In this paper the numerical implementation of two-scale modelling of bone microstructure is presented. The study is a part of long-term project on bone remodelling which drives bone microstructure change based directly on trabeculae surface energy. The proposed approach is based on a first-order computational homogenization technique. The coincidence of macro-and micro-model kinematics is done with the use of uniform displacement and traction boundary conditions. The computational homogenization procedure is driven by a self-prepared manager which is coded in Python. The computation on real bone structure (a piece of female Wistar rat bone) is performed as well.

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Article citation info: (*) Tekst artykułu w polskiej wersji językowej dostępny w elektronicznym wydaniu kwartalnika na stronie www.ein.org.pl IntroductionDental implant is expected to be serviced as long as it is able to fulfill biological, esthetical and functional requirements. There is no service life for any of its components considered. Therefore, the proper design should based on the assumption that the implant service life has to be longer than the maximal patients' life expectancy regardless of biological and biomechanical conditions.According to the retrospective studies [12,26,30] one of the problems reported in long term service of the implants is fatigue failure. Systematic review of twentysix followup studies estimated a cumulative incidence of implant fractures after 5 years on the level of 0.14% [22]. However, the fracture ratio for the followup studies for up to 15 years [2] rises drastically and can reach even 16% in the maxilla. Dental implant failure usually results in an expensive, long term therapy often accompanied by the patient's trauma. It makes the fatigue resistance crucial feature to be include in implant designing. The significant rise in fatigue fracture cases after 5 years, which the followup studies are mostly limited to, can suggest that this period is inadequate to examine this phenomenon. Additionally, it should be taken into account that nowadays, market competition and patients' demands force the producers to introduce the new or modified design in very short design cycles. Therefore, there is the need to develop of the efficient procedure for fatigue fracture risk minimization.Many researchers undertake the implant failure problem using laboratory tests [7,9,10,11,13,20,23,27,29,31,32] and numerical approach [17]. Among the others, special attention should be paid to the studies done by Wierszycki [38] and Ilies [20]. Wierszycki proposed complete methodology and computational model for fatigue fracture estimation using strain based approach. The results were supported with clinical observations [39]. Ilies, on the other hand, proposed approach for fatigue estimation utilizing stresses and provided additional verification with laboratory tests. Another important work was done by Patterson and Johns [28] who presented the concept of fatigue resistance as a function of screw preload. These results prove the existence of the optimal value of screw preload in context of fatigue life of the implant screw. Finally, Genna [18,19] utilized shakedown analysis to examine lowcycle fatigue failure of dental implants. The results show that the 'worst' load case in context of fatigue fracture is characterized by pure transversal load or its strong domination on axial load.This conclusion was also confirmed for the prototype analyzed in the presented study by Szajek [35].Taking into account the results of the above mentioned studies, the complete designing methodology for improvement of two where K f is fatigue reduction factor (for fixture 1.25 -strongly roughed surface). Assuming consta...