Stress and strain

To describe deformations, we need a cause-effect relationship. The cause of the deformation is called stress, whilst the measure of the resulting deformation, usually compared to the original value of a dimension of the object, is called strain.

The greater the stress, the greater the strain that it causes. Within the so-called limit of proportionality, the strain is directly proportional to the stress. The constant of proportionality between them is called an elastic modulus. It is a material constant, and its definition depends on the type of deformation.

In the figure above, \(\epsilon\) denotes the strain and \(\sigma\) is the stress. We can observe that up to the limit of proportionality, there is a linear relationship between stress and strain. Above this is the plastic region, where increasing strains can be achieved with less and less increase in stress, up to a point where maintaining the same stress can cause the strain to keep increasing. In the yield region, straining the object further actually requires less stress. Finally, the object breaks (rupture).