Creep failure in concrete as a bifurcation phenomenon

Softening and time-dependence of fracture are two complex and coupled phenomena that have to be taken into account in order to simulate realistic concrete behaviour. Understanding the interaction between these two phenomena is important to design reliable civil engineering structures subjected to high level-loading for a long time. The aim of this paper is to develop a simple time-dependent softening model applied to concrete. Presentation is restricted to compression behaviour. A constitutive viscodamage model describes concrete phenomena like relaxation, creep and rate-dependent loading using a unified framework. The model could be viewed as a generalisation of a time-independent damage model and is based on strong thermodynamical arguments. The determination of the material parameters linked to the proposed constitutive equation results from constant strain rate experiments. Using these parameters values, creep and relaxation numerical tests give satisfactory qualitative responses. Phenomena as creep failure under high-sustained load are explained quite simply within stability theory. Creep failure appears as the manifestation of a bifurcation phenomenon. Conversely, for low-sustained load, the motion asymptotically converges towards an equilibrium configuration. Consequently, this model is able to predict creep failure for various stress levels. Implementation of this theological model in a structural code is envisaged in the future: a non-local approach would be probably necessary in order to simulate objective structural behaviour.