Young's modulus, also known as longitudinal modulus of elasticity or elastic modulus, is a mechanical property of materials that describes their stiffness or resistance to elastic deformation when an external force is applied.
Young's modulus is represented by the letter "E" and is defined as the ratio between stress (force applied per unit area) and strain (relative change in original length) in the longitudinal direction of the material.
The Young's modulus concept is valid only within the elastic range of deformation of a material, that is, when the deformation is reversible and the material can return to its original shape once the applied force is removed.
Formula
Mathematically, it is expressed as follows:
E = σ / ε
Where:

E: Young's modulus (in pascals, Pa)

σ: Effort (in pascals, Pa)

ε: Strain (unitless)
What does a high or low Young's modulus value mean?
Young's modulus is a measure of the stiffness of the material.
The higher the Young's modulus, the stiffer the material and the more resistant it is to elastic deformation.
On the other hand, the lower the value, the more flexible the material will be and will deform more easily under the same applied force.
Relation to Hooke's law
There is a relationship between Hooke's law and Young's modulus (E): Young's modulus is the proportionality constant that relates stress and strain in an elastic material.
Relation to elastic limit
The elastic limit is the maximum stress or stress that a material can withstand without undergoing permanent or plastic deformation. It is the point at which the material stops behaving elastically and begins to deform permanently. That is, above the elastic limit, the material will not return to its original shape once the applied load is removed.
On the other hand, Young's modulus is a measure of the stiffness or resistance to elastic deformation of a material. However, it is only valid while the deformation is reversible.
Therefore, when a material deforms, if it exceeds its elastic limit, the Young's modulus is no longer applicable, the material can be permanently deformed and its behavior is governed by different laws, such as rigidity modulus or plasticity.
Young's modulus applications
Young's modulus, as a mechanical property of materials, has several applications and uses in different fields of engineering and science. Here are some of the main applications of Young's modulus:

Structural Design: Allows you to calculate and predict how a material will deform under applied loads, which helps determine the strength and stability of structures.

Material Selection: Allows you to compare and evaluate the stiffness and strength of different materials for specific applications.

Finite Element Analysis: In finite element analysis, a computational modeling technique used to simulate the behavior of complex structures, Young's modulus is used to define the elastic properties of materials in numerical models.

Deformation prediction: Young's modulus is used to predict deformations in materials and structures due to applied loads. This is useful to evaluate the elastic deformation and the behavior of materials subjected to different loading conditions.

Stress and Stress Calculations: Also used to determine the relationship between the force applied to a material and the resulting deformation using Hooke's Law. This is essential to understand the behavior of materials and ensure structural integrity.

Material Development: This property is useful in the development of new materials with specific properties.
Examples
Below is a table with examples of some materials with a brief description of each material and its respective Young's modulus:
Material  Description  Young's Modulus (GPa) 

Structural steel 
Iron alloy with carbon and other elements, used in the construction of structures. 
190210 
Aluminum 
Light metal with high strength and low density, used in various industrial applications. 
70 
Glass 
Amorphous, transparent and fragile solid material, used in windows and containers, among others. 
6090 
Wood (construction) 
Natural material composed of plant tissue, used in construction and carpentry. 
1020 
Concrete 
Mixture of cement, aggregates and water, used in the construction of structures and pavements. 
2540 
polymers 
Organic materials composed of molecular chains, widely used in various products and applications. 
Various MPa  GPa 
Copper 
A metal that conducts heat and electricity, used in cables, pipes, and electronic components. 
110130 
Titanium 
A lightweight, corrosionresistant metal used in aerospace and medical applications. 
100120 
Granite 
Hard and resistant igneous rock, used in construction and architectural finishes. 
5080 
Asphalt 
Viscous and sticky material used in the construction of roads and pavements. 
15 
Gum (rubber) 
Elastic and flexible material, used in tires, seals and various products. 
0.010.1 
Ice 
Solid state water, used in applications such as food storage and ice sports. 
915 
Diamond 
Crystalline form of carbon, known for its extreme hardness, used in jewelry and tools. 
10501220 
ceramics (general) 
Nonmetallic inorganic materials, widely used in industry and construction. 
100400 
Plexiglass (PMMA) 
Transparent and resistant plastic material, used in applications such as windows and sheets. 
2.73.5 
Stainless steel 
Iron alloy with chromium and other elements, resistant to corrosion, used in various industrial and structural applications. 
190210 
Carbon fiber 
Material composed of intertwined carbon fibers, known for its high strength and low weight. 
230630 