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

مراجع

  1. Consensus, N., ‟Osteoporosis prevention, Diagnosis, And Therapy”, NIH Consensus Statement, Vol. 17, pp. 1–45, 2000.
  2. Cooper, C., Campion, G., and Melton, Lr., ‟Hip fractures In The Elderly: A World-Wide Projection”, Osteoporosis International”, Vol. 2, pp. 285–289, 1992.
  3. Gharib, H., Papini, E., Paschke, R., Duick, D. S., Valcavi, R., Hegedüs, L., Vitti, P., ‟American Association of Clinical Endocrinologists, Associazione Medici Endocrinologi, and European Thyroid Association Medical Guidelines for Clinical Practice for the Diagnosis and Management of Thyroid Nodules: Executive Summary of Recommendations”. Journal of Endocrinological Investigation, Vol. 33, pp. 287–291, 2010.
  4. Fahimfar, N., Noorali, S., Yousefi, S., Gharibzadeh, S., Shafiee, G., Panahi, N., Sanjari, M., Heshmat, R., Sharifi, F., Mehrdad, N., Rareisi, A., Nabipour, I., Larijani, B., Ostovar, A., ‟Prevalence of osteoporosis among the elderly population of Iran”, Archives of Osteoporosis, Vol. 16, pp. 1–10, 2021.
  5. Abdel-Wahab, A. A., and Silberschmidt, V. V., ‟Numerical Modelling of Impact Fracture of Cortical Bone Tissue Using X-FEM”, Journal of Theoretical and Applied Mechanics, Vol. 49, No. 3, pp. 599–619, 2011.
  6. Ascenzi, M. G., and Roe, A. K., ‟The Osteon: The Micromechanical Unit of Compact Bone”. Front Biosci, Vol. 17, No. 524, pp. 1551, 2012.
  7. Vallet-Regi, M., and González-Calbet, J. M., ‟Calcium Phosphates as Substitution of Bone Tissues”. Progress in Solid State Chemistry, Vol. 32, No. 1-2, pp. 1–31, 2004.
  8. Jee, W., Integrated Bone Tissue Physiology: Anatomy and Physiology in: Cowin, SC. Bone Mechanics Handbook, CRC, New York, 2001.
  9. Allahyari, P., Silani, M., Yaghoubi, V., Milovanovic, P., Schmidt, F., Busse, B., and Qwamizadeh, M., ‟On the Fracture Behavior of Cortical Bone Microstructure: The Effects of Morphology and Material Characteristics of Bone Structural Components”, Journal of the Mechanical Behavior of Biomedical Materials, Vol. 137, pp. 105530, 2023.
  10. Dong, X. N., Zhang, X., and Guo, X. E., ‟Interfacial Strength of Cement Lines in Human Cortical Bone”, Molecular & Cellular Biomechanics, Vol. 2, No. 2, p. 63, 2005.
  11. Bourdin, B., Francfort, G. A., and Marigo, J. J., ‟Numerical experiments in Revisited Brittle Fracture”. Journal of the Mechanics and Physics of Solids, Vol. 48, No. 4, pp. 797–826, 2000.
  12. Gravouil, A., Moës, N., and Belytschko, T., Non‐Planar 3D Crack Growth By the Extended Finite Element and Level Sets—Part II: Level Set Update. International Journal for Numerical Methods in Engineering, Vol. 53, No. 11, pp. 2569–2586, 2002.
  13. Moës, N., Dolbow, J., and Belytschko, T., ‟A Finite Element Method for Crack Growth Without Remeshing”, International Journal for Numerical Methods in Engineering, Vol. 46, No. 1, pp. 131–150, 2012.
  14. Peng, G. L., and Wang, Y. H., ‟A Node Split Method for Crack Growth Problem”, Applied Mechanics and Materials, Applied Mechanics and Materials, 2012.
  15. Qin, R., and Bhadeshia, H., ‟Phase Field Method”, Materials Science And Technology, Vol. 26, No. 7, pp. 803–81, 2010.
  16. Jafarzadeh, H., Shchyglo, O., and Steinbach, I., ‟Multi-Phase-Field Approach to Fracture Demonstrating the Role of Solid-Solid Interface Energy on Crack Propagation”, International Journal of Fracture, Vol. 245, pp. 75–87, 2024.
  17. Anderson, T. L., Fracture Mechanics: Fundamentals And Applications, CRC press, 2017.
  18. Borden, M. J., Verhoosel, C. V., Scott, M. A., Hughes, T. J., and Landis, C. M., ‟A Phase-Field Description of Dynamic Brittle Fracture”, Computer Methods in Applied Mechanics and Engineering, Vol. 217, pp. 77–95, 2012.
  19. Hofacker, M., and Miehe, C., ‟Continuum Phase Field Modeling of Dynamic Fracture: Variational Principles and Staggered FE Implementation”, International Journal of Fracture, Vol. 178, No. 1, pp. 113–129, 2012.
  20. Miehe, C., Hofacker, M., and Welschinger, F., ‟A Phase Field Model for Rate-Independent Crack propagation: Robust Algorithmic Implementation Based on Operator Splits”, Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 45-48, pp. 2765–2778, 2012.
  21. Mousavion, M., Mashayekhi, M., Jamshidian, M., Badnava, H., ‟Implementation of the phase-field method for brittle fracture and application to porous structures‟, Modares Mechanical Engineering, 18 (7) :217-225, 2018.
  22. Miehe, C., Aldakheel, F., and Raina, A., ‟Phase Field Modeling Of Ductile Fracture At Finite Strains: A Variational Gradient-Extended Plasticity-Damage Theory”, International Journal of Plasticity, Vol. 84, pp. 1–32, 2016.
  23. Ambati, M., Gerasimov, T., and De Lorenzis, L., ‟Phase-Field Modeling of Ductile Fracture”, Computational Mechanics, Vol. 55, No. 5, pp. 1017–1040, 2015.
  24. Ambati, M., Kruse, R., and De Lorenzis, L., ‟A Phase-Field Model for Ductile Fracture at Finite Strains and Its Experimental Verification”, Computational Mechanics, Vol. 57, No. 1, pp. 149–167, 2016.
  25. Badnava, H., Etemadi, E., and Msekh, M. A., ‟A Phase Field Model for Rate-Dependent Ductile Fracture”, Metals, Vol. 7, No. 5, p. 180, 2017.
  26. Badnava, H., "Ductile fracture modelling based on the Drucker-Prager plasticity and phase field approach", Modares Mechanical Engineering, 18 (3) :351-360, 2018.
  27. Msekh, M. A., Silani, M., Jamshidian, M., Areias, P., Zhuang, X., Zi, G., He, P., Rabczuk, T., ‟Predictions of J Integral And Tensile Strength Of Clay/Epoxy Nanocomposites Material Using Phase Field Model” Composites Part B: Engineering, Vol. 93, pp. 97–114, 2016.
  28. Arash, B., Exner, W., and Rolfes, R., ‟A Finite Deformation Phase-Field Fracture Model for the Thermo-Viscoelastic Analysis of Polymer Nanocomposites” Computer Methods in Applied Mechanics and Engineering, Vol. 381, pp. 113821, 2021.
  29. Li, S., Abdel-Wahab, A., Demirci, E., and Silberschmidt, V. V., ‟Fracture Process in Cortical Bone: X-FEM Analysis of Microstructured Models”, Fracture phenomena in nature and technology, Springer, pp. 43-55, 2014.
  30. Idkaidek, A., and Jasiuk, I., ‟Cortical Bone Fracture Analysis Using XFEM–case Study”, International Journal for Numerical Methods in Biomedical Engineering, Vol. 33, No. 4, pp. e2809, 2017.
  31. Wang, M., Li, S., vom Scheidt, A., Qwamizadeh, M., Busse, B, and Silberschmidt, V. V., ‟Numerical Study of Crack Initiation and Growth in Human Cortical Bone: Effect of Micro-Morphology”, Engineering Fracture Mechanics, Vol. 232, No. 107051, 2020.
  32. Gustafsson, A., Wallin, M., and Isaksson, H., ‟Age-Related Properties at the Microscale Affect Crack Propagation in Cortical Bone”, Journal of Biomechanics, Vol. 95, No. 109326, 2019.
  33. Levitas, V. I., Jafarzadeh, H., Farrahi, G. H., and Javanbakht, M., ‟Thermodynamically Consistent and Scale-Dependent Phase Field Approach for Crack Propagation Allowing for Surface Stresses”, International Journal of Plasticity, Vol. 111, pp. 1–35, 2018.
  34. Abdel-Wahab, A. A., Maligno, A. R., and Silberschmidt, V. V., ‟Micro-Scale Modelling of Bovine Cortical Bone Fracture: Analysis of Crack Propagation and Microstructure Using X-FEM” Computational Materials Science, Vol. 52, No. 1, pp. 128–135, 2012.
  35. Nalla, R., Stölken, J., Kinney, J., and Ritchie, R., ‟Fracture in Human Cortical Bone: Local Fracture Criteria and Toughening Mechanisms” Journal of Biomechanics, Vol. 38, No. 7, pp. 1517–1525, 2005.
  36. Jafarzadeh, H., Farrahi, G. H., Levitas, V. I., and Javanbakht, M., ‟Phase Field Theory for Fracture at Large Strains Including Surface Stresses” International Journal of Engineering Science, Vol. 178, No. 103732, pp. 66–77, 2022.
  37. Mohsin, S., O'Brien, F. J., and Lee, T. C., ‟Osteonal Crack Barriers in Ovine Compact Bone” Journal of Anatomy, Vol. 208, No. 1, pp. 81–89, 2006.

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