Network-like propagation of cell-level stress in random foams

TL;DR

This study investigates how cell-level stress propagates in random foams under shear, revealing network-like stress release domains and non-local cooperative cell rearrangements that influence foam rheology.

Contribution

It introduces a novel analysis of stress propagation in foams, showing network-like stress release domains and their role in foam rheology during shear deformation.

Findings

Stress release domains are network-like and highly non-local.

T1 cascades sustain the foam's yield-stress plateau.

Cell shape and stress anisotropy are quantified by the scalar measure Q.

Abstract

Quasistatic simple shearing flow of random monodisperse soap froth is investigated by analyzing Surface Evolver simulations of spatially periodic foams. Elastic-plastic behavior is caused by irreversible topological rearrangements (T1s) that occur when Plateau's laws are violated; the first T1s occur at the elastic limit and at large strains frequent cascades of T1s, composed of one or more individual T1s, sustain the yield-stress plateau. The stress and shape anisotropy of individual cells is quantified by $Q$, a scalar measure derived from the interface tensor that gauges each cell's contribution to the global stress. During each T1 cascade, the connected set of cells with decreasing $Q$, called the \textit{stress release domain}, is network-like and highly non-local. Geometrically, the network-like nature of the stress release domains is corroborated through morphological analysis using the Euler characteristic. The stress release domain is distinctly different from the set of cells that change topology during a T1 cascade. Our results highlight the unique rheological behavior of foams, where complex large-scale cooperative rearrangements of foam cells are observed as a consequence of distinctly local events.