High-performance model reduction techniques in computational multiscale homogenization

J HERNANDEZ; J. OLIVER,; A E. HUESPE; M. CAICEDO; J.C. CANTE

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

ELSEVIER SCIENCE SA

Lugar: Amsterdam; Año: 2014 vol. 276 p. 149 - 189

0045-7825

A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version ?that accounts for the elastic/inelastic character of the solution ? of the Proper Orthogonal Decomposition (POD). On theother hand, it is shown that the standard approach of replacing the nonaffine term by an interpolant constructed using onlyPOD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching theapproximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation pointsare chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed inthe homogenization of a highly complex porous metal material. Computed results show that computational complexityis independent of the size and geometrical complexity of the Representative Volume Element. The speedup factor is overthree orders of magnitude ? as compared with finite element analysis ? whereas the maximum error in stresses is less than10%.