Local versus Equal Load Sharing in the Fiber Bundle Model

Abstract

Fracture is a huge field of research that includes physics, geology, materials science, and engineering. Most approaches are very specialized, but what if we instead want to focus on the big picture to look for general behavior and effects?

The fiber bundle model is a highly simplified model that can still describe many characteristic features of fracture phenomena, and is therefore very useful when investigating fracture processes generally. This thesis studies the equal load sharing (ELS) and local load sharing (LLS) variants of the fiber bundle model.

The holy grail of fracture research is to predict when catastrophic failure will occur. The first two articles develop two different approaches that can potentially be used to predict failure: energy considerations and the distribution of smaller fracture events.

The last two articles describe effects that occur in the LLS model, but are absent in the ELS model. The first is a statistical effect that can cause an apparent stability, where the model looks stable in a region where it is unstable. The second is a shielding effect that protects weak fibers at the expense of stronger ones. This effect can, surprisingly, make the LLS model – which contains local stress enhancement at the edges of cracks – more stable than the ELS model.