Deformation (engineering)

In engineering, deformation is the change in the size or shape of an object. This process is vital for understanding how structures and machines respond to forces. When forces act on a material, the object may stretch, squash, or bend. If the change in size is so small that it cannot be measured, the object is called rigid.

To study this, engineers distinguish between displacement and deformation. Displacement refers to a change in position, such as a whole body moving or rotating. Deformation is different because it involves changes in the relative positions of internal points within the object. This internal change is known as strain.

Deformation occurs through specific mechanical processes. When an external force, or stress, is applied, it acts on the internal structure of the material. This stress can cause the material to change its dimensions. For example, compressive stress can shorten an object while causing it to bulge outward laterally.

This happens because the material is strong enough to avoid cracking, but not strong enough to resist the load without changing shape. Internal forces at right angles to the deformation work to resist the applied load. The relationship between the applied stress and the resulting strain is a core focus of structural analysis and the field of strength of materials.

Materials generally undergo two distinct types of deformation: elastic and plastic. Elastic deformation is temporary and recoverable. This occurs when the applied stress does not exceed the energy required to break molecular bonds. Once the stress is removed, the material returns to its original shape.

In many metals and crystals, this relationship is linear and follows Hooke's law. Hooke's law states that stress is equal to the elastic modulus, or Young's modulus, multiplied by the strain. The area under this elastic region is referred to as resilience.

If the stress continues past a specific threshold called the yield point, plastic deformation begins. Plastic deformation is permanent and irreversible. Even after the applied forces are removed, the object remains distorted.

Some materials, like soft thermoplastics, copper, and gold, have large plastic deformation ranges. These are described as ductile materials. Conversely, materials like ceramics, glass, and cast iron have very minimal plastic deformation ranges. These materials are considered brittle because they tend to fracture rather than change shape permanently.

When a ductile material is pulled under tensile stress, it follows a specific sequence of stages. First, it undergoes elastic deformation, followed by a period of strain hardening. During strain hardening, the material actually becomes stronger due to the movement of atomic dislocations. Eventually, the material reaches its ultimate tensile strength. After this point, it enters the necking region. Necking is characterized by a rapid reduction in the cross-sectional area of the specimen.

Finally, the process ends when the material undergoes a fracture, also known as a rupture.

Engineers use different mathematical models to measure these changes. Engineering stress and strain are approximations used when the change in size is considered negligible. These calculations assume the cross-sectional area of the object remains constant. However, in reality, the area decreases as the object deforms. To account for this, scientists use true stress and true strain. True stress is calculated using the instantaneous cross-sectional area and length of the object.

In a tension test, the true stress is larger than the engineering stress, while the true strain is less than the engineering strain.

Understanding these principles is essential for preventing structural failure. Failure can occur in several ways depending on the material and the force. In brittle materials, failure usually happens through sudden rupture. In ductile materials, failure can occur through yielding. For long, slender elements like columns, failure often occurs through buckling. Buckling happens when an increase in compressive force causes the structure to bend at a stress level lower than its actual compressive strength.

By analyzing these stress-strain curves, engineers ensure that buildings, bridges, and machines can safely withstand the loads they are designed to carry.