3D-printed biomimetic composite structures of the human cortical bone

In the last decades, there is an increasing interest in materials that are able to overcome the limitations of traditional ones, especially regarding their low versatility. The scientists start to look to the natural world, that is considered a source of inspiration. This insatiable curiosity has given rise to the science of biomimetics, whose key concept concerns the inspiration from nature, so as to mimic its morphologies, bringing out innovative solutions to scientific problems. Among the existing materials, the study of the human bone structure has found fertile ground and, in particular, the cortical bone has often been taken as model since it shows noteworthy mechanical properties, comparable with the ones of the engineering materials like ceramics and metal alloys. This is due to its internal structure, arranged in hierarchically organised components. It is proved that this tissue presents considerable fracture resistance, especially if subjected to torsion, due to its fundamental functional unit, the osteons. In this project, the purpose lies in the design of a 3D bioinspired composite structure, a macroscopic cylindrical specimen, characterized by a matrix made of a polymeric stiff material (VeroCyanTM, E≈735 MPa), inside which a soft rubber is embedded (Agilus30TM, E≈0.8 MPa), capable of providing adequate resistance to the applied load. The stiff matrix imitates the mineralized lamellae which surround the osteons, while the soft inclusions mimic the osteons themselves. Focusing on this and considering the torsional load, analytical, numerical and experimental methods are developed and various geometrical features are analysed like the cortex thickness, which is a sort of circumferential lamellar cover that coats the set of osteons, the b/a ratio and the inclination angle, seeking in them the possible reasons for these remarkable characteristics. For all the studied structures, some parameters are maintained constant such as the osteon volume fraction, fixed to 50%, and the osteon area, set to ≈7.07 mm2 with an osteon diameter of 3 mm. In order to replicate and test the small-scale geometries of the structures, the additive manufacturing process of 3D-printing is exploited, printing three samples for each selected structure. For these reasons, the laboratories of Industrial Design (IDE) and Biomechanical Engineering (BMechE) at TU Delft University offered the computational and experimental instruments to deepen the topic of the project, contributing to identify the mechanical behaviours and their variability. At the end of the analyses, increasing the cortex thickness and decreasing the b/a ratio, so going from more spindle-shaped structures to cylindrical ones, the mechanical response increases consequently and the shape of osteon influences structure’ properties. The inclination angle seems not to make any remarkable contribution. The best structures in terms of reached stress and deformations are the ones with concentric circular layer, Conc Lay, and with cylindrical osteons, Cyl. Furthermore, it is noticed that, in terms of the stiffness k parameter and shear modulus G, the analytical and numerical results are quite reliable within the fixed linearity range of 20°. Some mismatches arise between the computational and experimental ones due to plastic behaviour at the borders of structures. In this region, the results are well predicted just within low deformations. To overcome this problem, a preliminary calibration of the VeroCyanTM is performed, in order to predict accurately the linear range and a first post-yield part. In the last decades, there is an increasing interest in materials that are able to overcome the limitations of traditional ones, especially regarding their low versatility. The scientists start to look to the natural world, that is considered a source of inspiration. This insatiable curiosity has given rise to the science of biomimetics, whose key concept concerns the inspiration from nature, so as to mimic its morphologies, bringing out innovative solutions to scientific problems. Among the existing materials, the study of the human bone structure has found fertile ground and, in particular, the cortical bone has often been taken as model since it shows noteworthy mechanical properties, comparable with the ones of the engineering materials like ceramics and metal alloys. This is due to its internal structure, arranged in hierarchically organised components. It is proved that this tissue presents considerable fracture resistance, especially if subjected to torsion, due to its fundamental functional unit, the osteons. In this project, the purpose lies in the design of a 3D bioinspired composite structure, a macroscopic cylindrical specimen, characterized by a matrix made of a polymeric stiff material (VeroCyanTM, E≈735 MPa), inside which a soft rubber is embedded (Agilus30TM, E≈0.8 MPa), capable of providing adequate resistance to the applied load. The stiff matrix imitates the mineralized lamellae which surround the osteons, while the soft inclusions mimic the osteons themselves. Focusing on this and considering the torsional load, analytical, numerical and experimental methods are developed and various geometrical features are analysed like the cortex thickness, which is a sort of circumferential lamellar cover that coats the set of osteons, the b/a ratio and the inclination angle, seeking in them the possible reasons for these remarkable characteristics. For all the studied structures, some parameters are maintained constant such as the osteon volume fraction, fixed to 50%, and the osteon area, set to ≈7.07 mm2 with an osteon diameter of 3 mm. In order to replicate and test the small-scale geometries of the structures, the additive manufacturing process of 3D-printing is exploited, printing three samples for each selected structure. For these reasons, the laboratories of Industrial Design (IDE) and Biomechanical Engineering (BMechE) at TU Delft University offered the computational and experimental instruments to deepen the topic of the project, contributing to identify the mechanical behaviours and their variability. At the end of the analyses, increasing the cortex thickness and decreasing the b/a ratio, so going from more spindle-shaped structures to cylindrical ones, the mechanical response increases consequently and the shape of osteon influences structure’ properties. The inclination angle seems not to make any remarkable contribution. The best structures in terms of reached stress and deformations are the ones with concentric circular layer, Conc Lay, and with cylindrical osteons, Cyl. Furthermore, it is noticed that, in terms of the stiffness k parameter and shear modulus G, the analytical and numerical results are quite reliable within the fixed linearity range of 20°. Some mismatches arise between the computational and experimental ones due to plastic behaviour at the borders of structures. In this region, the results are well predicted just within low deformations. To overcome this problem, a preliminary calibration of the VeroCyanTM is performed, in order to predict accurately the linear range and a first post-yield part. In conclusion, despite the results obtained,future developments will focus on the implementation of more complex structures, analysing other parameters like the dimension of osteons or moving to three materials composite structures, able to mimic the role played by Havers canals in the osteon and by the cement line, lightening the structure and optimizing its torsional properties.

Nelle ultime decadi, si è verificato un interesse crescente nei materiali che sono in grado di superare i limiti dei materiali tradizionali, specialmente per quanto riguarda la loro versatilità. Gli scienziati hanno rivolto il loro sguardo al mondo naturale che, fin dai tempi antichi, è stato considerato come una fonte di ispirazione. Questa insaziabile curiosità ha dato vita alla scienza della biomimetica, il cui perno è l’ispirazione alla natura, imitandone le sue morfologie, per apportare soluzioni innovative ai problemi scientifici. Tra i materiali esistenti, lo studio della struttura dell’osso umano è risultato di particolare interesse ed in particolare l’osso corticale è stato preso spesso come modello poiché mostra proprietà meccaniche sorprendenti, comparabili a quelle dei materiali ceramici o delle leghe metalliche. Ciò è dovuto ad una struttura interna, disposta in componenti organizzati gerarchicamente. Soggetto a differenti carichi, è stato dimostrato che questo tessuto presenta una considerevole resistenza alla frattura, specialmente se sottoposto a torsione, a causa della sua unità funzionale fondamentale: gli osteoni. In questo progetto, lo scopo è progettare una struttura bioinspirata a materiali compositi: si tratta di, un provino cilindrico, caratterizzato da una matrice costituita da un materiale polimerico rigido (VeroCyanTM, E≈735 MPa), dentro cui è integrata una gomma morbida (Agilus30TM, E≈0.8 MPa), capace di fornire un’adeguata resistenza al carico applicato. Il materiale più rigido dovrebbe imitare le lamelle mineralizzate che circondano gli osteoni, mentre l’altro polimero gli osteoni stessi. Focalizzandosi su ciò e considerando il carico a torsione, sono stati sviluppati metodi analitici, numerici e sperimentali. Sono inoltre stati analizzati vari parametri geometrici, come lo spessore della corteccia, che è uno strato che riveste l’insieme di osteoni, il rapporto tra assi b/a per l’ellisse e l’angolo di inclinazione, ricercando in essi le possibili ragioni per queste elevate proprietà meccaniche a torsione dell’osso corticale. Per tutte le strutture studiate, alcuni parametri sono stati mantenuti costanti come la frazione di volume dell’osteone, fissata al 50% tra materiale rigido e soft, e l’area dell’osteone, stabilita a 7.07 mm2 con un diametro di 3 mm. Per replicare e testare la geometria delle strutture ad una scala ridotta, si sfrutta il processo di stampa mediante additive manufacturing, producendo tre campioni per ogni struttura scelta. Per queste ragioni, i laboratori di Industrial Design (IDE) e Biomechanical Engineering (BMechE) alla TU Delft University hanno dato la possibilità di usufruire delle loro attrezzature per analisi ed esperimenti, contribuendo ad identificare i comportamenti meccanici delle strutture considerate. Alla fine delle analisi, tra i parametri geometrici sopracitati, incrementando lo spessore della corteccia e diminuendo il rapporto b/a, andando dunque da una forma più affusolata ad una cilindrica, la risposta meccanica aumenta di conseguenza. Di conseguenza, la forma dell’osteone influenza le proprietà della struttura. L’angolo di inclinazione, invece, sembra non portare alcun contributo degno di nota. Le migliori strutture in termini di sollecitazioni e deformazioni raggiunte sono quelle con strato circolare concentrico, Conc Lay, e con osteoni cilindrici, Cyl. Inoltre, si nota che, in termini di parametri di rigidezza k e modulo di taglio G, utilizzati per misurare la risposta meccanica, i risultati analitici e numerici sono abbastanza affidabili entro l'intervallo di linearità fissato di 20 °. Alcune discrepanze sorgono tra i risultati computazionali e sperimentali a causa degli elevati effetti plastici ai bordi delle strutture, che sono considerabili solo a basse deformazioni. Per ovviare a questo problema, viene eseguita una calibrazione preliminare del VeroCyanTM, riuscendo a prevedere tutto il tratto elastico ed una prima parte dopo lo snervamento del materiale. Per concludere, nonostante i risultati ottenuti, futuri sviluppi saranno focalizzati nell’implementare strutture più complesse, analizzando altri parametri come la dimensione degli osteoni o spostandosi V verso strutture composite a tre materiali, imitando la struttura del canale Haversiano nell’osteone e la linea cementizia, in modo tale da sopportare carichi maggiori ed ottimizzare le proprietà a torsione.