12 octobre 2020 /
Workshop Matherials : Model-Reduction in nonlinear Micromechanics of Materials
Title: Model-Reduction in nonlinear Micromechanics of Materials
Pierre Suquet (Laboratoire de Mécanique et d’Acoustique, Marseille – Académie des Sciences). Joint work with J.C. Michel.
A common practice in structural problems involving heterogeneous materials with well separated scales, is to use homogenized, or effective, constitutive relations. In linear elasticity the structure of the homogenized constitutive relations is strictly preserved in the change of scales. The linear effective properties can be computed once for all by solving a finite number of unit-cell problems.
Unfortunately there is no exact scale-decoupling in multiscale nonlinear problems which would allow one to solve only a few unit-cell problems and then use them subsequently at a larger scale. Computational approaches developed to investigate the response of representative volume elements along specific loading paths, do not provide constitutive relations. Most of the huge body of information generated in the course of these costly computations is often lost.
Model reduction techniques may be used to exploit the information generated along such computations and, at the same time, to account for the commonly observed patterning of the local plastic strain field. A model (called NTFA for Nonuniform Transformation Field Analysis) will be developed and illustrated in this talk, with the aim of preserving the underlying variational structure of the constitutive relations, while using approximations which are common in nonlinear homogenization.
The seminar will take place by visio-conference, via Zoom, starting from 11h30. Please subscribe to the mailing list at firstname.lastname@example.org to be kept aware of the connection information.
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12 octobre 2020
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