On the Validity of Saint Venant’s Principle in Finite Strain Plasticity

Abstract

Diffusion of effects from a local disturbance in a homogeneous stress field is analyzed within the framework of continuum plasticity. An axial rate of decay for the variability of the effects of a nonuniform disturbance imposed on one end of a long circular cylinder is determined as a function of the axial stress (or stretch). The analysis considers constitutive equations corresponding to incompressible, finite strain versions of J2 flow and deformation theories. Both theories result in effects that oscillate and decay exponentially with distance from the imposed disturbance; the rate of decay decreases as the uniaxial tension increases. Deformation theory predicts a larger rate of decay than flow theory except within a small range of stress near the ultimate (necking) load; at necking the rate of decay vanishes.