Damage growth in fibre bundle models with localized load sharing and environmentally-assisted ageing

Abstract

One of the most fundamental models for the complex behaviour of damage accumulation in earth materials is the fibre bundle model. One distinguishes between models with localized load sharing (LLS) and models with equal load sharing (ELS). While ELS models can be treated by mean field theory, the behaviour of LLS models is usually more complicated. Here, we consider a fibre bundle model with LLS where, in addition, we introduce a time scale by incorporating time dependent ageing of the fibres due to the accumulation of damage driven by the locally acting stress in a chemically active environment. If the accumulated damage exceeds a random threshold, the fibres fail. The non-trivial time dependence of the cumulative damage in the system can be attributed to different mechanisms that dominate at different time scales. We include this information into an analytical description of the damage accumulation process and show that the analytical description is in agreement with numerical results. © Published under licence by IOP Publishing Ltd.