PSI - Issue 37

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2021) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2021) 000 – 000 Available online at www.sciencedirect.com ScienceDirect

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Procedia Structural Integrity 37 (2022) 257–262

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira trabecular bone reported in the lit rature. Effective parameters of the trabecu a one tissue – ultimate compr ssi and tensile strength as w ll as yield stress – are considerably lower than those of individual trabeculae: some 8% of the respective magnitudes for trabeculae. © 2022 The Authors. Published by ELSEVIER B.V. This is an ope access article under the CC BY-NC-ND lic nse (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira ICSI 2021 The 4th International Conference on Structural Integrity Failure behaviour of human trabecular bone Ekaterina Smotrova a , Simin Li a , Mikhail Tashkinov b , Alexandr Shalimov b , Vadim V. Silberschmidt a,b * a Wolfson School of Mechanical, Electrical and Manufacturing Engineering, Loughborough University, Loughborough, UK b Laboratory of Mechanics of Biocompatible Materials and Devices, Perm National Research Polytechnic University, Perm, Russia Abstract A trabecular bone tissue with its complex microstructural morphology can demonstrate a complex and random pattern of fracture. This paper analyses the effect of material ’s mechanical behaviour on failure modelling of human trabecular bone. For this purpose, a 3D unit cell of trabecular tissue was obtained from scans of human distal tibia performed with high-resolution peripheral quantitative computed tomography (HR-pQCT). In simulations, two types of fracture of trabeculae were considered - brittle and ductile, with respective elastic and elastoplastic formulations. Two types of loading – tension and compression – were applied to the unit cell in order to assess its stress state and locations of the failure onset. Positions of damaged areas in case of brittle-fracture approach differed for tension and compression, while the same damage regions were observed for the ductile criterion in both loading conditions. It was found that the first modelling approach resulted in about two times higher effective strength of trabecular bone as compared to that for the second approach: 11.49 MPa and 4.94 MPa, respectively. The calculated values of effective strength for brittle and ductile material models are in good agreement with the magnitudes of tensile and compressive strength of trabecular bone reported in the literature. Effective parameters of the trabecular bone tissue – ultimate compressive and tensile strength as well as yield stress – are considerably lower than those of individual trabeculae: some 8% of the respective magnitudes for trabeculae. ICSI 2021 The 4th International Conference on Structural Integrity Failure behaviour of human trabecular bone Ekaterina Smotrova a , Simin Li a , Mikhail Tashkinov b , Alexandr Shalimov b , Vadim V. Silberschmidt a,b * a Wolfson School of Mechanical, Electrical nd Manufactur ng Engineering, Loughbo ough Univers ty, Loughborough, UK b Laboratory of Mechanics of Biocompatible Materials and Devices, Perm National Research Polytechnic University, Perm, Russia Abstract A trabecular bone tissue with its complex microstru tural morphology can demonstrate a co plex and random patte n of fractur . This paper analyses the effect of material ’s mechanical beh viour on failure modelling of human trabecular bone. For this purpose, a 3D un t cell of trabecular tissue was obtained fro scans of human distal tibia performed with high-resolution peripheral q antitative computed tomography (HR- QCT). In simulations, two types of fracture of trabeculae were considered - brittl and ductile, with respective ela tic and lastoplastic f rmulati ns. Two types of loading – tension and compression – were applied to the unit cell in or er to as ess its stress state and locations of the failure ons t. Po itions of damaged areas in as of brittle-fracture approach differed for tensi n and compre sion, while the same damage regions ere ob erved for the ductil criterion in both loading conditions. It was found that the first m delling approach resulted in about two times higher effective strength of trab ular bone as c mpared to that for the second approach: 11.49 MPa and 4.94 MPa, respectively. The calculated values of ffective strength for brittl and uctile ma ial models are in good ag eement with the magnitude of tensile nd r i strength of

Keywords: HR-pQCT; trabecular bone; mechanical competence; strength; fracture Keywords: HR-pQCT; trabecular bone; mechanical competence; strength; fracture

* Corresponding author. E-mail address: V.Silberschmidt@lboro.ac.uk * Correspon ing author. E-mail address: V.Silberschmidt@lboro.ac.uk

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an ope acces article under the CC BY-NC-ND lic nse (https://c eativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 10.1016/j.prostr.2022.01.082