Fracture safety of double- porous hydroxyapatite biomaterials Alexander Dejaco PhD Institute for Mechanics of Materials and Structures, TU Wien – Vienna University of Technology, Vienna, Austria Vladimir S. Komlev PhD A.A. Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, Moscow, Russia Jakub Jaroszewicz PhD Department of Materials Science and Engineering, Warsaw University of Technology, Warsaw, Poland Wojciech Swieszkowski PhD Department of Materials Science and Engineering, Warsaw University of Technology, Warsaw, Poland Christian Hellmich PhD* Institute for Mechanics of Materials and Structures, TU Wien – Vienna University of Technology, Vienna, Austria Biological requirements call for substantial porosities in clinical biomaterials – challenging the mechanical integrity and strength of the latter. In this study, the authors resort to quantitative engineering principles to assess the fracture safety of double-porous hydroxyapatite ceramics: micro-computed tomography scans give access to the morphology of macropores at the submillimeter scale, as well as to voxel-specific microporosities. Advanced micromechanics of porous ceramics with needle-shaped elementary units then allows for translating voxel-specific microporosities to corresponding elasticity and strength properties, as well as to macro-to-micro scale transition (‘concentration’) tensors. These mechanical properties and tensors are fed into a large-scale finite-element model of a biomaterial granule as used for mandibular tissue regeneration. Loading the granule in splitting mode, up to physiological strain, evidences stress concentrations at the loaded poles and close to internal macropores and cracks. A parallel computing-supported subvoxel analysis of needle orientations evidences that in highly loaded regions, the intravoxel ‘single crystals’ oriented perpendicular to the loading direction undergo the most unfavorable loading. Still, only 0·6% of the finite- elements show stresses indicating failure, and the mean safety factor against fracture is as high as 7. This analysis confirms, from an engineering science viewpoint, the successful use of the investigated biomaterials in clinical practice. Notation a ij matrix element at position i,j B HA ðj ; ϑÞ fourth-order stress concentration tensor of needle-shaped hydroxyapatite phase oriented in the (j, ϑ) direction C poly fourth-order stiffness tensor of porous hydroxyapatite polycrystal c HA fourth-order stiffness tensor of pure hydroxyapatite E (voxel-specific) micromechanics-derived Young’s modulus e x , e y , e z unit base vectors of orthonormal reference base frame e ϑ , e j , e r unit base vectors of orthonormal local base frame of a single hydroxyapatite needle GV (voxel-specific) X-ray attenuation-related 8-bit gray value GV air most frequently occurring gray value of air-related voxels GV HA gray value corresponding to a voxel of pure hydroxyapatite GV thr threshold gray value between air-related voxels and voxels containing ceramics I fourth-order identity tensor i index j index k total number of finite elements in the finite-element model M matrix dimension N orientation vector aligned with the longitudinal axis of hydroxyapatite needle N cn total number of computing nodes N cr number of central processing unit (CPU) cores per computing node N cpu total number of CPU cores N eval number of evaluation steps n matrix dimension n orientation vector perpendicular to N O(·) big O notation of computational complexity of quantity (·) p(·) probability density function of quantity (·) pr father father process *Corresponding author e-mail address: christian.hellmich@tuwien.ac.at 24 Dejaco A, Komlev VS, Jaroszewicz J, Swieszkowski W and Hellmich C (2016) Fracture safety of double-porous hydroxyapatite biomaterials. Bioinspired, Biomimetic and Nanobiomaterials 5(1): 24–36, http://dx.doi.org/10.1680/jbibn.15.00021 ice | science Bioinspired, Biomimetic and Nanobiomaterials Volume 5 Issue BBN1 Research Article Received 01/10/2015 Accepted 18/01/2016 Published online 21/01/2016 Keywords: biomaterials//mechanical properties/simulation Published with permission by the ICE under the CC-BY license. (http://creativecommons.org/licenses/by/3.0/) Downloaded by [] on [05/06/20]. Published with permission by the ICE under the CC-BY license