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

Edited By Team Careers360 | Updated on Jul 02, 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

Elastic or Deforming Force
What is Stress?
Types of Stress
What is Strain?
Hooke's Law
Types of Modulus of Elasticity

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

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

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.

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

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

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

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)

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

Frequently Asked Questions (FAQs)

1. What is stress and strain? or define stress and strain or difference between stress and strain

When a deforming force is applied on a body then the deforming force acting per unit area is called stress and change in the configuration to the original configuration is called strain.

2. What is the stress strain curve?

It is the graph that plots stress on y axis and strain on x axis which conveys how the stress on the body changes with respect to the strain applied. It has several regions called Hooke’s region, yield limit, plastic region etc.

3. Discuss the stress and strain formula

Strain =Change in configuration/Original configuration

Stress = Force/Area

And Hookes law states that within elastic limits,

Stress α Strain

4. What are the units of stress and strain?

Unit of stress is Newton per meter square but strain do not have any unit, is just a number. That is it is a dimensionless quantity

5. Compressive strain is what?

It is the reciprocal of volumetric strain so it can be referred to as the ratio of original volume to the change in volume.

6. What is work softening, and how does it differ from work hardening?

Work softening is the opposite of work hardening; it's a phenomenon where a material becomes easier to deform with continued plastic deformation. This can occur in some materials due to mechanisms like dynamic recrystallization or the breaking down of strengthening precipitates. While work hardening is common in many metals at room temperature, work softening is more often observed at elevated temperatures or in certain alloys and composites.

7. How does grain size affect the mechanical properties of polycrystalline materials?

Grain size has a significant impact on the mechanical properties of polycrystalline materials. Generally, materials with smaller grain sizes are stronger and harder but less ductile than those with larger grains. This relationship is described by the Hall-Petch equation, which states that the yield strength is inversely proportional to the square root of the grain size. The grain boundaries act as obstacles to dislocation movement, thereby strengthening the material.

8. What is the significance of the proportional limit in a stress-strain curve?

The proportional limit is the point on the stress-strain curve up to which stress is directly proportional to strain (following Hooke's Law). It's often close to, but not always identical to, the elastic limit. Beyond the proportional limit, the relationship between stress and strain becomes non-linear, even if the material is still behaving elastically. Understanding the proportional limit is important for precise engineering calculations and for determining the range over which simple linear elastic models can be applied.

9. How do polymers differ from metals in their stress-strain behavior?

Polymers often exhibit more complex stress-strain behavior than metals. Many polymers show viscoelastic properties, meaning their response to stress depends on both the magnitude of the stress and the rate at which it's applied. Polymers typically have lower stiffness and strength but higher ductility than metals. Their stress-strain curves often lack a clear yield point and may show features like strain softening or hardening. Temperature has a more pronounced effect on polymer properties compared to metals.

10. What is the significance of the Bauschinger effect in cyclic loading?

The Bauschinger effect is a phenomenon where a material's yield strength decreases when the direction of strain is changed. For example, if a metal is loaded in tension beyond its yield point and then compressed, it will yield at a lower stress in compression than it would if it had not been previously deformed. This effect is important in understanding material behavior under cyclic loading and in predicting fatigue life in components subjected to alternating stresses.

11. What is Hooke's Law, and when does it apply?

Hooke's Law states that the force needed to extend or compress a spring by some distance is directly proportional to that distance. In the context of stress and strain, it means that stress is directly proportional to strain for small deformations. This law applies to many materials within their elastic limit, but it breaks down for large deformations or when materials enter their plastic region.

12. What is resilience in the context of stress and strain?

Resilience is the ability of a material to absorb energy when deformed elastically and then release that energy upon unloading. It's represented by the area under the stress-strain curve up to the elastic limit. Materials with high resilience, like rubber, can absorb more energy without permanent deformation, making them useful in applications requiring energy absorption or vibration damping.

13. How does creep differ from instantaneous deformation under stress?

Creep is the tendency of a solid material to slowly deform permanently under the influence of persistent mechanical stresses, typically at elevated temperatures. Unlike instantaneous deformation, which occurs immediately upon loading, creep is a time-dependent process. It's particularly important in materials used in high-temperature applications, such as turbine blades in jet engines.

14. How do crystalline and amorphous materials differ in their stress-strain behavior?

Crystalline materials, like most metals, have a regular, repeating atomic structure. They typically exhibit distinct elastic and plastic regions in their stress-strain curves, with a clear yield point. Amorphous materials, like many polymers and glasses, lack this ordered structure. Their stress-strain behavior is often more gradual, without a clear transition from elastic to plastic deformation. Amorphous materials may also exhibit viscoelastic properties, showing time-dependent strain.

15. How does the strain rate affect a material's mechanical properties?

The strain rate, or the speed at which deformation occurs, can significantly impact a material's mechanical properties. Generally, higher strain rates lead to increased yield strength and reduced ductility. This effect is particularly pronounced in polymers and some metals. Understanding strain rate effects is crucial in designing for impact resistance and in simulating material behavior under dynamic loading conditions.

16. What is Young's modulus, and why is it important?

Young's modulus, also known as the elastic modulus, is a measure of a material's stiffness. It's calculated as the ratio of stress to strain in the linear elastic region of the stress-strain curve. Young's modulus is important because it helps predict how much a material will deform under load, which is crucial for engineering design and material selection.

17. How does temperature affect stress and strain in materials?

Temperature can significantly impact a material's response to stress. Generally, as temperature increases, materials become more ductile and less resistant to deformation. This can lead to lower yield strengths and elastic moduli. Conversely, low temperatures can make materials more brittle. Understanding these effects is crucial in designing structures and machines that operate across various temperature ranges.

18. What is Poisson's ratio, and what does it tell us about a material?

Poisson's ratio is the negative ratio of transverse strain to axial strain in a material under uniaxial stress. It describes how a material expands in directions perpendicular to the direction of compression, or contracts in directions perpendicular to the direction of extension. This ratio provides insight into a material's behavior under load and its compressibility.

19. How does the stress-strain curve help us understand material properties?

The stress-strain curve provides a visual representation of a material's behavior under load. It shows how stress and strain are related, revealing important properties like elastic limit, yield strength, ultimate strength, and ductility. Engineers use this curve to determine how materials will perform under various conditions.

20. How do composite materials behave differently in terms of stress and strain compared to homogeneous materials?

Composite materials, made from two or more constituent materials with significantly different physical or chemical properties, often exhibit complex stress-strain behavior. Unlike homogeneous materials, composites can be engineered to have different properties in different directions (anisotropy). This allows for tailored strength and stiffness in specific directions, making them useful in applications where directional properties are important.

21. Why do we use different types of stress (tensile, compressive, shear)?

Different types of stress are used to describe how forces act on materials in various situations. Tensile stress occurs when a material is pulled apart, compressive stress when it's pushed together, and shear stress when forces act parallel to a surface. Understanding these types helps engineers and scientists predict how materials will behave under different loading conditions.

22. What is the difference between engineering stress and true stress?

Engineering stress is calculated using the original cross-sectional area of a specimen, regardless of how that area changes during deformation. True stress, on the other hand, accounts for the instantaneous cross-sectional area, which typically decreases as the material is stretched. True stress provides a more accurate representation of the material's behavior, especially at large strains, but engineering stress is often used for practical calculations due to its simplicity.

23. How does the concept of stress concentration impact material failure?

Stress concentration refers to the localization of high stresses in certain areas of a material, often due to changes in geometry like holes, notches, or sharp corners. These areas of high stress can lead to premature failure, even when the average stress across the material is below its yield strength. Understanding stress concentration is crucial in designing structures and components to avoid unexpected failures.

24. What is the significance of the ultimate tensile strength in material science?

The ultimate tensile strength (UTS) is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking. It's a key indicator of a material's strength and is often used as a benchmark for material selection in engineering applications. The UTS is typically higher than the yield strength and represents the point of maximum engineering stress on the stress-strain curve.

25. What is fatigue in materials, and how is it related to cyclic stress?

Fatigue is the weakening of a material caused by repeatedly applied loads. It occurs when a material is subjected to cyclic stress, even at levels below its yield strength. Over time, microscopic cracks can form and propagate, eventually leading to failure. The relationship between cyclic stress and the number of cycles to failure is often represented by an S-N curve (stress vs. number of cycles).

26. How does strain relate to stress?

Strain is the response of a material to stress. It's a measure of the deformation of the material relative to its original dimensions. When stress is applied, the material experiences strain, which can be observed as a change in length, volume, or shape. The relationship between stress and strain is crucial in understanding a material's behavior under load.

27. What's the difference between elastic and plastic deformation?

Elastic deformation is reversible

28. What are the SI units for stress and strain?

The SI unit for stress is Pascal (Pa), which is equivalent to one Newton per square meter (N/m²). Strain, being a ratio of change in dimension to original dimension, is dimensionless and has no units. However, it's often expressed as a percentage.

29. How does the concept of toughness differ from strength?

While strength refers to a material's ability to withstand stress without failing, toughness is a measure of a material's ability to absorb energy before fracturing. Toughness is represented by the total area under the stress-strain curve, including both elastic and plastic regions. A tough material may not necessarily be strong, and vice versa. For example, ceramics are often strong but not tough, while some polymers are tough but not particularly strong.

30. What is work hardening, and how does it affect a material's stress-strain curve?

Work hardening, also known as strain hardening, is the strengthening of a metal by plastic deformation. As a metal is plastically deformed, dislocations in its crystal structure multiply and interact, making further deformation more difficult. This process changes the material's stress-strain curve, increasing its yield strength but often reducing its ductility.

31. What is stress in physics, and how is it different from everyday stress?

In physics, stress refers to the internal forces that particles of a material exert on one another when an external force is applied. Unlike everyday stress, which is a psychological state, physical stress is a measure of force per unit area within a material. It's calculated by dividing the applied force by the cross-sectional area of the object.

32. What is the significance of the yield strength in engineering design?

The yield strength is the stress at which a material begins to deform plastically. It's a crucial parameter in engineering design because it represents the upper limit of stress that can be applied to a component without causing permanent deformation. Designers typically use a factor of safety to ensure that applied stresses remain well below the yield strength, accounting for uncertainties and variations in loading conditions.

33. How do dislocations in crystal structures affect a material's response to stress?

Dislocations are line defects in crystal structures that play a crucial role in plastic deformation. They allow planes of atoms to slip past each other more easily than if the entire plane had to move at once. The presence and movement of dislocations explain why materials often have much lower yield strengths than theoretical calculations based on perfect crystals would predict. Controlling dislocation movement is key to strengthening materials.

34. What is the relationship between stress, strain, and energy in elastic deformation?

In elastic deformation, the energy input to deform the material is stored as elastic potential energy. This energy is represented by the area under the stress-strain curve up to the elastic limit. When the stress is removed, this stored energy is released, allowing the material to return to its original shape. The relationship between stress (σ), strain (ε), and elastic modulus (E) in this region is given by the equation σ = Eε, which is a form of Hooke's Law.

35. How does the presence of residual stress affect a material's mechanical behavior?

Residual stresses are stresses that remain in a material when all external loads are removed. They can significantly impact a material's mechanical behavior. Compressive residual stresses at the surface can improve fatigue life and stress corrosion resistance by inhibiting crack initiation and growth. However, tensile residual stresses can be detrimental, potentially leading to premature failure. Understanding and controlling residual stresses is crucial in many manufacturing processes and in predicting component performance.

36. What is the difference between isotropic and anisotropic materials in terms of stress-strain behavior?

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.

37. How does porosity affect the stress-strain behavior of materials?

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.

38. How does the concept of stress relaxation differ from creep?

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.

39. How does strain hardening affect a material's ductility?

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.

40. What is the difference between engineering strain and true strain?

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).

41. What is the significance of the elastic aftereffect in some materials?

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.

42. How does the concept of stress intensity factor relate to fracture mechanics?

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.

43. What is the difference between brittle and ductile fracture in terms of stress-strain behavior?

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