A homogenization-enriched viscodamage model for cement-based material creep

• A viscodamage model based on the concept of pseudo-strains is developed.
• The moduli are estimated in the Laplace–Carson space with the Mori–Tanaka scheme.
• Exact semi-analytical expressions for the moduli are derived in the time space.
• The model is applied to the simulation of a classical cement paste creep test.
• Damage and its evolutions appear to have a small influence on the total strains.

We develop in this study a viscodamage model for cementitious materials based on the concept of pseudo-strains introduced by Schapery [1] coupled with the damage model of Mazars [2]. The pseudo-strains approach allows for reformulation of the initial viscoelastic problem as an equivalent elastic one by using a simple correspondence principle. The viscoelastic model results from a homogenization procedure in which the Mori–Tanaka scheme is applied in the Laplace–Carson space for estimating the effective linear viscoelastic bulk and shear moduli of the material. A composite made of a linear viscoelastic matrix described by a generalized Maxwell model and containing distributed spherical elastic inclusions and pores is adopted as a simplified representation of the material under consideration. One interesting feature of our approach is that exact analytical expressions for both bulk and shear moduli in the time space are derived in simple cases where a limited number of Maxwell chains are involved to describe the matrix behavior. The evolutions of the damage variable are governed by an equivalent pseudo-strain calculated from the pseudo-strains. The viscodamage model is applied to the simulation of cement paste basic creep tests available in the literature. After a proper identification of the parameters, an analysis of the results obtained with moderate creep loading reveals that the total strains evolutions are due mainly to the viscous characteristics of the material and to a lesser extent to the damage growth. The effects of the pore volume fraction of the material and of high load-levels leading to the specimen rupture on the creep response are further investigated and discussed.