مروری بر روش‌های چندمقیاسی همزمان در تحلیل مسائل ناپیوستگی در مقیاس ریز

نوع مقاله : مقاله مروری

نویسندگان

1 آزمایشگاه محاسبات سریع، دانشکده مهندسی عمران، دانشکدگان فنی، دانشگاه تهران

2 دانشکده مهندسی عمران، دانشگاه تهران

چکیده

مدلسازی مسائل ترک و ناپیوستگی اهمیت بسزایی در صنایع مختلف دارد و از دیرباز مورد توجه بوده است. مدلسازی رفتار ترک در مقیاس‌های مختلف بویژه مقیاس‌های اتمی می‌تواند باعث شناخته شدن بهتر رفتار ریز ساختار ماده و پیش بینی رفتار آن در مقیاس‌های بزرگتر گردد. از سوی دیگر مدلسازی مبتنی بر مقیاس‌های اتمی بدلیل بیشتر بودن تعداد درجات آزادی نیاز به صرف هزینه محاسباتی بسیار زیادی در مقایسه با سایر روش‌ها دارد. مجموعه روش‌های چندمقیاسی همزمان برای حل این مشکلات بوجود آمده‌اند و به عنوان تکنیک‌های قابل پذیرش برای مدلسازی ناپیوستگی در دهه‌های اخیر مورد استقبال محققین قرار گرفته است. مطالعات نشان می‌دهد روش‌های چندمقیاسی همزمان توانسته‌اند کلیه رفتارهای ریز مقیاس در مقابل تحریک‌های مکانیکی را شبیه‌سازی نمایند و ضمن دستیابی به تطابق مناسبی با مدل‌های آزمایشگاهی، ارتباط پیوسته با مقیاس‌های بزرگتر را برقرار کنند. در مطالعه حاضر، روش‌های چندمقیاسی همزمان همگن سازی و دامنه مجزا که در طول چند دهه گذشته در مدلسازی مسائل ناپیوستگی مورد استفاده قرار گرفته‌اند بررسی شده اند. جهت ایجاد زمینه مناسب برای مقایسه روش‌های توسعه داده شده در طول چد دهه گذشته، مسئله گسترش ترک لبه بازطراحی و مدلسازی شده است و نتایج حاصل از شبیه‌سازی و دقت محاسباتی مهم‌ترین روش‌ها با یکدیگر مقایسه شده اند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A review of concurrent multiscale methods for the analysis of fine scale discontinuity problems

نویسندگان [English]

  • Omid Alizadeh 1
  • S. Mohammadi 2
1 High Performance Computing Lab, School of Civil Engineering, College of Engineering, University of Tehran
2
چکیده [English]

Modeling of crack and discontinuity related problems has had a great influence on numerous industries for a long time. Simulation of discontinuity behavior in different scales, especially in atomistic scales, can lead to better insight of the crack/discontinuity initiation and propagation phenomena and prediction of its behavior in larger scales. On the other hand, modeling based on fully refined scales requires huge computational effort compared to other methods due to the higher number of degrees of freedom. Concurrent multiscale methods have been developed to overcome the high computational cost issues of refined models, while preserving sufficient accuracy. Studies have shown that concurrent multiscale methods are capable of simulating all atomic behaviors in order to establish a compatible solution with larger scales, and to accurately resemble the laboratory results. In the present review, concurrent multiscale methods, which could be categorized into homogenization and partitioned-domain methods, are briefly investigated and compared. These methods have been widely used for modelling of cracks, discontinuities and impurities in different types of problems in the past two decades. To create a suitable basis for comparing the main concurrent methods, the problem of edge crack propagation is redesigned and modeled, and the simulation results and their computational accuracy are compared.

کلیدواژه‌ها [English]

  • Concurrent multiscale methods
  • homogenization
  • discrete domain methods
  • discontinuity

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