Optimization clustering technique for PieceWise Uniform Transformation Field Analysis homogenization of viscoplastic composites

Aim of the present study is to propose an enhanced method for the domain decomposition (clustering) of the representative volume element (RVE) of composite materials to be used with homogenization techniques, based on the PieceWise Uniform Transformation Field Analysis (PWUTFA). With PWUTFA, both constitutive and evolutive equations for the constituents of the composite material are written in terms of averages in each cluster; moreover, it is not required to solve via FEM the nonlinear micro-mechanical problem, allowing to drastically reduce the number of internal variables. PWUTFA is founded on the idea that it is possible to divide the RVE into large subdomains (clusters) that should group together finite elements having, under any applied loading condition, the most similar values of strain. Accordingly, in this study a multi-objective optimization-based approach is proposed with the aim to simultaneously reduce both the error in the approximation of the strain fields and the number of clusters in which the domain is decomposed. Different clustering solutions, obtained through the proposed optimization approach are analyzed, and the corresponding mechanical responses are compared with the ones obtained by the finite element analysis and by uniform transformation field analysis.