Lattice structures are periodic cellular materials whose geometry can be designed so as to obtain a unique set of physical and mechanical properties. Their implementation in innovative multi-functional design contexts allows to relax the constraints imposed by the use of common monolithic materials, thus giving extreme advantages. Despite the scientific literature provides a detailed insight about their physical, dynamic and mechanical behaviour, as well as their implementation for a broad range of applications, open points that hinder their diffusion and narrow their potential are still present. The aim of this doctoral research thesis is to fill some of the literature gaps on the knowledge of the effective mechanical behaviour of lattice structures and on the methodologies to design novel metamaterials. The first part of the current work was dedicated to metallic lattice structures. A preliminary work was conducted on compression testing methods for lattices, given the lack of a comprehensive and general reference standard. The knowledge acquired was then applied in a following work, where we characterized and described numerically the multi-axial strength of an aluminium lattice structure that exhibits a brittle behaviour, focusing also on the effet of as-built defects. Finally, a third work on the experimental characterization of the random fatigue behaviour of a triply periodic minimal surface lattice structure was carried out. This topic represents a totally uncharted territory, yet of great relevance for all the applications where a component is subjected to variable amplitude cyclic loading. In the second part of the research, we focused on the cyclic behaviour of elastomeric lattices that undergo local instabilities during the deformation process. These metamaterials find important applications mainly in soft-robotics and in small biomedical pneumatic actuators. Although many works can be found in the literature about the static response of soft elastomeric lattices under uniaxial and multi-axial loads, their behaviour under cyclic loads is still unexplored. We performed experimental tests and built numerical models to better understand the coupled role of material non-linearities (non-linear hyperelasticity, creep and damaging), geometric non-linearities and manufacturing defects. We found that the cyclic response is strongly affected by this coupled interactions and may significantly differ from the static one, thus highlighting the practical importance of considering the investigated aspects. Finally, the last part of the thesis work was devoted to improve the state of the art design methods for novel cellular structures. The potentiality offered by lattices in multi-functional design can be extremely increased by the use of topology optimization at the micro-scale to obtain target effective properties, by means of an inverse homogenization technique. Despite this method is well established in the literature, it suffers from the typical problems of topology optimization, such as non-uniqueness of the solution, mesh dependency, checker-board, grey-scale, and staircase effects, together with geometric complexity issues. All these issues can be even exacerbated when performing the optimization at the micro-scale. To overcome these problems, we extended and improved an inverse homogenization approach based on a mesh adaptation procedure to a multi-physics environment where we control both elastic and thermal conductivity effective properties. In this scheme, an anisotropic mesh is iteratively adapted in the optimization loop, allowing to mitigate some of the typical issues of topology optimization and to obtain clean and smooth geometries, ready to be manufactured with a very contained post-processing.
Le strutture lattice sono materiali cellulari periodici che possono essere progettati per ottenere diverse combinazioni di proprietà fisiche e meccaniche. L’uso di tali strutture in contesti di progettazione innovativi e multifunzionali permette di rilassare i vincoli imposti dall’uso dei materiali tradizionali monolitici, fornendo così importanti vantaggi. Sebbene la letteratura scientifica proponga una panoramica dettagliata sulle proprietà fisiche, meccaniche e dinamiche delle strutture lattice, così come sui possibili campi applicativi, sono ancora presenti dei punti aperti che ostacolano la diffusione di questi metamateriali. Lo scopo di questa tesi di dottorato è di colmare alcune lacune della letteratura sulla conoscenza del comportamento meccanico effettivo e sulle metodologie di design delle strutture lattice. La prima parte di questo lavoro è dedicata alle strutture lattice metalliche. Data la mancanza di una normativa completa sulle metodologie di test meccanici a compressione, è stata inizialmente svolta un’attività preliminare su tale argomento. Le conoscenze sviluppate sono state poi applicate in un successivo lavoro, dove è stata caratterizzata e descritta numericamente la resistenza statica multi-assiale di una struttura in alluminio con comportamento fragile, focalizzando in particola l’attenzione sul ruolo dei difetti di manifattura. Infine, in un terzo lavoro è stata caratterizzata la resistenza a fatica random di una struttura lattice a superficie. La resistenza a fatica ad ampiezza variabile delle strutture lattice è un argomento del tutto inesplorato, tuttavia di grande interesse per tutte le applicazioni in cui le sollecitazioni dipendono da vibrazioni. Nella seconda parte della ricerca esposta in questa tesi, ci si è focalizzati sulla risposta ciclica di lattice elastomerici che esibiscono fenomeni di non-linearità locale durante il processo di deformazione. Questo tipo di metamateriali trova importanti applicazioni principalmente nel campo della robotica “soft” e degli attuatori pneumatici in ambito biomedico. Sebbene si possano trovare numerosi lavori sulla loro riposta statica, sia mono-assiale che multi-assiale, la loro risposta ciclica rappresenta un argomento inesplorato. Il lavoro presentato affronta la tematica sperimentalmente, tramite test ciclici, e numericamente, tramite modelli non-lineari a elementi finiti, per una maggiore comprensione dell’effetto mutuale tra non-linearità del materiale (iperelasticità, creep e danneggiamento), non-linearità geometriche e difetti di processo. È stato osservato che la risposta ciclica è fortemente influenzata da queste mutue interazioni e può differire significativamente dalla risposta statica, evidenziando così la rilevanza pratica del considerare tali aspetti. Infine, l’ultima parte del lavoro di tesi è stata indirizzata al miglioramento delle attuali tecniche di progettazione di materiali lattice innovativi. La potenzialità offerta da queste strutture in contesti multifunzionali, infatti, può essere significativamente aumentata dall’uso della ottimizzazione topologica alla micro-scala, al fine di garantire determinate proprietà alla macro-scala, tramite un approccio di omogenizzazione inversa. Nonostante questa metodologia sia consolidata in letteratura, non è esenta dai tipici problemi numerici legati all’utilizzo dell’ottimizzazione topologica, come ad esempio la non-unicità della soluzione, la dipendenza dalla griglia di discretizzazione, la presenza di valori intermedi e scarsa qualità della geometria ottenuta. Questi problemi possono addirittura essere esacerbati dall’utilizzo di uno schema di omogenizzazione inversa. Come soluzione, è stato esteso e migliorato un approccio precedentemente sviluppato basato su tecniche di adattazione di griglia per ottenere strutture lattice con proprietà elastiche e di conduzione termiche controllate, in un setting multi-fisica. I problemi tipici di queste metodologie sono stati mitigati dall’utilizzo di adattazione di griglia anisotropa che consente di ottenere geometrie precise e ben definite, pronte per essere stampate e richiedendo un post-processing molto limitato.
Mechanical characterization and design of lattice structures for innovative multi-functional applications
Gavazzoni, Matteo
2021/2022
Abstract
Lattice structures are periodic cellular materials whose geometry can be designed so as to obtain a unique set of physical and mechanical properties. Their implementation in innovative multi-functional design contexts allows to relax the constraints imposed by the use of common monolithic materials, thus giving extreme advantages. Despite the scientific literature provides a detailed insight about their physical, dynamic and mechanical behaviour, as well as their implementation for a broad range of applications, open points that hinder their diffusion and narrow their potential are still present. The aim of this doctoral research thesis is to fill some of the literature gaps on the knowledge of the effective mechanical behaviour of lattice structures and on the methodologies to design novel metamaterials. The first part of the current work was dedicated to metallic lattice structures. A preliminary work was conducted on compression testing methods for lattices, given the lack of a comprehensive and general reference standard. The knowledge acquired was then applied in a following work, where we characterized and described numerically the multi-axial strength of an aluminium lattice structure that exhibits a brittle behaviour, focusing also on the effet of as-built defects. Finally, a third work on the experimental characterization of the random fatigue behaviour of a triply periodic minimal surface lattice structure was carried out. This topic represents a totally uncharted territory, yet of great relevance for all the applications where a component is subjected to variable amplitude cyclic loading. In the second part of the research, we focused on the cyclic behaviour of elastomeric lattices that undergo local instabilities during the deformation process. These metamaterials find important applications mainly in soft-robotics and in small biomedical pneumatic actuators. Although many works can be found in the literature about the static response of soft elastomeric lattices under uniaxial and multi-axial loads, their behaviour under cyclic loads is still unexplored. We performed experimental tests and built numerical models to better understand the coupled role of material non-linearities (non-linear hyperelasticity, creep and damaging), geometric non-linearities and manufacturing defects. We found that the cyclic response is strongly affected by this coupled interactions and may significantly differ from the static one, thus highlighting the practical importance of considering the investigated aspects. Finally, the last part of the thesis work was devoted to improve the state of the art design methods for novel cellular structures. The potentiality offered by lattices in multi-functional design can be extremely increased by the use of topology optimization at the micro-scale to obtain target effective properties, by means of an inverse homogenization technique. Despite this method is well established in the literature, it suffers from the typical problems of topology optimization, such as non-uniqueness of the solution, mesh dependency, checker-board, grey-scale, and staircase effects, together with geometric complexity issues. All these issues can be even exacerbated when performing the optimization at the micro-scale. To overcome these problems, we extended and improved an inverse homogenization approach based on a mesh adaptation procedure to a multi-physics environment where we control both elastic and thermal conductivity effective properties. In this scheme, an anisotropic mesh is iteratively adapted in the optimization loop, allowing to mitigate some of the typical issues of topology optimization and to obtain clean and smooth geometries, ready to be manufactured with a very contained post-processing.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/183685