tensile and compressive stress differ in their effect on a material?

Tensile stress arises when forces pull on a material, causing it to elongate or stretch. The internal restoring forces act outwards, trying to resist this pulling apart. Compressive stress, conversely, occurs when forces push on a material, causing it to shorten or compress. Here, the internal restoring forces act inwards, resisting the squashing. Both are types of normal stress, acting perpendicular to the cross-section, but their direction relative to the material's original dimensions and their resulting deformation (elongation vs. shortening) are opposite.

What is the difference between longitudinal strain and shear strain?

Longitudinal strain (a type of normal strain) describes a change in length along the direction of the applied normal force. It's the ratio of change in length to original length ($Delta L/L$). It affects the size of the object. Shear strain, on the other hand, describes a change in the shape of an object, specifically an angular deformation, caused by tangential forces. It's the ratio of relative displacement of layers to their perpendicular distance ($Delta x/h$) or the angle of deformation ($ heta$). Shear strain does not change the volume of the object, only its shape.

Stress and Strain

Physics

NEET UG

Version 1Updated 23 Mar 2026

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In the realm of material science and solid mechanics, 'stress' is defined as the internal restoring force developed per unit cross-sectional area of a body when it undergoes deformation due to an external deforming force. It is a measure of the intensity of the internal forces acting within a deformable body. 'Strain', on the other hand, quantifies the deformation itself, representing the fraction…

Quick Summary

Stress and strain are fundamental concepts in understanding how solid materials respond to external forces. Stress ( $sigma$ ) is defined as the internal restoring force developed per unit cross-sectional area of a body when it is deformed.

Its SI unit is Pascal ( $Pa$ or $N/m^2$ ). There are three main types: Normal stress (tensile or compressive, acting perpendicular to the surface), Tangential or Shear stress (acting parallel to the surface), and Volumetric or Hydraulic stress (uniform normal stress causing volume change).

Strain ( $epsilon$ ) is the dimensionless measure of deformation, defined as the ratio of the change in dimension to the original dimension. Corresponding to stress types, we have Longitudinal strain ( $Delta L/L$ ), Shear strain ( $Delta x/h$ or $heta$ ), and Volumetric strain ( $Delta V/V$ ).

Materials exhibit elasticity if they regain their original shape after force removal, up to an elastic limit. Beyond this limit, they show plasticity, undergoing permanent deformation. Within the elastic limit, stress is proportional to strain, a relationship known as Hooke's Law.

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Key Concepts

Normal Stress Calculation

Normal stress occurs when the deforming force is perpendicular to the cross-sectional area. It can be tensile…

Longitudinal Strain Calculation

Longitudinal strain is the fractional change in length of a body when subjected to a normal force. It is…

Shear Strain Calculation

Shear strain quantifies the angular deformation of a body when subjected to a tangential force. It is defined…

Stress ($sigma$) — Internal restoring force per unit area.

\sigma = F/A

. Unit:

Pa

N/m^2

Normal Stress — Force perpendicular to area. Tensile (pulling), Compressive (pushing).

Shear Stress — Force parallel to area. Causes shape change.

Volumetric Stress — Uniform pressure, causes volume change.

Strain ($epsilon$) — Dimensionless ratio of change in dimension to original dimension.

Longitudinal Strain —

\epsilon_L = \Delta L/L

. Change in length.

Shear Strain —

\epsilon_S = \Delta x/h = \tan \theta \approx \theta

. Angular deformation.

Volumetric Strain —

\epsilon_V = \Delta V/V

. Change in volume.

Elastic Limit — Max stress before permanent deformation.

To remember the types of Stress and Strain: Nice Students Verify Long Stories Vigorously.

Normal Stress, Volumetric Stress

Longitudinal Strain, Volumetric Strain

(And don't forget Shear Stress and Shear Strain, which are the other main types!)