# Is the Young's modulus the same for compressive and tensile test?

I want to know the Young's modulus for a compressive test, but I have just a tensile test. Are they of the same value?

## 2 Answers

For a linear isotropic Hookean material, the Young's modulus of elasticity is the same for compression and tension.

$$E = \frac{\sigma}{\epsilon}$$

where $$E$$ is the Young's modulus, $$\sigma$$ is the normal stress and $$\epsilon$$ is the normal strain.

The equivalence is derived here, for example. Briefly, any smooth energy minimum examined up close looks like a parabola, which is symmetric around the equilibrium point. A parabolic strain energy corresponds to a linear restoring force (corresponding to Hooke's Law) and a constant stiffness in both tension and compression.