A HOMOGENIZATION METHOD FOR STIFFNESS CHARACTERISTICS OF CEMENT PASTE UNDER VISCOELASTIC BEHAVIOR
DOI:
https://doi.org/10.36773/1818-1112-2024-135-3-38-42Keywords:
cement paste, viscoelasticity, homogenization, solidification theory, FEAAbstract
The microstructure of cement paste is extremely complex and heterogeneous, consists of randomly distributed phases with an arbitrary geometry, formed during the hydration process. The key phase of cement paste – calcium silicate hydrate exhibits distinct viscoelastic behavior causing creep in cement-based composites. These reasons make the problem of evaluating effective stiffness characteristics rather difficult, since stress-strain relationships under viscoelastic behavior are usually described using the principle of aging-time superposition, represented in the form of the Stiltes integral, which has not an analytical solution.
Existing approaches to solving this problem involve two principles: the Laplace–Carson transform and the effective medium theory. This makes possible to find a solution for the evaluate effective stiffness characteristics under viscoelastic behavior, but only for a limited geometric shape of inclusions in the form of an ellipsoid and its related shapes. However, such shapes are not fully matching the real geometric shape of most phases of cement paste, especially for capillary porosity.
The paper presents one more approach to solving the problem of effective stiffness characteristics of cement paste based on a FEA homogenization facilitates to evaluate effective stiffness properties for an arbitrary phase geometry, through introducing into the variational formulation the numerical inversion of the Stieltjes integral describing its viscoelastic behaviour. In addition, this approach best implements the solidification mechanism for the history of the aging stress-strain relation during the hydration process.
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