مروری بر تئوری پریداینامیک و کاربردهای آن؛ بخش اول: مدل های مبتنی بر پریداینامیک
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: Persian
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JR_JCME-41-1_001
تاریخ نمایه سازی: 12 آبان 1401
Abstract:
پریداینامیک نسخه غیرمحلی مکانیک محیط های پیوسته است که در آن از معادلات انتگرالی به جای معادلات دیفرانسیل استفاده شده است. به دلیل عدم استفاده از مشتقات مکانی متغیرها در روابط این تئوری، استفاده از آن برای تحلیل مسائل دارای ناپیوستگی امکان پذیر است. در اولین پژوهش های منتشر شده، از پریداینامیک برای تحلیل رشد ترک در مواد ترد استفاده شده است. با اثبات قابلیت های این تئوری، ایده استفاده از آن برای بررسی رفتار مواد شبه ترد و تحلیل رفتار پلاستیک نیز به تدریج مطرح شده است. بدین منظور، فرمول بندی ها و مدل های جدید مبتنی بر پریداینامیک توسعه یافته اند. در کنار این موارد، هزینه محاسباتی زیاد روش های مبتنی بر پریداینامیک همواره به عنوان نقطه ضعف اصلی این تئوری عنوان شده است. با توسعه روش های پریداینامیک و نیز معرفی روش های ترکیبی مبتنی بر پریداینامیک و تئوری های محلی، مشکل هزینه محاسباتی روش های پریداینامیک تا حد زیادی رفع شده است. مقاله حاضر به معرفی پریداینامیک و مدل های مبتنی بر آن می پردازد. بدین منظور، ابتدا تئوری پریداینامیک، فرمول بندی ها و روش های مبتنی بر آن مرور شده است. سپس در مورد نحوه مدل سازی مواد شبه ترد، تعریف رفتار پلاستیک و نیز استفاده از عملگرهای دیفرانسیلی در این تئوری بحث شده است.
Keywords:
Peridynamics , Fracture mechanics , Nonlocal model , Crack growth , Damage , پریداینامیک , مکانیک شکست , مدل غیرمحلی , رشد ترک , آسیب
Authors
پوریا شیخ بهائی
Department of Civil Engineering, University of Isfahan, Isfahan, Iran
فرشید مسیبی
Department of Civil Engineering, University of Isfahan, Isfahan, Iran
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