بررسي رفتار پس از تسليم استخوان كورتيكال در آزمايش فروروي نانو با استفاده از روش اجزاء محدود اويلر-لاگرانژ دلخواه

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در اين مقاله با به­ كارگيري روش اجزاء محدود اويلر-لاگرانژ دلخواه، جريان ماده و ميزان برآمدگي استخوان در آزمايش فروروي نانو با خطاي كمتر از 1% پيش­ بيني گرديد. همچنين پارامترهاي مناسب براي مدل دراكر-پراگر براي پيش­ بيني رفتار پس از تسليم استخوان كورتيكال گاوي ارائه شد، به‌طوري‌كه نتايج به‌دست‌آمده از ميزان نيروي وارده بر استخوان برحسب جابجايي ابزار فرورونده، با انحراف كمتر از 5% از نتايج آزمايشگاهي بدست آمد. همچنين نشان داده شد كه تغيير زاويه اتساع از صفر به 10 درجه تا 40% مي­تواند بيشترين نيروي وارد بر استخوان را افزايش دهد

Nano-indentation test is one of the most common method to study the material post-yielding behavior providing a suitable material model. Nowadays, this test is also used to investigate the pressure-dependent behavior and other mechanical behaviors of bone. Different material models such as Johnson-Cook, von-Mises, Drucker-Prager, and Hill models have been presented to consider the anisotropy, pressure dependency, strain rate, and temperature dependency of cortical bovine bones similar to human bone in tension and compression. In the present study, using the Arbitrary Eulerian-Lagrangian (ALE) finite element method in Abaqus software with appropriate contact conditions, the material flow and the results of bone pile-up was well predicted with an error of less than 1%. Also, suitable parameters of the extended Drucker-Prager model for predicting post-yielding bovine cortical bone behavior were presented such that the force-displacement curve of test, showed less than 5% deviation from the experimental results. The friction angle 46°, and zero-degree dilation angle along with the frictional contact conditions between the tool and the bone with a coefficient of 0.3 provided the best parameters to predict post-yielding behavior. It was also shown that changing the angle of dilation from zero to 10 degrees can increase the maximum force applied to the bone up to 40%.