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A Comparison Between an Embedded FE2 Approach and a TFA-Like Model

2004; Begell House; Volume: 2; Issue: 4 Linguagem: Inglês

10.1615/intjmultcompeng.v2.i4.20

1940-4352

Nicolas Carrère, Frédéric Feyel, Pascale Kanouté,

Advanced Numerical Methods in Computational Mathematics

Two multiscale models are considered in this paper: one is based on an imbricated FE2 approach, while the second rests on a transformation field analysis (TFA) framework. Both models are presented and compared. They are similar regarding the computation cost for nonlinear problems. This conclusion is not obvious since a finite element computation of the representative volume element is usually considered to be more resource consuming than a simple phenomenological model. In fact, a nonlinear TFA model is not a simple model: it involves costly operations and may be even more expensive than a direct finite element computation. Special attention is paid to the microscale spatial discretization. A new method called "subvolumes reduction" is presented to reduce the number of subvolumes used in the TFA model, while preserving a good and controlled accuracy of the results. Various discretizations of the same problem are presented to discuss this method.