# Compressional Strain Definition

Strain in the x and y directions are defined by the following equations:

$$ε_x=\frac{du}{dx}+\frac{1}{2}[(\frac{du}{dx})^2 + (\frac{du}{dy})^2]$$

$$ε_y=\frac{dv}{dx}+\frac{1}{2}[(\frac{dv}{dx})^2 + (\frac{dv}{dy})^2]$$

My question is when the strain is negative, the first term will be negative and the terms in the square brackets will always be positive. However, this does not occur if the strain is positive, does this mean that the terms in the square brackets need to be directional?

For small (infinitesimal) strains, the second order (squared) terms are negligible compared with $$\partial u/\partial x$$, and are simply ignored. This gives what is commonly called "engineering strain".