نویسندگان

گروه مهندسی عمران، دانشکده‌ مهندسی عمران و حمل ‌و ‌نقل، دانشگاه اصفهان، اصفهان

چکیده

پریداینامیک نسخه‌ غیرمحلی مکانیک محیط‌های پیوسته است که در آن از معادلات انتگرالی به‌جای معادلات دیفرانسیل استفاده شده است. به‌دلیل عدم استفاده از مشتقات مکانی متغیرها در روابط این تئوری، استفاده از آن برای تحلیل مسائل دارای ناپیوستگی امکان‌پذیر است. در اولین پژوهش‌های منتشر شده، از پریداینامیک برای تحلیل رشد ترک در مواد ترد استفاده شده است. با اثبات قابلیت‌های این تئوری، ایده‌‎ استفاده از آن برای بررسی رفتار مواد شبه‌ترد و تحلیل رفتار پلاستیک نیز به ‌تدریج مطرح شده است. بدین منظور، فرمول‌بندی‌ها و مدل‌های جدید مبتنی بر پریداینامیک توسعه یافته‌اند. در کنار این موارد، هزینه محاسباتی زیاد روش‌های مبتنی بر پریداینامیک همواره به‌عنوان نقطه‌ ضعف اصلی این تئوری عنوان شده است. با توسعه‌ روش‌های پریداینامیک و نیز معرفی روش‌های ترکیبی مبتنی بر پریداینامیک و تئوری‌های محلی، مشکل هزینه ‌محاسباتی روش‌های پریداینامیک تا حد زیادی رفع شده است. مقاله‌ حاضر به معرفی پریداینامیک و مدل‌های مبتنی بر آن می‌پردازد. بدین منظور، ابتدا تئوری پریداینامیک، فرمول‌بندی‌ها و روش‌های مبتنی بر آن مرور شده است. سپس در مورد نحوه‌ مدل‌سازی مواد شبه‌ترد، تعریف رفتار پلاستیک و نیز استفاده از عملگرهای دیفرانسیلی در این تئوری بحث شده است.

کلیدواژه‌ها

عنوان مقاله [English]

A Review of Peridynamics and its Applications; Part1: The Models based on Peridynamics

نویسندگان [English]

  • P. Sheikhbahaei
  • F. Mossaiby

چکیده [English]

Peridynamics is a nonlocal version of the continuum mechanics, in which partial differential equations are replaced by integro-differential ones. Due to not using spatial derivatives of the field variables, it can be applied to problems with discontinuities. In the primary studies, peridynamics has been used to simulate crack propagation in brittle materials. With proving the capabilities of peridynamics, the idea of using this theory to simulate crack propagation in quasi-brittle materials and plastic behavior has been proposed. To this end, formulations and models based on peridynamics have been developed. Meanwhile, the high computational cost of peridynamic methods is the main disadvantage of this theory. With the development of peridynamic methods and introduction of hybrid methods based on peridynamics and local theories, the computational cost of peridynamic methods has been reduced to a large extent. This paper introduces peridynamics and the models based on it. To this end, we first review peridynamics, its formulations, and the methods based on it. Then we discuss the modeling of quasi-brittle materials, simulation of plastic behavior and employing the differential operators in this theory.

کلیدواژه‌ها [English]

  • Peridynamics
  • Fracture mechanics
  • Nonlocal model
  • Crack growth
  • Damage
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