A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations

By J. Michel, Pierre Suquet. 2016

87 citations recorded by the source corpus.

Abstract In 2003 the authors proposed a model-reduction technique, called the Nonuniform Transformation Field Analysis (NTFA), based on a decomposition of the local fields of internal variables on a reduced basis of modes, to analyze the effective response of composite materials. The present study extends and improves on this approach in different directions. It is first shown that when the constitutive relations of the constituents derive from two potentials, this structure is passed to the NTFA model. Another structure-preserving model, the hybrid NTFA model of Fritzen and Leuschner, is analyzed and found to differ (slightly) from the primal NTFA model (it does not exhibit the same variational upper bound character). To avoid the “on-line” computation of local fields required by the hybrid model, new reduced evolution equations for the reduced variables are proposed, based on an expansion to second order (TSO) of the potential of the hybrid model. The coarse dynamics can then be entirely expressed in terms of quantities which can be pre-computed once for all. Roughly speaking, these pre-computed quantities depend only on the average and fluctuations per phase of the modes and of the associated stress fields. The accuracy of the new NTFA-TSO model is assessed by comparison with full-field simulations. The acceleration provided by the new coarse dynamics over the full-field computations (and over the hybrid model) is then spectacular, larger by three orders of magnitude than the acceleration due to the sole reduction of unknowns.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/622def37bcd818e6a9561fdcddb89e9725b83358

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials (2018, methodology): “However, both NTFA and POD methods require extensive a priori simulations for interpolating nonlinear inelastic material behaviors, and the offline stages need to be recomputed for different combinations of material constituents.”