Strain is a measure of the change in the length of a material along a particular direction per unit length of the material (such as 0.0001 inch/inch of length). Strain is a unitless or dimensionless quantity, since the length unit appears in both the numerator and the denominator, and they cancel out. So, using the example just given, 0.0001 inch/inch = 0.0001 mm/mm, and so on. The length unit has no effect on the magnitude of the strain. A positive (+) strain indicates elongation of the material, and a negative (-) strain indicates compression.
The following equations describe the relationship between stress (σ) and strain (ε), in a particular common direction. These equations are applicable to isotropic materials loaded within their elastic range and assume that the stress vector and strain vector are collinear. An isotropic material has the same modulus of elasticity and Poisson's ratio for loads applied in any direction. Poisson's ratio is a measure of how much a material deforms laterally when stressed axially.
σ = ε·E
or
ε = σ/E
where E is the Young's Modulus (or elastic modulus) of the material.
Important: The same tensor, equivalent (or von Mises), and principal values that apply to stresses are also available for strains.