Bifurcation and creep effects in a viscoelastic non-local damageable continuum

The conditions for localization in a material described by a non-local damage-based constitutive relation coupled with a Kelvin type creep relation are derived in a closed form. The inception of a localized mode is considered as a bifurcation into Preprint submitted to Elsevier Science 15 February 2006 a harmonic mode. The criterion of bifurcation is reduced to the classical form of singularity of a pseudo acoustic tensor ; this tensor involves the ratio between the elasto-damage strain and the total one at the inception of localization and the wavelength of the bifurcation mode through the Fourier transform of the weight function used in the definition of non-local damage. A geometrical approach was adopted to analyze localization. The proposed coupled model preserves the properties of localization limiters; the minimum wavelength of the localization modes cannot be zero. This wavelength increases when the material parameter α (0 ≤ α ≤ 1), which is the fraction of creep strain entering into the evolution of damage, is decreasing. Moreover, the normal n to the localization band depends only upon the elastodamage state of strain. Under some conditions on the growth of the yield function of damage, the wavelength decreases as the creep strain increases. The proposed model fails to predict creep rate-effects when damage is supposed, as it is common practice, to be driven solely from the elastic release energy (α = 0).