A theoretical model for the description of static and creep-induced damage in brittle materials under non-proportional loading

A theoretical model suitable for the description of the time evolution of mechanical damage in concrete and masonry structures is presented. Starting from a recent proposal of the authors, based on the incorporation of damage variables in the rheological Burger’s model, a numerical model is obtained capable of accounting for creep-induced damage phenomena that affect the mechanical properties of the material. The model is extended to the three-dimensional case, by making use of damage variables of tensorial nature. A peculiar feature of the model is that the principal direction of damage, which are somehow associated to the presence of “cracks” in the material, do not rotate as the stress history evolves in time, leading to a sort of non-rotating smeared-crack model. The capabilities of the model in describing the mechanical response of material elements subjected to non-proportional loading are illustrated. Also, some numerical examples show the possibility to capture the three phases of creep peculiar of brittle materials subjected to heavy persistent stresses, namely primary, secondary and tertiary creep. In the present version, the model is found to be appropriate for rubble-like masonry and concrete, which can be macroscopically assumed to be isotropic in the undamaged state.