Mechanics of materials
Stresses in a material cause deformations. A material which behaves itself according to Hooke's law, shows a linear behaviour between the applied stresses and its deformation. The strain is calculated by dividing the internal stresses by the elasticitymodulus of the material. The ratio in which the material deforms in the longitudinal and transversal direction is specified by the Poisson ratio.
Material which is stretched with respect to its equilibrium position contains energy. The strain energy density can be calculated.

An axle to which a moment is applied is subjected to torsion. The torque causes an angle of twist in the material. The angle of twist is proportional to the magnitude of the torque and the length of the axle. It is inversely proportional to the polair moment of inertia and the elasticity modulus of the material.

Both the shear force diagram and the moment diagram are used to obtain the state of stress of a material element. The integration method is used to obtain the deformations. Those deformations consist of rotations and translations. More complex problems can be solved by splitting the system in subsystems, calculating the deformations caused by the individual forces and add them according to the superposition theorem.

Stress & strain