High-performance model reduction techniques in computational multiscale homogenization

By J. A. Hernández, Javier Oliver, Alfredo Huespe, M. Caicedo, Juan Carlos Cante. 2014

189 citations recorded by the source corpus.

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 the other hand, it is shown that the standard approach of replacing the nonaffine termby an interpolant constructed using only POD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching the approximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation points are chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed in the homogenization of a highly complex porous metal material. Computed results show that computational complexity is independent of the size and geometrical complexity of the representative volume element. The speedup factor is over three orders of magnitude —as compared with finite element analysis— whereas the maximum error in stresses is less than 10%.

Subfields: Computational Theory and Mathematics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f0ab4a682689459b8f6ec980eb2b915279a306cf

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In Computational Theory and Mathematics

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics (2017, methodology): “In principle, any other hyper reduction methods can be used to overcome the aforementioned computational bottleneck: however, a substantial effort may be required in this case to achieve numerical stability [20].”
Nonlinear reduced order homogenization of materials including cohesive interfaces (2015, methodology): “, [36]).”
A PGD-based homogenization technique for the resolution of nonlinear multiscale problems (2013, methodology): “The use of this type of techniques to address homogenization is discussed in [27].”
Multiscale structural topology optimization with an approximate constitutive model for local material microstructure (2015, unknown): “Most of the existing ROMs constructed using reduction strategies such as Proper Orthogonal Decomposition (POD) [24,25], Proper Generalized Decomposition (PGD) [26–28], material map model [29,30], eigendeformation-based reduction [31,32], Nonuniform Transformation Field Analysis (NTFA) [33–36], and N”
Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method (2016, methodology): “adaptive strategies to solve the micro-scale problem only the minimum number of times necessary [93, 124], adaptive sub-incremental strategies to ensure the convergence of the multiscale solution in the presence of several sources of non-linearity [100, 110], model-order reduction techniques [41, 64”