This paper presents a means of reducing the computational cost of finite element (FE) simulations coupled to polycrystal plasticity theory. One typically assumes that a polycrystal with a large number of grains underlies every integration point of the FE mesh. Instead, it is suggested here using reduced samplings of grains which differ from one integration point to another. On average, every set of 5 to 25 finite elements contains a variety of lattice orientations that is representative of the macroscopic texture. The model is applied to deep-drawing of a cylindrical cup made of steel. In a first set of simulations, grains are assigned orientations representative of a cold rolling texture and the “earing” profile is compared to experiment. In a second set of simulations, lattice orientations are random and an isotropic deep-drawing result is expected. It is demonstrated that using a minimum of 20 grains per integration point allows properly predicting the final shape of the cup and the texture development.
Nadal, E.; Beringhier, M.; Ródenas García, JJ.; Fuenmayor Fernández, FJ. (2015). A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework. Computational Mechanics. 55 (2)
AbstractToday industries do not only require fast simulation techniques but also verification techniques for the simulations. The Proper Generalized Decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.
Purpose -The purpose of this paper is to solve non-linear parametric thermal models defined in degenerated geometries, such as plate and shell geometries. Design/methodology/approach -The work presented in this paper is based in a combination of the proper generalized decomposition (PGD) that proceeds to a separated representation of the involved fields and advanced non-linear solvers. A particular emphasis is put on the asymptotic numerical method. Findings -The authors demonstrate that this approach is valid for computing the solution of challenging thermal models and parametric models. Originality/value -This is the first time that PGD is combined with advanced non-linear solvers in the context of non-linear transient parametric thermal models.
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