# Modelling of Concrete Subjected to Cyclic Loading

[Doktorsavhandling]

The infrastructure of today depends heavily on concrete structures. Most of these structures are subjected to repeated loads, known as fatigue or cyclic loads: the loads weaken the structure. As this phenomenon is of high cost to society, a deeper understanding of the deterioration process of cyclic loading would be beneficial. The aim of this thesis is to add to the knowledge of the deterioration phenomenon and to develop models that can describe the response of concrete subjected to cyclic loading. In analyses of structures of today, finite element modelling is gaining ground and is being used more frequently in research and structural design. The investigations here use only the finite element method. Many structures incorporate details that are subjected to complicated loading, which results in complex crack patterns. A suitable tool for describing these crack patterns is anisotropic damage material models. However, anisotropic models are difficult to implement and are often computationally inefficient. One of the investigations in this thesis aims to find out what makes the anisotropic formulation suitable for complex crack patterns. This is done by implementing a model which can control the amount of coupling between volumetric- and deviatoric strains. It was found that this coupling is essential for describing complex crack patterns. To deepen the understanding of concrete subjected to cyclic loading, the phenomenon was investigated on the meso-scale level. An interface model was developed and applied to a three phase representation of concrete that incorporates: aggregates, cement paste, and interfacial zones around the aggregate. The model in itself does not yield cyclic behaviour, i.e. no hysteresis loops were generated at the constitutive level. Instead, the cyclic response was generated by the meso-structure. It was found that the interfacial transition zones are crucial in amount and strength. Concrete subjected to cyclic loading was also investigated on the macro-level, with the ambition to describe the response of concrete structures subjected to cyclic loading. Two investigations were made: one aims to describe cyclic response in tension and the other aims to cover tension and the transition to reasonable high states of compression. The investigations are based on the theory of plasticity and damage mechanics, which are combined in both a serial and a parallel fashion. In the serial configuration the nominal stress is computed by adding the damage to the effective stress; for the parallel configuration, the damage stress and the effective stress are evaluated separately for the same strain and then added to yield the nominal stress. Furthermore, both models use two yield surfaces to describe the hysteresis loops. The result of the analyses show an overall agreement with experimental observations.

**Nyckelord: **concrete, plasticity, damage, cyclic loading, energy dissipation

Denna post skapades 2009-03-05. Senast ändrad 2014-11-10.

CPL Pubid: 91098