Forces and the existence of stresses in invariant continuum mechanics

In an invariant formulation of pth-grade continuum mechanics, forces are defined as elements of the cotangent bundle of the Banach manifold of C ^P embeddings of the body in space. It is shown that forces can be represented by measures which generalize the stresses of continuum mechanics. The mathematical representation procedure makes the restriction of forces to subbodies possible. The local properties of the stress measures are examined. For the case where stresses are given in terms of smooth densities, it is shown that the structure of forces agrees with the form of forces one assumes in the traditional formulation, and the equilibrium differential equations are obtained.