Cauchy's stress theorem

Here we have Cauchy's theorem: The stress vector t can be written as the vector dot product of the stress tensor, sigma, and the unit vector normal to the surface, n. Whereas t depends on n, sigma does not. Sigma is a function only of position in the elastic body.

However, being a symmetric tensor (defined in the next blog), sigma also requires six numbers to specify - six of the nine components of the tensor.

So while a vector has only three components, a tensor has as many as nine (some of the components may be the same, as we'll see in the next blog).

This formula for Cauchy's theorem is in vector notation, a shorthand form which can be understood by writing it out in matrix form, which I'll add to the next post.