Lateral Strain and Stress Concentration in Liquid Foam Fracture

The rupture of successive films in a layer of liquid foam bubbles, resembling a brittle crack, has been understood theoretically as a self-similar dynamical feature growing out of fluid dynamical principles involving surface tension, nonlinear dissipation, and interfacial instability. The fracture mechanism is so robust that its features (such as a velocity gap) persist in reductive modeling including a continuum limit in one dimension. However, 2D simulations show a systematic dependence of propagation speed and critical fracture stress on the width of the foam channel (its dimension perpendicular to the direction of fracture), indicating the importance of dynamical processes in the lateral direction. Here we extend the continuum theory to two dimensions, uncovering a peculiar, width-dependent mechanism of lateral strain concentration. The resulting fracture dynamics and anisotropic stress fields are compared and contrasted with experiments, 2D simulations, and classical 2D continuum fracture mechanics.