This paper presents a new constitutive model describing the mechanical behavior of concrete at early age and beyond. This model, entitled solidification–microprestress–microplane (SMM) model, amalgamates the microplane model and the solidification–microprestress theory and takes into account all the most\ud
significant aspects of concrete behavior, such as creep, shrinkage, thermal deformation, and cracking starting from the initial stages of curing up to several years of age. Age-dependent viscoelastic behavior under variable hygro–thermal conditions is described according to the solidification–microprestress theory.\ud
Cracking/damage behavior is modeled through an age-dependent microplane model, in which the model parameters are assumed to be dependent on an aging variable evolving with the extent of early-age chemical reactions (hydration, silica-fume reaction, etc.) and temperature. Calibration and validation\ud
of the model is performed by the numerical simulations of the age-dependent response of sealed and unsealed specimens subject to a variety of loading conditions and/or drying. Comparison with experimental data shows that the SMM model can reproduce well the interplay of shrinkage, creep, and cracking\ud
phenomena during curing and drying
The paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials, i.e., materials for which the yield limits soften as a function of the total strain. Both plasticity and damage models are considered. It is verified analytically in a simple way that the nonlocal integral-type model with degrading yield limit depending on the total strain works correctly if and only one adopts an unconventional nonlocal formulation introduced in 1994 by Vermeer and Brinkgreve (and in 1996 by Planas, and by Stro¨mberg and Ristinmaa), which is here called, for the sake of brevity, over-nonlocal because it uses
a linear combination of local and nonlocal variables in which a negative weight imposed on the local variable is compensated
by assigning to the nonlocal variable weight greater than 1 (this is equivalent to a nonlocal variable with a smooth positive weight function of total weight greater than 1, normalized by superposing a negative delta-function spike at the center). The spectral approach readily confirms that the nonlocal integral-type generalization of softening plasticity with an additive format gives correct localization properties only if an over-nonlocal formulation is adopted. By contrast, the nonlocal integral-type generalization of softening plasticity with a multiplicative format provides realistic localization behavior, just like the nonlocal integral-type damage model, and thus does not necessitate an over-nonlocal formulation. The localization behavior of explicit and implicit gradient-type models is also analyzed. A simple
analysis shows that plasticity and damage models with gradient-type localization limiter, whether explicit or implicit,
have very different localization behaviors
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