Generalized stress concentration factors

The classical stress concentration factor is regarded as the ratio between the maximal value of the stress in a body and the maximal value of the applied force for a given distribution of material properties. An optimal stress concentration factor is defined as the lowest stress concentration factor if we allow any stress field that is in equilibrium with the given load. The generalized stress concentration factor, a purely geometric property of a body, is the maximal optimal stress concentration factor for any applied force. We show that the generalized stress concentration factor is equal to the norm of an extension mapping of Sobolev functions.