Category: Physics

Summary: Finding how much weakening of one module is needed before the softest mode of a braced modular spring network collapses onto that weakest module.

Mechanical networks can localize their softest deformations onto weak regions, but the amount of heterogeneity required to trigger that capture is not always clear. This experiment asks when a single weakened module in a modular spring network becomes dominant enough to attract the softest mode despite fixed inter-module bracing.

The script builds dense symmetric stiffness operators for modular spring ensembles and uses GPU iterative deepening to locate the weakening threshold. By tracking the softest mode itself, it measures when the network stops sharing compliance across modules and instead concentrates deformation in the weakest one.

That makes the project useful as a structural localization study for modular metamaterials. It targets weakest-module capture directly, which is different from asking only when the whole network becomes softer on average.

Method: GPU dense symmetric eigensolves with iterative deepening and bisection on module-specific weakening in modular stiffness matrices.

What is measured: Critical weakening threshold, localization of the softest mode, stiffness-spectrum changes, and bracket width.