Stress and Strain - Definition, Curve, Hooke's Law, SI Units, Types, FAQs

Stress and Strain - Definition, Curve, Hooke's Law, SI Units, Types, FAQs

Team Careers360Updated on 02 Jul 2025, 04:36 PM IST

Stress and strain are fundamental concepts in physics and engineering that describe how materials respond to external forces. Stress refers to the internal force per unit area within a material, caused by an applied load, while strain is the deformation or displacement that occurs as a result of this stress. These principles aren't just theoretical but have practical applications in everyday life. For example, when we apply pressure on a rubber band (stress), it stretches (strain). Similarly, the way a bridge or building bends or flexes under the weight of vehicles or wind is a real-life demonstration of stress and strain. Understanding these concepts helps engineers design safe structures and products that can withstand various forces without breaking or deforming. Even in our bodies, bones and muscles experience stress and strain during physical activities like running or lifting, making these ideas crucial in biomechanics and medical science.

This Story also Contains

  1. Elastic or Deforming Force
  2. What is Stress?
  3. Types of Stress
  4. What is Strain?
  5. Hooke's Law
  6. Types of Modulus of Elasticity
Stress and Strain - Definition, Curve, Hooke's Law, SI Units, Types, FAQs
Stress and Strain

Elastic or Deforming Force

It is the applied force onto a body by which its shape or size changes over time, the change can be in length, breadth volume or change on all three of these. That is there will be a change in the normal shape of the molecule implying that there is a change in the arrangement of molecules.

Elasticity

It is the special ability of a body to regain its initial original configuration on the removal of the deforming force. Those materials showing the elastic property are called elastic materials. The more elastic the material is faster it can turn back into its original state.

Examples of elastic materials are quartz fibre. phosphor bronze, etc

Plasticity

It is the inability of a body to regain its original status on the removal of the deforming forces, the objects or materials that obey the plasticity property are called plastic materials

Examples of materials that show plasticity or plastic materials are - bakelite, plastic etc.

What is Stress?

The restoring force or deforming force experienced per unit area on a body is called stress. It has the dimension of force per area or the same dimension as that of pressure.

Stress $=\frac{\text { Force }}{\text { Area }}$

$
1 \mathrm{~N} / \mathrm{m}^2=1 \mathrm{~Pa}(\text { pascal })
$

The SI unit of stress is pascal ( Pa ).

Types of Stress

Usually, stress is classified into four types of stress depending on the way in which the stress is applied: they are Normal stress, tensile stress, compressive stress, and Tangential stress.

1. Normal Stress

Normal stress occurs when the elastic restoring force or deforming force operates perpendicular to the region. The following are some of the most common types of normal stress.

A. Tensile Stress

The stress developed inside the body is called tensile stress when the length of the body increases In the direction of the applied force.

Here in the below image, you can see that when the force is applied in a particular direction the length of the body increases in the same direction as that of the applied force.

Tensile Stress

B. Compressive Stress

The stress developed inside the body is called compressive stress when the length of the body decreases in the direction of the force applied.

Here in the figure below you can see that the length of the body decreases in the direction of the applied force.

compressive stress

  1. Tangential or Shearing Stress

Tangential stress occurs when an elastic restoring force or deforming force operates parallel to the surface area. Here in the figure below you can see that the force is applied along a surface and it is called tangential because the force is not perpendicularly applied rather it is applied tangentially to the surface.

Shearing Stress

What is Strain?

The strain has several meanings in literature here we are going to look at what is strain in physics. Strain definition can be made as it is a fraction which compares the change in the configuration of the body to the original configuration or the initial configuration of the body. Since the numerator and denominator of the term have the same dimension they cancel out each other and hence strain in a dimensionless quantity.

Strain =Change in configuration original configuration

There are different types of strains discussed below

Depending on the surface of the applied force and the change in the shape of the objects, strains can be classified as three – Longitudinal strain, volumetric strain, and shearing strain.

  1. Longitudinal Strain

It is the relation between the change in length and the original length of the body where force is applied. This type of strain is calculated in the case where the deforming force is acting perpendicular to the surface

Longitudinal Strain =Change in length/Original length

  1. Volumetric Strain

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It has the same definition as that of the strain but here the force acting on the body from all directions not only causes the change in length but totally the entire volume is changed. So it can be written as the ratio of change in volume of the body to the original volume.

Volumetric Strain = Change in volume/Original volume

3. Shearing Strain

A tangential force causes a plane perpendicular to the fixed surface of the cubical body to turn via an angle (in radians).

Shearing Strain

Stress vs strain curve or stress-strain diagram or stress-strain curve for brittle material

Stress vs. strain

Hooke's Law

In the case of small deformations that is when the applied force is small but it should be enough to cause deformations, in such conditions the stress acting on the body is directly proportional to the strain, which can be seen in the above stress and strain curve. It is also called stress-strain theory.

Stress $\propto$ Strain

Stress $=k \cdot$ Strain

Where, K is the proportionality constant, and is known as the modulus of elasticity, in the above stress-strain curve diagram, the region that obeys Hooke’s law is called Hooke” 's law curve.

Elastic Moduli: Modulus of elasticity - According to Hooke's law, within clastic limit stress is directly proportional to the strain, which can be seen in the stress-strain graph above. Which implies

Stress $\propto$ Strain

Stress $=E \cdot$ Strain

$\frac{\text { Stress }}{\text { Strain }}$ is constant for elastic deformations.

Where E is known as the modulus of elasticity or elastic moduli, the ratio of stress and strain is known as the modulus of elasticity, there are different kinds of modulus of elasticity according to the type of stress and strain which is discussed below

Types of Modulus of Elasticity

  1. Young's Modulus of Elasticity (Y)

When the force acted is normal to the surface the stress and strain will be normal and hence its proportionality constant is discussed here as Young’s modulus

Y = Normal stress/Longitudinal strain

  1. Bulk modulus of elasticity (B)

The bulk modulus is the ratio of normal stress to the volumetric strain.

B = Normal stress/Volumetric strain

Its Unit is - Nm or Pascal

Compressibility (A) - Reciprocal of bulk modulus of elasticity (B)

  1. Modulus of Rigidity or shear modulus of elasticity (G)

When the deforming force is acting shear to the surface or tangential surface the stress and strain developed will be shear strain and tangential stress. The proportionality constant in this case is called the rigidity modulus or the shear modulus.

G = Tangential stress/Shearing strain

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Frequently Asked Questions (FAQs)

Q: What is the difference between isotropic and anisotropic materials in terms of stress-strain behavior?
A:
Isotropic materials have the same properties in all directions, meaning their response to stress is uniform regardless of the direction of applied force. Anisotropic materials, on the other hand, have properties that vary with direction. This means their stress-strain behavior can be different depending on how the force is applied relative to the material's structure. Many composites and single crystals are anisotropic, while most metals and amorphous materials are approximately isotropic.
Q: How does porosity affect the stress-strain behavior of materials?
A:
Porosity, the presence of small voids or gas-filled spaces in a material, generally reduces its strength and stiffness. Pores act as stress concentrators and reduce the effective cross-sectional area that can bear load. As a result, porous materials typically have lower elastic moduli, yield strengths, and ultimate strengths compared to their fully dense counterparts. However, porosity can be beneficial in some applications, such as in materials designed for energy absorption or thermal insulation.
Q: How does the concept of stress relaxation differ from creep?
A:
While both stress relaxation and creep involve time-dependent material behavior, they are distinct phenomena. Creep occurs when a material deforms over time under constant stress. Stress relaxation, on the other hand, is the decrease in stress over time when a material is held at constant strain. In stress relaxation, the initial deformation is maintained, but the force required to hold that deformation decreases. This is particularly important in applications like gaskets and seals.
Q: How does strain hardening affect a material's ductility?
A:
Strain hardening, or work hardening, generally increases a material's strength but decreases its ductility. As a material is plastically deformed, dislocations multiply and interact, making further deformation more difficult. This increases the material's yield strength and ultimate strength. However, it also reduces the material's ability to undergo further plastic deformation before fracture, thus decreasing ductility. This trade-off between strength and ductility is a key consideration in material processing and selection.
Q: What is the difference between engineering strain and true strain?
A:
Engineering strain is calculated using the original length of a specimen, while true strain accounts for the instantaneous length as deformation occurs. Engineering strain is simpler to calculate and is commonly used in practical applications. True strain provides a more accurate representation of large deformations, as it accounts for the continuous change in the specimen's length. The relationship between true strain (ε) and engineering strain (e) is given by ε = ln(1 + e).
Q: What is the significance of the elastic aftereffect in some materials?
A:
The elastic aftereffect, also known as anelasticity, is a phenomenon where a material continues to deform slightly after an applied stress is removed, and then slowly returns to its original shape. This behavior is more pronounced in some polymers and certain metal alloys. It's different from plastic deformation because the material eventually returns to its original shape, but it's not instantaneous like ideal elastic behavior. Understanding the elastic aftereffect is important in applications requiring precise dimensional stability.
Q: How does the concept of stress intensity factor relate to fracture mechanics?
A:
The stress intensity factor is a parameter used in fracture mechanics to predict the stress state near the tip of a crack caused by a remote load or residual stresses. It's crucial in determining whether a crack will propagate and lead to failure. The stress intensity factor depends on the applied stress, crack size, and geometry of the component. When it reaches a critical value (the fracture toughness of the material), rapid crack growth and failure can occur. This concept is fundamental in designing against fracture in structures and components.
Q: What is the difference between brittle and ductile fracture in terms of stress-strain behavior?
A:
Brittle fracture occurs with little or no plastic deformation before failure. On a stress-strain curve, this is characterized by a linear elastic region followed by sudden failure, with no significant plastic region. Ductile fracture, conversely, involves substantial plastic deformation before failure. The stress-strain curve for ductile fracture shows a clear plastic region, often with necking in tensile specimens. Ductile materials typically absorb more energy