Stress and Strain
Stress and Strain are two of the most important parameters in structural mechanics and therefore they play a paramount role in structural design of aircrafts. Aircrafts undergo different types of loading ( air loads, inertia loads, landing, taxi, powerplant,etc)[3]. These loads in turn create different types of stresses, which causes strains at different locations of an aircraft structure. Stress beyond permissible limit will cause failure of the aircraft structure. So, it is very important to do an accurate stress-strain analysis while designing an aircraft.

Stress

Definition

Augustin-Louis Cauchy introduced the concept of stress in continuum mechanics around 1822. It is a measure of the average internal force exerted per unit area of a surface within a deformable body (Figure 1.1). There are two types of forces which cause stresses in a deformable body. One is surface force, acting on the surface of the body and the other one is body force, acting on each element of the body. For many practical applications body forces are negligible compared to the surface forces. So while defining stress, we use mainly surface forces [2]

Types

As shown in figure 1.2, the resultant stress Tn can be resolved in two components. Based on the orientation of the two components stress can be divided into two types, normal stress and shear stress.

Normal Stress

Shear Stress

Strain

Definition

When a body is subjected to system of forces, individual points of the body, in general will move. This movement is known as displacement, which is a vector quantity. If the displacement of different points of the body are different, each of them can be represented by its own vector. So, motion of a body experiencing a system of forces can be considered as a sum of two parts, (1) translation or rotation of the body as a whole, (2) movement of points within the body relative to each other. The first is known as the rigid body motion, which is applicable both the idealized rigid body and real deformable body. The second one known as deformation is a property of real bodies only [2]. Rigid body motion does not produce deformation. 'Strain is the geometrical measure of deformation of a body, representing the relative displacement between particles in that body.

Types

Strain and stress are two inseparable quantities. From the definition strain we can see that, stress is the cause and strain is the outcome. There will be no strain in a material, if there is no stress (i.e. no load) working on it. So, strains have the same classification as stresses, normal strain and shear strain

Normal Strain

Shear Strain