Anisotropic Yield Surfaces Based on Elastic Projection Operators

Abstract

Although most materials are anisotropic to some extent, most yield surfaces are either chosen to be isotropic or to be a smooth anisotropic surface with no connection to the elastic anisotropic features. Here, the elastic projection operators obtained from the spectral decomposition of the elasticity tensor are used to define anisotropic yield surfaces with a yield surface defined for each of the projection operators. The advantages of the approach are (1) plastic deformation modes are associated with the elastic anisotropic behavior, (2) the spectral decomposition of the tangent tensor is readily available for a bifurcation analysis, (3) the composite yield surface has vertices which are thought to be important for predicting plastic buckling, and (4) the contributions to plastic deformations from each yield surface are uncoupled. The result is a theory that is actually quite simple but yet reflects some of the observed features for materials to yield in specific modes.