# 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?

• Are you sure these equations are correct? If $\varepsilon$ is Green's strain, then the first equation is $ε_x=\frac{du}{dx}+\frac{1}{2}[(\frac{du}{dx})^2 + (\frac{dv}{dx})^2]$, and the second is likewise. source: the equation after "This could be written more explicitly as" Commented Nov 22, 2019 at 13:08

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".