Mathematical analysis of strain localization

ABSTRACT First it is shown by a simple one-dimensional example that stress-strain laws with softening cannot provide an objective description of response on the structural level. The phenomenon of discontinuous bifurcation from a uniform state is then analyzed in a general threedimensional setting. Localization conditions for isotropic damage models are derived in the general form and then specialized for models with damage driven by equivalent strain dependent on the stored elastic energy, on the maximum principal effective stress, or on the positive part of the strain tensor.