IJE TRANSACTIONS A: Basics Vol. 22, No. 4 (November 2009) 359-368   

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M.H. Farahani and N. Amanifard*
Department of Mechanical Engineering, Faculty of Engineering, University of Guilan
P.O. Box 3756, Rasht, Iran
mh.farahani@gmail.com - namanif@guilan.ac.ir

S.M. Hosseini
Department of Chemical and Biological Engineering, University of British Columbia
Vancouver, British Columbia V6T 1Z3, Canada

* Corresponding Author
( Received: April 07, 2008 – Accepted in Revised Form: July 02, 2009 )

Abstract    In this paper, a new smoothed particle hydrodynamics (SPH) algorithm for simulation of elastic-plastic deformation of solids was proposed. The key point was that materials under highvelocity impact (HVI) behave like fluids. This led to propose a method which was similar to the socalled SPH-projection method, in which the momentum equations are solved as the governing equations. The method consisted of three steps. In the first step, a temporary velocity field was provided according to the relevant body forces. This velocity field was renewed in the second step to include the viscosity effect. Unlike the standard SPH method for elastic-plastic simulations, a Poisson equation was employed in the third step as an alternative for the equation of state in order to evaluate pressure by projecting the provisional velocity. This Poisson equation considered a trade-off between density and pressure which was utilized in the third step to impose the incompressibility effect. To illustrate the accuracy of this method a HVI problem was simulated. Results showed a good agreement with other previous works.


Keywords    Smoothed Particle Hydrodynamic (SPH), High Velocity Impact (HVI), Projection Method, Meshfree Method


چکیده    در اين مقاله الگوريتم جديدي بر اساس هيدروديناميک ذرات متصل (SPH) براي شبيه سازي تغيير شکل هاي الاستيک-پلاستيک جامدات ارائه شده است. نکته کليدي اين است که مواد در ضربه سرعت بالا (HVI) رفتاري مانند سيالات از خود نشان مي دهند. اين ديدگاه به ارائه روشي منجر شده است که به روش تصويري شباهت دارد و در آن معادلات ممنتوم به عنوان معادلات حاکم حل مي شوند. روش ارائه شده از سه گام تشکيل شده است. در گام نخست، ميدان سرعت موقتي با توجه به نيروهاي بدني مربوط ايجاد مي شود. اين ميدان سرعت در گام دوم با در نظر گرفتن اثر لزجت تجديد مي شود. برخلاف روش استاندارد SPH براي شبيه سازي هاي الاستيک-پلاستيک، از يک معادله پواسون در گام سوم به عنوان جايگزيني براي معادله حالت براي محاسبه فشار، با تصوير کردن سرعت موقتي، استفاده مي شود. اين معادله پواسون موازنه اي را بين چگالي و فشار ايجاد مي کند که از آن در گام سوم براي عمل تراکم ناپذيري استفاده مي شود. براي نشان دادن درستي اين روش يک مسئله HVI شبيه سازي شده است. نتايج توافق خوبي را با کارهاي گذشته نشان مي دهد.


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