Finite deformations of elastic–plastic filamentary networks

Finite elastic–plastic deformation of a thin sheet formed by several families of perfectly flexible extensible fibers is described using an idealized theory in which the fibers are assumed to be continuously distributed to form a surface. The constitutive properties of the surface are deduced directly from those of the constituent fibers. The equilibrium equations are cast in rate form and associated rate potentials are derived. Physically plausible sufficient conditions for the existence of an exact dual extremum principle are proposed and used to prove uniqueness of solutions. Yielding and plastic flow criteria for individual fibers are given in a strain-space setting and adapted to model the elastic–plastic response of the sheet as a whole.