Cracks in random brittle solids: From fiber bundles to continuum mechanics

TL;DR

This paper introduces a soft membrane fiber bundle model to better understand fracture mechanics in brittle solids, connecting discrete fiber models with continuum crack propagation theories.

Contribution

It presents a novel fiber bundle variant with membrane load transfer, bridging discrete models and continuum mechanics for fracture analysis.

Findings

Derived an equivalent toughness for the fiber bundle model.

Connected the model to crack front propagation and depinning phenomena.

Provided insights into nucleation of critical defects in brittle solids.

Abstract

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.