Self-equilibrated stress fields in a continuous medium

It is proved that the solutions of the static equations of a continuous medium constructed in terms of a stress function are self-equilibrated. From a mathematical point of view, these functions can be treated as the connectivity coefficients of the intrinsic geometry of the medium. It is shown that from a physical point of view, the existence of self-equilibrated stress fields is due to a nonuniform entropy distribution in the medium. As an example, for a circle in polar coordinates and a cylindrical sample, a self-equilibrated stress field and an elastic field compensating for its surface component are constructed and it is shown how to write the equation for the intrinsic geometrical characteristics.