Survivability of Suddenly Loaded Arrays of Micropillars

Abstract

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.

Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

“…We consider a problem of loading the arrays determined by the following structural parameters: pillars, whose random strength-thresholds are distributed according to Equation ( 1 ) with the shape parameter . In our simulations, the RV load transfer rule, given by Equation ( 2 ), operates in a regime characterized by which, in turn, corresponds to a short-range-like pillar-to-pillar interactions [ 14 ].…”

“…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.…”

“…The above density enables us to compute the corresponding survival function , which represents the probability that a given array safely supports an applied load Q [ 14 ]. Namely: …”

“…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.…”

Suddenly loaded arrays of pillars with variable range of load transfer

“…The pillars are positioned in the nodes that form a square grid, therefore L is the linear size of the system. Such pillar array is subjected to suddenly applied [9,12,13] axial load which induces pillar crushes. However, the pillars are functionally identical, but they differ in their quenched strength-thresholds σ th .…”