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Modeling of cement hydration in high performance concrete structures with hybrid finite elements. (English) Zbl 1352.74117

Summary: A hybrid finite element formulation is used to model the hygro-thermo-chemical process of cement hydration in high performance concrete. The temperature and the relative humidity fields are directly approximated in the domain of the element using naturally hierarchical bases independent of the mapping used to define its geometry. This added flexibility in modeling implies the independent approximation of the heat and moisture flux fields on the boundary of the element, the typical feature of hybrid finite element formulations. The formulation can be implemented using coarse and, eventually, unstructured meshes, which may contain elements with high aspect ratios, an option that can be advantageously used in the simulation of the casting of concrete structural elements. The resulting solving system is sparse and well suited to adaptive refinement and parallelization. It is solved coupling a trapezoidal time integration rule with an adaptation of the Newton–Raphson method designed to preserve symmetry. The relative performance of the formulation is assessed using a set of testing problems supported by experimental data and results obtained with conventional (conform) finite elements.

MSC:

74F25 Chemical and reactive effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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