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1

Suddenly loaded arrays of pillars with variable range of load transfer

Derda Tomasz

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 4

16--27

EN

This paper deals with multicomponent systems subjected to suddenly applied loads. Such multicomponent systems consist of functionally identical elements, but the elements differ in their ability to sustain the applied load. Specifically, arrays of pillars are an example of the multicomponent systems. The capability of the array to sustain the applied load depends not only on the strength of the pillars but also on how the load coming from failed pillars is redistributed to the intact ones. We employ a Fiber Bundle Model with load transfer restricted within a rectangular region generated dynamically after each pillar’s destruction. We investigate strength of the array and its survivability.

2

Stochastic local load redistribution in the fibre bundle model of nanopillar arrays

Derda T.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

19--30

EN

We study the breakdown of the nanopillar arrays subjected to axial loading. The pillar-strength-thresholds are drawn from a given probability distribution. Pillars are located in the nodes of the supporting regular lattice. In this work we introduce stochastic local load sharing - after pillar breakdown each of its nearest intact neighbours obtains a random fraction of the failing load. Two types of loading procedure are employed, namely quasi-static and finite force. We analyse critical loads, catastrophic avalanches as well as probabilities of cascade and breakdown.

3

Statistical analysis of mechanical damage in arrays of mixed nanopillars

Derda T.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 1

43--53

EN

We apply the Fibre Bundle Model to study critical loads and catastrophic avalanches in arrays of axially loaded nanopillars under so-called local load sharing. Nanopillars with assigned random strength-thresholds are located in the nodes of the supporting square lattice. We analyzed different mixtures of weak and strong pillars, i.e. we use distributions of strength-thresholds drawn from two different uniform distributions.

4

Damage evolution in the anisotropic range variable model of nanopillar array

Derda T.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 3

37--46

EN

We study mechanical-damage avalanches occurring in axially loaded nanopillars located in the nodes of the supporting square lattice. Nanopillars are treated as fibres in the framework of the stochastic Fibre Bundle Model and they are characterised by random strength thresholds. Once an element crashes, its load is transferred to the other intact elements according to a given load transfer rule. In this work we use a modified range variable model including an anisotropic-stress-transfer function. Avalanches of broken nanopillars, critical loads and clusters of damaged nanopillars are analysed by varying both the anisotropy and effective range coefficients.

5

Mechanical annealing model of damage in arrays of nanopillars

Derda T.

Journal of Applied Mathematics and Computational Mechanics

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2013

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Vol. 12, nr 4

31--40

EN

The mechanical damage accumulation occurring in an array of axially loaded nanopillars is studied within the stochastic approach. To each nanopillar, an initial strength--threshold is assigned which is drawn from the Weibull probability distribution. Under the influence of load exceeding the strength-threshold the pillar height is reduced. Then the reduced pillar gets new higher strength-threshold and its load is transferred to other working pillars. We analyse slip loads causing the system height reductions and avalanches of the pillar height reductions.

6

Damage evolution on two-dimensional grids : comparison of load transfer rules

Derda T., Domański Z.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2010

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Vol. 9, nr 1

5-15

EN

The damage evolution occurring in a set of elements located in the nodes of the supporting two-dimensional grid is analysed within the stochastic approach. The element-strength-thresholds are drawn from a given probability distribution and the elements are treated as fibres within the Fibre Bundle Model. If an element fails, its load has to be transferred to the other intact elements. For different grid geometries we compare the evolution of the number of intact elements under the load with respect to three different load transfer rules: the global, the local and recently introduced so called Voronoi load transfer rule. Our example system is an array of nanopillars.