Determination of mode II cohesive law of bovine cortical bone using direct and inverse methods

This study presents two alternative methods to determine the cohesive law of bovine cortical bone under mode II loading, employing the End Notched Flexure (ENF) test. The direct method results from the combination of the progress of the mode II strain energy release rate with the crack tip shear displacement, obtained by digital image correlation. The resulting cohesive law is determined by differentiation of this relation relatively to the crack shear displacement. The inverse method employs finite element analyses with cohesive zone modelling, in association with an optimization procedure. The resulting strategy enables determining the cohesive law without establishing a pre-defined shape. The significant conclusion that comes out of this work is that both methods offer consistent results regarding the estimation of the cohesive law in bone. Given that the inverse method dispenses the use of sophisticated equipment to obtain the cohesive law in bone, it can be used as a more convenient procedure to accomplish efficient studies in the context of bone fracture characterization under mode II loading.The authors acknowledge the Portuguese Foundation for Science and Technology (FCT) for the conceded financial support through the research project PTDC/EME-PME/119093/2010 and through grant no. SFRH/BD/80046/2011. The second author acknowledges the "Laboratorio Associado de Energia, Transportes e Aeronautica" (LAETA) for the financial support by the project UID/EMS/50022/2013. The third author acknowledges FCT for the conceded financial support through the reference project UID/EEA/04436/2013, COMPETE 2020 with the code POCI-01-0145-FEDER-006941.All other authors acknowledges the European Investment Funds by FEDER/COMPETE/POCI- Operacional Competitiveness and Internacionalization Programme, under Project POCI-01-0145-FEDER-006958 and National Funds by FCT - Portuguese Foundation for Science and Technology, under the project UID/AGR/04033/2013