# Elastic moduli (summery)

**ELASTIC MODULI**

Elastic moduli are the properties of a material that determine how it deforms in response to an external force. When an external force is applied to a solid, the atoms in the solid are displaced from their original positions. If the force is small enough, the atoms will return to their original positions when the force is removed. This property is called elasticity.

The elastic moduli of a solid are measured by the amount of deformation that occurs for a given amount of force. The three main elastic moduli are:

· **Young's modulus**: Young's modulus measures the resistance of a solid to longitudinal deformation, such as stretching or compressing.

· ** ****Shear modulus: **Shear modulus measures the resistance of a solid to transverse deformation, such as twisting or bending.

· **Bulk modulus:** Bulk modulus measures the resistance of a solid to uniform compression or expansion.

Elastic moduli are important for a variety of applications, including the design of structures, machines, and materials. For example, Young's modulus is used to design bridges and buildings so that they can withstand the weight of traffic and other loads. Shear modulus is used to design aircraft wings and other structures that are subjected to bending forces. Bulk modulus is used to design submarines and other deep-sea vessels so that they can withstand the high pressures of the deep ocean.

**Examples of elastic moduli**

The following table shows some examples of elastic moduli for common materials:

Material |
Young's modulus (GPa) |
Shear modulus (GPa) |
Bulk modulus (GPa) |

Steel |
200 |
79 |
160 |

Aluminum |
70 |
26 |
70 |

Copper |
110 |
42 |
130 |

Concrete |
25 |
10 |
18 |

Rubber |
0.001 |
0.0005 |
0.001 |

**Factors that affect elastic moduli**

The elastic moduli of a material depend on a number of factors, including:

· **Atomic structure**: The atomic structure of a material determines how strongly the atoms are bonded together. Materials with stronger bonds have higher elastic moduli.

· **Crystal structure: **The crystal structure of a material determines how the atoms are arranged in space. Materials with a more ordered crystal structure have higher elastic moduli.

· **Temperature:** The temperature of a material can affect its elastic moduli. In general, the elastic moduli of most materials decrease with increasing temperature.

**Applications of elastic moduli**

Elastic moduli are used in a variety of applications, including:-

· **Design of structures and machines**: Elastic moduli are used to design structures and machines so that they can withstand the loads and forces that they will be subjected to.

· ** ****Selection of materials:** Elastic moduli are used to select materials for specific applications. For example, materials with high elastic moduli are often used for structural applications, while materials with low elastic moduli are often used for vibration-damping applications.

· ** ****Testing of materials**: Elastic moduli can be used to test the quality and strength of materials. For example, Young's modulus of a material can be measured to determine its yield strength and ultimate strength.