LOCALIZATION ANALYSIS VIA A GEOMETRICAL METHOD

A geometrical technique is proposed in order to solve explicitly the c ritical conditions at localization for a quite general constitutive be haviour with isotropic elastic properties. These critical conditions a re shown to be closely related to the spectral properties (eigenvalues and eigenvectors) of the sum and difference of two tensors describing the inelastic effects. When these two tensors are coaxial, it is show n that the normal to a potential localization plane always lies in one of their principal planes. It is also demonstrated that, depending on the constitutive behaviour and the loading conditions, several expres sions for the critical hardening modulus at localization are available and their respective domain of validity well defined. The roles and i nteractions of both both deviatoric and hydrostatic non-associativitie s in the critical conditions of localization are emphasized.