Effect of localized loading on failure threshold of fiber bundles

Abstract

We investigate the global failure threshold of an interconnected set of elements, when a finite fraction of the elements initially share an externally applied load. The study is done under the framework of random fiber bundle model, where the fibers are linear elastic objects attached between two plates. The failure threshold of the system varies non-monotonically with the fraction of the system on which the load is applied initially, provided the load sharing mechanism following a local failure is sufficiently wide. In this case, there exists a finite value for the initial loading fraction, for which the damage on the system will be maximum, or in other words the global failure threshold will be minimum for a finite value of the initial loading fraction. This particular value of initial loading fraction, however, goes to zero when the load sharing is sufficiently local. Such crossover behavior, seen for both one and two dimensional versions of the model, can give very useful information about stability of interconnected systems with random failure thresholds.

Survivability of Suddenly Loaded Arrays of Micropillars

“…The local loads from these failing pillars are transferred to ones that remain intact. It turns out that the ultimate strength of the system crucially depends on how such a transfer happens [ 15 , 16 , 17 ], what the topology of interconnections among components is [ 18 ], what the loading conditions are [ 19 , 20 ], and whether the loading is applied step-wise, suddenly [ 21 ] or cyclically [ 22 , 23 ]. This means that a given ensemble of interconnected components, working together along with an established rule of load transfer between failed and intact components, may either sustain an externally applied load or become entirely destroyed if an unsuitable rule governs the load transfer or interconnections switch to unfavourable topology [ 18 , 24 ].…”