Creep damage modelling for quasi-brittle materials

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 or rock behaviour. Understanding the interaction between these two phenomena is important to design reliable civil engineering structures subjected to high level loading during a long time. The aim of this paper is to develop a simple time-dependent softening model applied to quasi-brittle materials such as rock or concrete. A three-dimensional constitutive visco-damage model describes 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. A general material stability analysis is proposed in case of uniaxial monotonic loading. 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. Consequently, this model is able to predict creep failure for various stress level. Conversely, for low-sustained load, the motion asymptotically converges towards an equilibrium configuration, also called equilibrium curve. As for endochronic models, no initial threshold is assumed. Nevertheless, an apparent elastic domain is identified for constant strain rate tests, which reveals the competition between the internal kinetics of damage and the strain rate imposed on the material.