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Neuber type methods are widely used to predict the local stress-strain behaviour
at notch root in specimens or industrial components. Some limitations of these
methods are pointed out in the present paper, especially when the global loading is
multiaxial and/or random. A fully new approach is then presented: it introduces a
phenomenological model describing the development of residual stresses that can
be calibrated by reference to Eshelby’s type approaches. A tensorial variable is used
for this purpose. Its evolution rule allows us to represent the stress redistribution at
the surface of the component. Isotropic and anisotropic constitutive equations are
accepted for the description of the material behaviour. It has been successfully used
for several complex situations (cyclic, multiaxial, random loadings).