نوع مقاله : مقاله پژوهشی
نویسندگان
دانشکده مهندسی مکانیک، دانشگاه صنعتی سهند، تبریز، ایران
چکیده
پیشنهاد و توسعه‌ی الگوریتم‌های انتگرال‌گیری زمانی در پلاستیسیته مبتنی بر هایپرالاستیسیته یا هایپرالاستوپلاستیسیته به دلیل پیچیدگی‌های موجود مانند عینیت همواره مورد توجه پژوهشگران بوده است. با تجزیه‌ی تانسور گرادیان تغییر شکل به صورت ضربی، علاوه بر هیات‌های اولیه و کنونی یک هیات محلی به نام هیات میانی یا پلاستیک به وجود می‌آید که با به‌کارگیری آن برای انتگرال‌گیری‌های زمانی، نیازی به بررسی تأثیر چرخش‌های صلب در هیات کنونی نیست و عینیت تنش کوشی با وجود محاسبه آن از پارامترهای موجود در هیات میانی، نیاز به بررسی ندارد. همچنین با تجزیه ضربی تانسور گرادیان تغییر شکل پلاستیک می‌توان برای سخت‌شوندگی سینماتیک معادلات را به گونه‌ای استخراج کرد که نیازی به بررسی عینیت نباشد. بنابراین در این مقاله، الگوریتم ارائه شده برای مدل سطح سابلودینگ بر اساس هیات میانی با اعمال تغییراتی برای مدل فون میزز ارائه شده است. علت استفاده از مدل فون میزز سادگی این مدل نسبت به مدل سطح سابلودینگ و پرکاربرد بودن این مدل در مسائل کاربردی است. همچنین به لحاظ پیاده‌سازی عددی، مدل سطح سابلودینگ نسبت به مدل فون میزز دارای پیچیدگی‌های بیشتری است. بر این اساس، مسئله تغییر شکل برش ساده در کرنش‌های الاستیکِ کوچک و بزرگ با سخت‌شوندگی‌های همسانگرد، سینماتیک و ترکیبی در پلاستیسیته بررسی شده و نتایج به‌‌دست آمده از الگوریتم انتگرال‌گیری زمانی پیشنهادی با داده‌های آزمایشگاهی و نتایج مراجع متفاوت مورد مقایسه قرار گرفته‌اند. مقایسه نتایج و داده‌های موجود نشان می‌دهد که تطابق قابل قبولی بین نتایج وجود دارد و استفاده از این مدل در مسائل کاربردی می‌تواند مورد توجه قرار گیرد.
کلیدواژه‌ها
موضوعات
عنوان مقاله [English]
Modeling Simple Shear Deformation in Hyperelastoplasticity: A Numerical Integration Algorithm in the Intermediate Configuration
نویسندگان [English]
- Reza Toluei
- Mahsa Kharazi
Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran
چکیده [English]
TThe proposal and development of time integration algorithms in hyperelastic-based plasticity or hyperelastoplasticity, are consistently required due to complex issues such as objectivity. Through the multiplicative decomposition of the deformation gradient tensor, a local configuration known as the intermediate or plastic configuration is generated alongside the reference and the current configurations. Utilizing the intermediate configuration for time integrations eliminates the need to analyze the impact of rigid rotations in the current configuration. Moreover, as the Cauchy stress is derived from parameters in the intermediate configuration, there is no necessity to assess its objectivity. By employing the multiplicative decomposition of the gradient tensor of plastic deformation, equations for kinematic hardening can be derived, eliminating the need to verify objectivity. Therefore, in this article, the algorithm for the subloading surface model, based on the intermediate configuration, is derived by adapting the von Mises model. The rationale behind employing the von Mises model lies in its simplicity compared to the subloading surface model, along with its widespread usage. Additionally, in numerical implementation, the subloading surface model is more complex than the von Mises model. Building upon this, the problem of simple shear deformation with small and large elastic strains, incorporating isotropic, kinematic, and combined hardening in plasticity, has been investigated. The obtained results have been compared with the experimental data and findings from various references. The comparison between the results presented in this article and the available data indicates agreement, suggesting the viability of employing this model in practical applications.
کلیدواژه‌ها [English]
- Hyperelastic-based plasticity
- objectivity
- time integration algorithm
- simple shear deformation
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