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

The conditions for localization in a material described by a non-local damage-basedconstitutive relation coupled with a Kelvin type creep relation are derived in aclosed form. The inception of a localized mode is considered as a bifurcation into a harmonic mode. The criterion of bifurcation is reduced to the classical form of singu-larity of a pseudo acoustic tensor ; this tensor involves the elasto-damage strain andthe total one at the inception of localization and the wavelength of the bifurcationmode through the Fourier transform of the weight function used in the definitionof non-local damage. A geometrical approach was adopted to analyze localizationfor loading paths such that the elastic strain tensor is a fraction of the total straintensor. Such loading paths are those for which changes in the loading state occuronly under time-independent processes (negligible creep strain during these changesof the stress state) and the uniaxial loading. The proposed coupled model preservesthe properties of localization limiters; the minimum wavelength of the localizationmodes cannot be zero. The critical wavelength which is related to the width of thelocalization zone increases when the material parameter α (0 ≤ α ≤ 1), which is thefraction of creep strain entering into the evolution of damage, is decreasing. Under acertain condition on the growth of the yield function of damage and the initial stateof deformation the critical wavelength decreases as the creep effect (creep strains)increases in accordance with experimental observations - increase of brittleness dueto creep. In uniaxial tension and for an experimentally determined yield function ofconcrete this condition is fullfilled whenever the initial elasto-damage strain is in aregion near the first occurence of localization.