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Dipasquale, Daniele (2017) Adaptive Grid Refinement and Scaling Techniques Applied to Peridynamics. [Ph.D. thesis]

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Abstract (english)

Peridynamics, a recently proposed non-local continuum theory, is particularly suitable to describe fracture phenomena in a wide range of materials. One of most common techniques for its numerical implementation is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon, the latter related to the length-scale of the material and/or of the phenomenon analysed. As a consequence of that, computational resources may not be used efficiently. The present work proposes adaptive refinement/scaling algorithms for 2D and 3D peridynamic grids, to reduce the computational cost of peridynamic based software. Adaptive refinement/scaling is here applied to the study of dynamic crack propagation in brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. The use of a varying horizon and grid spacing over the grid may introduce some anomalies on the numerical peridynamic solution, such anomalies are investigated in detail through static and dynamic analyses. Moreover, while the scientific community is working to assess the full potential of peridynamics, few researchers have observed indirectly that the evolution of crack paths can follow, in an unphysical way, the axes of symmetry of the grid. The main parameter affecting such a numerical phenomenon seems to be the value of the m ratio, namely the ratio between the horizon and the grid spacing. The dependence of the crack path on the grid orientation would be a serious drawback for peridynamic based software since it would undermine what is believed to be one of its most important advantages over other computational methods, i.e. its capability to simulate (multiple) crack nucleation, propagation, branching and interaction in solids in a simple way. Finally, in order to show the effectiveness of the proposed approach, several examples of crack propagation in both 2D and 3D problems are presented. Then, the results obtained are compared with those obtained with other numerical methods and with experimental data.

Abstract (italian)

La Peridynamica, una teoria non locale del continuo proposta recentemente, è particolarmente adatta a descrivere fenomeni di frattura in una vasta gamma di materiali. Una delle tecniche più comuni per la sua implementazione numerica è basata su un approccio senza mesh, in cui l'intero corpo viene discretizzato con una griglia uniforme e un orizzonte costante, essendo quest'ultimo in relazione con la lunghezza di scala del materiale e/o del fenomeno analizzato. Di conseguenza le risorse computazionali possono non essere utilizzate in modo efficiente. Il presente lavoro si propone di sviluppare gli algoritmi per l’implementazione dell’adaptive grid refinement and scaling per griglie peridinamiche 2D e 3D, con lo scopo di ridurre il costo computazionale dei software basati sulla peridynamica. Questo approccio viene applicato allo studio della propagazione dinamica di cricche in materiali fragili. Il refinement viene attivato utilizzando un nuovo concetto di “innesco” che si basa sullo stato di danneggiamento del materiale, accoppiato con il più tradizionale innesco basato su un criterio energetico, già proposto in letteratura. L' utilizzo di un orizzonte e di un passo di griglia variabile può introdurre nella soluzione numerica della peridynamica alcune anomalie, che vengono analizzate dettagliatamente tramite analisi statiche e dinamiche. Inoltre, mentre la maggior parte della comunità scientifica sta lavorando per valutare a pieno le potenzialità della peridynamica, solo alcuni ricercatori hanno osservato indirettamente come il percorso della cricca possa seguire, in modo chiaramente non realistico, gli assi di simmetria della griglia. Il principale parametro che influisce su tale comportamento sembra essere il valore assunto dal rapporto m, definito come il rapporto tra l'orizzonte e il passo della griglia. La dipendenza del percorso della cricca dall'orientamento della griglia sarebbe un grave ostacolo per lo sviluppo di un software basato sulla peridynamica, poiché ciò porterebbe a pregiudicare quella che si ritiene essere uno dei suoi vantaggi più importanti rispetto ad altri metodi di calcolo, ossia la sua capacità di simulare la nucleazione (anche multipla), la propagazione, la ramificazione e l’interazione di cricche in materiali solidi in modo semplice. Successivamente, al fine di dimostrare l'efficacia del metodo proposto, vengono presentati alcuni esempi di propagazione di cricche per problemi 2D e 3D. Infine, i risultati ottenuti sono confrontati con quelli ottenuti con altri metodi numerici e con dati sperimentali.

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EPrint type:Ph.D. thesis
Tutor:Galvanetto, Ugo
Supervisor:Zaccariotto, Mirco
Ph.D. course:Ciclo 29 > Corsi 29 > SCIENZE TECNOLOGIE E MISURE SPAZIALI
Data di deposito della tesi:07 February 2017
Anno di Pubblicazione:07 February 2017
Key Words:peridynamics, adaptive refinement, scaling, brittle fracture
Settori scientifico-disciplinari MIUR:Area 09 - Ingegneria industriale e dell'informazione > ING-IND/04 Costruzioni e strutture aerospaziali
Struttura di riferimento:Dipartimenti > Dipartimento di Ingegneria Industriale
Codice ID:10388
Depositato il:03 Nov 2017 09:13
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