آنالیز دوبعدی میکرومکانیکی شکست در بافت متراکم استخوان انسان به روش میدان فاز

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان

چکیده

استخوان دارای ساختار سلسله مراتبی است که با آرایش پیچیده‌ در مقیاس‌های طولی متفاوت دارای قابلیت‌های مکانیکی، شیمیایی و زیستی منحصربه-فردی است. برای شناخت خصوصیات مکانیکی استخوان، باید ساختار سلسله‌مراتبی و همچنین ترکیب استخوان در نظر گرفته شود. در پژوهش حاضر مدل‌های عددی دوبعدی از ریزساختار بافت متراکم استخوانی به صورت کامپوزیت‌های سه‌فازی و چهار‌فازی به کمک اسکرپیت‌نویسی به زبان پایتون ایجاد شد و به عنوان ورودی به نرم‌افزار آباکوس داده شد. سپس به کمک فرمول‌بندی روش میدان فاز به تحلیل شکست در برش عرضی بافت متراکم تحت بارگذاری کششی پرداخته شد. در ابتدا داده‌های مربوط به استخوان لگن گاو به کامپوزیت سه‌فازی نسبت داده شد و پس از اعتبارسنجی روش میدان فاز پیاده‌سازی شده، شبیه‌سازی اصلی برای مدل‌های سه‌فازی و چهار‌فازی با داده‌های مربوط به بافت متراکم استخوان انسان انجام گردید. سپس برای هر یک از مدل‌ها، نمودار تنش-کرنش در حالت بارگذاری کششی استخراج شد. خروجی‌های بدست آمده روی دو مدل عددی با یکدیگر متفاوت بود. این تفاوت نشان‌دهنده نقش مهم ریزساختار بافت استخوان در شکست است. نتایج نشان داد که استحکام نهایی مدل سه‌فازی از مدل چهارفازی بیش‌تر است. وجود خطوط سیمانی به عنوان یک فاز مادی ضعیف‌تر نسبت به سایر فاز‌های مادی موجب این اختلاف شد. در مقابل، انعطاف‌پذیری مدل چهار‌فازی نسبت به مدل سه‌فازی بیشتر شد. در این مطالعه، نقش خطوط سیمانی در افزایش انعطاف‌پذیری و کاهش استحکام نهایی نشان داده شد. این ویژگی می‌تواند مکانیزمی برای انحراف و یا حتی توقف ترک در مدل ساختاری باشد. همچنین در پایان کار، اثر افزایش تخلخل بر کاهش استحکام نهایی استخوان بررسی شد و نشان داده شد که با افزایش تخلخل، استحکام نهایی به طور چشمگیری کاهش پیدا خواهد کرد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Two-dimensional micromechanical analysis of fracture in human cortical bone tissue using the phase-field method

نویسندگان [English]

  • Mohammad Hossein Shojaiefard
  • Mohammad Silani
  • Mahdi Javanbakht
  • Hossein Jafarzadeh
Department of Mechanical Engineering, Isfahan University of Technology
چکیده [English]

Bone has a hierarchical structure which features a complex arrangement at different length scales, endowing it with unique mechanical, chemical, and biological capabilities. To understand the mechanical properties of bone, one must consider its hierarchical structure as well as its composition. In the current research, two-dimensional numerical models of the cortical tissue microstructure of bone were created as three-phase and four-phase composites by scripting in Python, and were imported into the Abaqus software. Subsequently, fracture analysis in the transverse section of dense tissue under tensile loading was conducted using the phase-field method formulation. Initially, as a benchmark problem, data related to bovine pelvic bone was attributed to a three-phase composite, and after validating the implemented phase-field method, the primary simulation was performed for three-phase and four-phase models, with data related to human cortical bone tissue. Then, for each of the simulated three-phase and four phase models with human data, a stress-strain diagram in the tensile loading state was extracted. The outputs, obtained from the simulation performed on the two numerical models, differed from each other. The difference indicates the significant role of the bone tissue microstructure in fracture. The results showed that the ultimate strength of the three-phase model is greater than that of the four-phase model. The presence of cement lines as a weaker material phase compared to other material phases caused this difference. Conversely, the flexibility of the four-phase model was greater than that of the three-phase model. This study demonstrated the role of cement lines in increasing flexibility and reducing ultimate strength. This feature could be a mechanism for deviation or even stopping a crack in the structural model. Additionally, at the end of the work, the effect of increased porosity on the reduction of the final strength of the bone was examined, and it was shown that with increased porosity, the final strength will significantly decrease.

کلیدواژه‌ها [English]

  • Cortical bone tissue
  • microstructure
  • fracture
  • phase-field method
  • three-phase composite
  • four-phase composite
  • cement line
  • porosity

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