Category: Physics

Summary: Finding how much interior defect softening is needed for the softest mode in a prestressed shell to abandon the boundary and localize on defects.

Mechanical metamaterials can localize soft motion near boundaries, but disorder and defects can compete for that same softest mode. This experiment asks when a shell-confined rescue mode created by prestress is overtaken by an interior defect band that pulls the softest response back into the bulk.

The calculation builds dense symmetric stiffness operators for disordered elastic networks with a prestressed shell and a tunable defect region. It bisects the defect-softening strength across increasing matrix sizes and checks whether the lowest mode remains shell concentrated or becomes defect captured.

That competition matters because boundary stabilization and defect localization are usually studied separately. Here they are forced into the same threshold problem, producing a direct finite-size estimate of when one mechanism defeats the other.

Method: Dense symmetric eigensolve with iterative deepening and bisection on interior defect softening in a prestressed elastic operator.

What is measured: Critical defect-softening threshold, shell-mode mass, defect-mode mass, softest-eigenmode capture statistics, and bracket width.