Schmid's law

In materials science, Schmid's law (also Schmid factor) describes the slip plane and the slip direction of a stressed material, which can resolve the most shear stress.

Schmid's Law states that the critically resolved shear stress ($τ$) is equal to the stress applied to the material ($σ$) multiplied by the cosine of the angle with the vector normal to the glide plane ($φ$) and the cosine of the angle with the glide direction ($λ$). Which can be expressed as:


 * $$ \tau = m \sigma$$

where $m$ is known as the Schmid factor


 * $$m = \cos(\phi) \cos(\lambda)$$

Both factors $τ$ and $σ$ are measured in stress units, which is calculated the same way as pressure (force divided by area). $φ$ and $λ$ are angles.

The factor is named after Erich Schmid who coauthored a book with Walter Boas introducing the concept in 1935.