شبيه‌سازي فرايندهاي با تغيير شكل‌هاي بزرگ با استفاده از روش اجزا محدود ALE

SIMULATION OF LARGE DEFORMATION PROCESSES USING ALE FINITE ELEMENT METHOD

در اين نوشتار تحليل اجزا محدود تغيير شكل موضعي در ميله‌ي تحت كشش و همچنين تغيير شكل كرنش صفحه‌يي ورق به‌وسيله‌ي دو سنبه‌ي تخت و متقابل براساس الگوريتم ALE در نرم‌افزار ABAQUS 6.7 بررسي شده است. فرايند تغيير شكل كرنش صفحه‌يي ورق به‌وسيله‌ي دو سنبه‌ي تخت و متقابل با سطوح تماس بدون اصطكاك شبيه‌سازي شده است. در آغاز اين فرايند بدون در نظر گرفتن اثرات نرخ كرنش شبيه‌سازي شده و سپس با در نظر گرفتن يك ماده وابسته به نرخ كرنش براي ورق، اثرات نرخ كرنش بر چگونگي شكل‌دهي ورق لحاظ شده است. براي نشان‌دادن قابليت الگوريتم ALE در شبيه‌سازي مسايل با تغيير شكل‌هاي بزرگ، نتايج به دست آمده از اين روش با نتايج روش لاگرانژي مقايسه و برتري اين روش نشان داده شده است. نتايج اين شبيه‌سازي با نتايج موجود در مقالات مقايسه شده كه مطابقت خوبي مشاهده مي‌شود.

In the present study, the local deformation of a cylindrical bar under uniaxial extension, and, also, the plane strain deformation of shell with two flat and reciprocal punches, were simulated via the decoupled ALE (Arbitrary Lagrangian Eulerian) finite element formulation in ABAQUS/Explicit code. In the ALE formulation, a reference computational domain is introduced and the finite element mesh is neither attached to the material nor fixed in space, so that the motion of the mesh is independent of that of the material. So, the mesh is managed by a procedure that tries to minimize mesh distortions and/or concentrate the mesh in a particular region. As a result, the ALE formulation can handle path-dependent material behavior and free surface conditions, while maintaining mesh fineness. An operator split procedure, a common and efficient choice in ALE analysis, is used to treat the independent mesh-material motion. Each time increment is divided into a Lagrangian phase considering material effects, which is done with the explicit time integration formulation, followed by an Eulerian phase, where the mesh smoothing is occurred, subsequently, taking into account the convective effects by solving the convection equation. The second-order Van Leer algorithm is employed to solve the convection equation. The mesh motion strategy is performed according to the mesh spatial constraints and volume smoothing method compatible with the problem type. For verifying the ALE finite element model, the local deformation of a cylindrical bar under uniaxial extension was simulated. The results were compared with reported ALE results in literature and good agreement was observed. In addition, the merits of the method for large deformation problems were discussed and the results were compared with those predicted by purely Lagrangian formulations. Although both results were almost the same, a remarkable decrease in simulation time was achieved using the ALE method. Frictionless contact is postulated in the analysis of the plane strain deformation of shell with two flat and reciprocal punches. Firstly, the problem was solved without considering strain rate effects. However, strain rate effects and dynamic effects due to high punch velocity were also investigated for a strain rate dependent material. It has been demonstrated that the inertia effects increase when the punch velocity becomes larger, resulting in different final shapes of the work-piece from those with low punch velocity. From the analyzed plane strain problem using an uncoupled ALE approach, the predicted punch load values and other comparison parameters are compatible with the coupled ones mentioned earlier in the literature.