Enhanced strength of cyclically preloaded arrays of pillars

Derda, Tomasz; Domański, Zbigniew

doi:10.1007/s00707-020-02708-5

Cited by 3 publications

(5 citation statements)

References 15 publications

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“…In our main problem, however, related to the loading process of the arrays of pillars, this limit is unknown. More precisely, all we know is the probability distribution of the load-capacity-limit, which can be approximated with the help of the Monte Carlo experiments [ 13 ]. Such a change in assumptions needs the extension/modification of the original blackjack-type problem.…”

Section: Blackjack-type Optimal Stopping Problemsmentioning

confidence: 99%

“…For such pillar arrays, the distribution of their carrying capacity (

) was determined with the help of simulation experiments presented in Section 2.3 , as well as described in greater detail in [ 13 , 14 ]. The resulting distribution is displayed in Figure 2 , see the left panel.…”

Section: Optimal Stopping Rules For a Pillar-array Loadingmentioning

confidence: 99%

“…It turns out, that after assembling a given bundle of pillars into an array with a prescribed geometry, the overall strength of such an array depends on the mutual positions of individual pillars. This means that the resulting arrays display non-negligible sample-to-sample fluctuations when subjected to an external load [ 13 , 14 ]. As a consequence, the carrying capacity is a random value known solely through its probability distribution.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

2023

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When random-strength components work as an interconnected parallel system, then its carrying capacity is random as well. In a case where such a multicomponent system is a subject of the stepwise-growing workload, some of its components fail and their loads are taken over by the ones that are intact. When the loading process is continued, the additional loads trigger consecutive failures that degrade the system, eventually leading to a complete failure. If the goal of the system is to carry as much load as possible, then the loading process should be continued, but no longer than until the loading capacity of the whole system is reached. On the other hand, with every additional load step, a failure of the system becomes more probable, as the carrying capacity is random and known solely through its probability distribution. In such cases, the decision on when to cease the loading process is not obvious. We introduce and analyse a minimal model of failure spreading in an array of progressively loaded pillars controlled by a decision-maker who stops the process when a required load is attained. We show how to construct an optimal stopping rule. Under some additional assumptions regarding the adopted loss function, it is argued that the optimal stopping rule is of the threshold type and it significantly depends on the shape of the load-step probability distribution.

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Section: Blackjack-type Optimal Stopping Problemsmentioning

confidence: 99%

“…For such pillar arrays, the distribution of their carrying capacity (

Section: Optimal Stopping Rules For a Pillar-array Loadingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

2023

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“…It turns out that after carefully tuned low-amplitude cyclic loading, a single sub-micron pillar obtains a significantly higher strength [14,15]. Numerical simulations show that application of optimally tailored cyclic preloading on pillar arrays induces noticeable strengthening of the system, even though some of the pillars may be destroyed during precompression [16]. Inspired by this, we are interested in the effect of elimination of some pillars from the system done prior to actual critical loading.…”

Section: Introductionmentioning

confidence: 99%

Critical loading of pillar arrays having previously eliminated elements

Derda

2023

J. Appl. Math. Comput. Mech.

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The paper analyzes critical loads of pillar arrays with fraction of elements removed prior to actual critical loading. Two different methods of elimination are considered. In the first case, a fraction p of weakest pillars is physically removed from the array. The second method relies on conducting a subcritical preloading. When the sudden loading is applied to the system, the destruction follows in a cascade-like manner. Subsequent cascades take place due to the redistribution of load. We explore different types of load redistribution. It turns out that the type of load transfer as well as the distribution of pillar-strength-thresholds are of crucial importance regarding the strength enhancement of critically loaded pillar arrays.

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“…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 ].…”

Section: Introductionmentioning

confidence: 99%

Survivability of Suddenly Loaded Arrays of Micropillars

Derda

Domański

2021

Materials

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When a multicomponent system is suddenly loaded, its capability of bearing the load depends not only on the strength of components but also on how a load released by a failed component is distributed among the remaining intact ones. Specifically, we consider an array of pillars which are located on a flat substrate and subjected to an impulsive and compressive load. Immediately after the loading, the pillars whose strengths are below the load magnitude crash. Then, loads released by these crashed pillars are transferred to and assimilated by the intact ones according to a load-sharing rule which reflects the mechanical properties of the pillars and the substrate. A sequence of bursts involving crashes and load transfers either destroys all the pillars or drives the array to a stable configuration when a smaller number of pillars sustain the applied load. By employing a fibre bundle model framework, we numerically study how the array integrity depends on sudden loading amplitudes, randomly distributed pillar strength thresholds and varying ranges of load transfer. Based on the simulation, we estimate the survivability of arrays of pillars defined as the probability of sustaining the applied load despite numerous damaged pillars. It is found that the resulting survival functions are accurately fitted by the family of complementary cumulative skew-normal distributions.

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Enhanced strength of cyclically preloaded arrays of pillars

Cited by 3 publications

References 15 publications

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

Critical loading of pillar arrays having previously eliminated elements

Survivability of Suddenly Loaded Arrays of Micropillars

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