Direct and inverse methods applied to the determination of mode I cohesive law of bovine cortical bone using the DCB test

This work addresses the determination of the cohesive law under mode I loading of bovine cortical bone tissue using the Double Cantilever Beam (DCB) test. Direct and inverse methods were proposed to assess the cohesive laws representative of bone fracture under mode I loading. The direct method combines the evolution of the strain energy release rate under mode I loading with the crack tip opening displacement that is monitored by digital image correlation technique. According to this method, the cohesive law is obtained by differentiation of such relation with respect to the crack opening. The inverse procedure is performed through a finite element analysis including cohesive zone modelling, conjointly with a devel- oped optimization algorithm. This identification strategy does not require a pre-established shape of the cohesive law as with the conventional inverse based procedures, which is viewed as a novelty of this work. It was concluded that both methods provide consistent results, being appellative tools concerning systematic and methodical studies dedicated to bone fracture characterization.

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 through grant no. SFRH/BD/80046/2011 and 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. This work is also supported by FCT with the reference project UID/EEA/04436/2013, COMPETE 2020 with the code POCI-01-0145-FEDER-006941.