DISCONTINUOUS BIFURCATION STATES FOR ASSOCIATED SMOOTH ELASTICITY ANDDAMAGE WITH ISOTROPIC ELASTICITY

For many constitutive equations the tangent tensor consists of a rank one modification to the isotropic elasticity tensor with a total of tw o elasticity parameters and one parameter describing the current state of inelasticity. For small deformations, general expressions are deri ved for the loss of ellipticity, the corresponding normal to the bifur cation plane and the mode of discontinuous bifurcation for the velocit y gradient. If the principal basis of an evolution tensor is used, the current stress or strain state is characterized by two additional par ameters. The small number of material and state parameters makes it fe asible to use contour plots to illustrate all possible combinations th at can provide a discontinuous bifurcation. These bifurcation maps can be used to illustrate the bifurcation properties of a particular plas ticity or continuum damage constitutive model. Conversely, the bifurca tion maps can be used in conjunction with experimental data on bifurca tion features to assist in the development of constitutive equations t hat provide the correct failure criterion for a given material under a ll possible stress paths.