Load capacity of bodies

For the stress analysis in a plastic body ΩΩ, we prove that there exists a maximal positive number C, the load capacity ratio  , such that the body will not collapse under any external traction field tt bounded by CY0CY0, where Y0Y0 is the yield stress. The load capacity ratio depends only on the geometry of the body and is given by1C=supw∈LD(Ω)D∫∂Ω|w|dA∫Ω|ε(w)|dV=∥γD∥.Here, LD(Ω)DLD(Ω)D is the space of incompressible vector fields ww for which the corresponding linear strains ε(w)ε(w) are assumed to be integrable and γDγD is the trace mapping assigning the boundary value γD(w)γD(w) to any w∈LD(Ω)Dw∈LD(Ω)D.