FATIGUE AND CYCLIC LOADINGS IN CONCRETE MATERIALS

In this work, a 3D visco-elasto-plastic damage model is developed to describe the creep and fatigue failure mechanism of plain concrete. The physical micro-structural degradation due to fatigue is interpreted as a gradual reduction of size of the elastic domain as the number of cycle increases. The fatigue behaviour is driven by an internal variable based on the amount of extension experienced by the material. Similarly, the creep failure is explained by an excessive accumulation of plastic strains, until failure. The modeling aspect related to plasticity is based on the pressure-dependent Menétrey-Willam plastic surface, extended to include a scalar damage variable accounting for the reduction in size of the elastic domain as concrete undergoes damage. The modeling aspect related to damage, on the other side, is inspired by the formulation of the isotropic damage by Mazars. Specifically, in the proposed formulation a stress-dependent damage variable is introduced to account for crack closure effects. The long-term effects are taken into account via the B3 creep model of Bažant and Baweja, where aging is considered through the solidification theory. The fatigue degradation is considered by an extension of the modified Ménétrey- Willam yield function to include a fatigue softening function that represents the effects of the cumulative and irreversible micro-structural degradation as the number of cycle increases. Some challenging aspects related to the numerical implementation and interaction of the afore-mentioned models are addressed, amongst which the choice of a suitable loading scheme for the numerical implementation of the coupled model, and the mathematical derivation of the visco-elasto-plastic tangent operator. A ”return to apex” procedure is described to account for situations in which the return-mapping vector does not intersect the yield surface. Each component of the model is calibrated and validated against experimental results. In particular, the performances of the constitutive model are evaluated considering multi-axial stress conditions in the monotonic and fatigue regimes. Then, the numerical simulations have been extended to the meso-scale. Interestingly, by studying the interaction between the aggregates and the cement matrix at the meso-scale, it comes out that the coupled model is able to account for non-linear creep or tertiary stage creep, which is not included in the B3 model of Bažant and Baweja, and without considering additional parameters related to creep. Furthermore, it can reproduce the experimental three-stage pattern of the fatigue curves, for specimen subjected to multi-axial stress conditions The fatigue model is then coupled with a visco-plastic model to account for inelastic and creep deformations, and with the Mazars damage model to account for stiffness degradation. In the coupled model, the fatigue failure is explained by the progressive accumulation of inelastic strains and the evolution of micro-cracks, as the size of the elastic domain decreases. A random distribution algorithm for the placement and compaction of polyhedral shaped aggregates, in agreement with a prescribed gradation curve, is used for the solid modeling of concrete samples at the meso-scale. The effectiveness of the model is discussed based on the juxtaposition of numerical results obtained by the presented model, and experimental ones available in literature. \\