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Hyper-reduction of generalized continua

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Abstract

This paper deals with the reduced order modeling of micromorphic continua. The reduced basis model relies on the proper orthogonal decomposition and the hyper-reduction. Two variants of creation of reduced bases using the proper orthogonal decomposition are explored from the perspective of additional micromorphic degrees of freedom. In the first approach, one snapshot matrix including displacement as well as micromorphic degrees of freedom is assembled. In the second approach, snapshots matrices are assembled separately for displacement and micromorphic fields and the singular value decomposition is performed on each system separately. Thereafter, the formulation is extended to the hyper-reduction method. It is shown that the formulation has the same structure as for the classical continua. The relation of higher order stresses introduced in micromorphic balance equations to creation of the reduced integration domain is examined. Finally, the method is applied to examples of microdilatation extension and clamped tension and to a size-dependent stress concentration in Cosserat elasticity. It is shown that the proposed approach leads to a good level of accuracy with significant reduction of computational time.

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Acknowledgements

This study was carried out in the framework of project MICROMORFING (ANR-14-CE07-0035-03) funded by the Agence Nationale de la Recherche (ANR, France). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Centre des Matériaux, CNRS UMR 7633, Mines, Paristech, BP 87, 91003, Evry Cedex, France

    Martin Horák, David Ryckelynck & Samuel Forest

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  1. Martin Horák
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  2. David Ryckelynck
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  3. Samuel Forest
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Correspondence to David Ryckelynck.

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Horák, M., Ryckelynck, D. & Forest, S. Hyper-reduction of generalized continua. Comput Mech 59, 753–778 (2017). https://doi.org/10.1007/s00466-016-1371-2

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  • DOI: https://doi.org/10.1007/s00466-016-1371-2

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