Solid Deformation: Types, Properties & Solved Questions

Every object or matter occupies a space with its size and shape properties. The change in size and shape of an object through the action of external forces is called deformation. The deformation is a mechanical property of a solid which occurs due to the action of either stress or strain. Even a small force or pressure can deform any object. Deformation takes place when the intermolecular forces within an object oppose the applied external force, sometimes an object moves into a complete deformation state (permanent deformation) due to the application of higher external forces. 

Key Terms: Solid Deformation, Deformations, Young’s Modulus, Bulk Modulus, Shear Modulus, Bulk Stress, Tensile Stress, Shear Stress

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Types of Solid Deformation

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There are two types of solid deformations, and they are:

• Temporary Deformation
• Permanent deformation

Temporary Deformation

It is defined as short or reversible deformation where the object tends to remain deformed until external forces are applied. When the forces are eliminated, the object retains its initial state and is also known as elastic deformation.

Permanent Deformation

It can be defined as irreversible deformation where the object completely moves into a deformation state and its initial state cannot be restored. Mostly this kind of deformation occurs due to heavier external force and it can be called plastic deformation.

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Stress and Strain Factor

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In the physics of solids, stress and strain are principal factors responsible for the deformation of solids. 

• Stress
• Strain

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Stress and Its Types

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It is defined as the restoring force per unit area whereas it explains the magnitude of forces. The SI unit of stress is N/m² It can be mathematically written as

\(\partial = \frac{F}{A}\) (Unit: N/m2)

Where, σ - is the applied stress

F - force applied

A – area of any object 

Types of Stress

• Bulk Stress: Defined as the deformation of a body due to applied external forces from all directions. Example: Pressure experienced by an ocean diver in ocean depth.
• Compressive Stress: Defined as Compression of an object due to resultant forces. Example: Formation of the mountain at convergent boundary and concrete pillar.
• Tensile Stress: Defined as the elongation of an object due to the action of forces (pull). An example of tensile stress is the stretching of a rubber band or rubber tubes.
• Shear Stress: Defined as the deformation of an object due to applied tangential force. Example: Force experienced between the ground and feet during the walk.

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Strain and Its Types

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It is defined as the degree of how much an object is stretched or buckled. It can be mathematically expressed as

\(\sigma\)=\(\frac{\eth l }{L}\) (Unit: No unit - dimensionless)

Where,

• \(\sigma\) - strain due to applied stress
• δl – change in length of the material
• L – Initial or original length of the material

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Types of Strain

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• Tensile Strain: It is defined as the change in area or length of a body due to applied tensile stress.
• Compressive Strain: It is defined as the change in the area or length of a body due to applied compressive strain.

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Stress-Strain Curve

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The Stress-strain curve establishes a materialistic relationship between stress and strain. The curve reflects numerous properties.

Stress-Strain Curve

• Proportional Limit: The point in the graph where the material obeys Hooke’s law. Here, the ratio of stress and strain gives a proportionality constant called Young’s modulus.
• Elastic Limit: The region of limit where the material has the capability to restore its initial position after deformation. 
• Yield Point: The point of limit from where the material starts to deform drastically. Beyond this limit, the material undergoes permanent deformation.
• Ultimate Stress Point: The point which defines the maximum stress tolerance capability of any materials before they undergo failure.
• Breaking Point: Beyond the ultimate stress point, the material leads to a state of failure or degradation. 

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Features of Solid Deformations

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• Deformation occurs when the internal intermolecular forces act against the applied external forces.
• Weak external forces may lead to negligible deformation, and acquire a new equilibrium state resulting in reformation or return to the original state.
• Heavier external forces over any object can either lead to permanent deformation or complete structural failure
• Deformation in solid takes place depending on the type of material, geometry, size, and magnitude of external forces.

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Properties of Solid Deformations

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The properties of solid deformations are as follows:

Elastic Modulus & Young’s Modulus

The elastic modulus is the proportionality constant of the ratio of stress and strain. It can also be called Young' Modulus. Its SI unit is Pa. It defines the stiffness of any material whose elastic property can be understood from equation

Elastic Modulus = \( \frac{Stress}{Strain}\)

Young’s Modulus, Y = \(\frac{\sigma}{\epsilon}\)

Where,

• Y – Young’s modulus
• σ – stress
• \(\epsilon\) - strain

Shear Modulus

It is defined as the measure of the ratio of shear stress to the shear strain. The SI unit of shear modulus is Pa (pascal). It can be mathematically written as

G= \(\frac{Fl}{A\bigtriangleup x}\)

Where,

• G – Shear modulus
• F – Force on the object
• l – initial length of an object
• A – Area over which the force is acting.
• \(\bigtriangleup x\) – transverse displacement

Read More: Shear Modulus

Bulk Modulus

It is the measure of the ratio of applied pressure to the corresponding decrease in volume of any material. It can be expressed as

B = \(\frac{\bigtriangleup P}{\frac{\bigtriangleup V}{V}}\)

Where,

• B – Bulk modulus
• ΔP – Change in applied pressure
• ΔV – Change in volume of the material
• V – Initial volume of the material

Read More: Bulk Modulus

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Things to Remember

• The change in size or shape of an object due to the action of applied external forces is termed deformation. It is a mechanical property and categorized into two types which are temporary and permanent deformation.
• Temporary deformation is reversible and occurs due to weak external forces whereas permanent deformation is irreversible due to large or heavy forces. Then, temporary deformation can also be called elastic deformation whereas permanent deformation is plastic deformation.
• The effect of stress and strain factors are responsible for deformation in solids. The stress is the measure of magnitude which is force per unit area, and strain is the measure of the degree of elongation or stretch.
• The stress factor exhibits four solid deformation properties such as bulk, compressive, tensile, and shear modulus whereas the strain exhibits tensile and compressive strain properties.
• The stress-strain curve responsible for solid deformations gives out five significant terms which are proportional limit, elastic limit, yield point, ultimate stress point, and breaking point.
• Finally, the type of deformation in solid occurs depending on the type of material, geometry, size, and magnitude of external forces. 

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