Learning Objectives:

• Understand the importance of deformation and stiffness for engineering design.

• Young’s modulus measures the resistance of a material to elastic (recoverable) deformation under load.

• A stiff material has a high Young’s modulus and changes its shape only slightly under elastic loads (e.g. diamond). A flexible material has a low Young’s modulus and changes its shape considerably (e.g. rubbers).

• A stiff material requires high loads to elastically deform it - not to be confused with a strong material, which requires high loads to permanently deform (or break) it.

• The stiffness of a component means how much it deflects under a given load. This depends on the Young’s modulus of the material, but also on how it is loaded (tension, or bending) and the shape and size of the component.

Solved Example: 91-1-01

The stiffness is the ability of a material to resist:

A. Deformation under stress

B. Fracture due to high impact loads

C. Externally applied forces with breakdown or yielding

D. None of the above

Correct Answer: A

Solved Example: 91-1-02

The stiffness of an axially loaded bar is defined as________(E = modulus of elasticity, A = Area of cross section of bar, L = Length of bar)

A. $\dfrac{{AE}}{L}}$

B. $\dfrac{L}{{AE}}$

C. $\dfrac{E}{{AL}}$

D. $\dfrac{{AL}}{E}$

Correct Answer: A

Learning Objectives:

• Identify the three elastic moduli related to changes in an object’s length, shape and volume in response to applied stress.

The relation between E, G, $\mu$, and K will be, \[E = 2G (1 + \mu),\] \[E = 3K(1 -2 \mu)\] Where,
E = Young's modulus,
G = Modulus of rigidity,
$\mu$ = Poisson ratio,
K= Bulk modulus of elasticity.

Solved Example: 91-2-01

In the relation, stress = k $\times$ strain, k is __________________:

A. Spring constant

B. Relative density

C. Modulus of elasticity

D. Factor of plasticity

Correct Answer: C

Solved Example: 91-2-02

Choose the wrong statement regarding moduli of elasticity.

A. Greater the value of moduli of elasticity, more elastic is material

B. With rise in temperature, elasticity of material decreases.

C. For incompressible fluids the bulk modulus is infinite

D. Shear modulus of material increases with rise in temperature

Correct Answer: D

Solved Example: 91-2-03

For a given material assume, Young's modulus E = 300 GN/m$^2$ and Modulus of rigidity G = 150 GN/m$^2$. Its Bulk modulus K will be: (ISRO RAC 2015)

A. 120 GN/m$^2$

B. 100 GN/m$^2$

C. 200 GN/m$^2$

D. 250 GN/m$^2$

Correct Answer: B

Learning Objectives:

• Understand the difference between elastic and plastic deformation.

Once the forces are no longer applied, the object returns to its original shape. This type of deformation is reversible.
When a sufficient load is applied to a metal or other structural material, it will cause the material to change shape. This change in shape is called deformation. A temporary shape change that is self-reversing after the force is removed, so that the object returns to its original shape, is called elastic deformation. In other words, elastic deformation is a change in shape of a material at low stress that is recoverable after the stress is removed. This type of deformation involves stretching of the bonds, but the atoms do not slip past each other.
This type of deformation is irreversible. However, an object in the plastic deformation range will first have undergone elastic deformation, which is reversible, so the object will return part way to its original shape.

A loose noose, CC0, via Wikimedia Commons

Solved Example: 91-3-01

The property of a body, by virtue of which it tends to regain its original size and shape when the applied force is removed, is known as _________:

A. Elasticity

B. Plasticity

C. Viscosity

D. Rigidity

Correct Answer: A