Explicit parametric solutions of lattice structures with Proper Generalized Decomposition (PGD): Applications to the design of 3D-printed architectured materials

Author (s): Sibileau, A.; García-González, A.; Auricchio, F.; Morganti, S. and Díez, P.
Journal: Computational Mechanics

Volume: 62
Pages: 871 – 891
Date: 2018

Abstract:
Architectured materials (or metamaterials) are constituted by a
unit-cell with a complex structural design repeated periodically forming a bulk
material with emergent mechanical properties. One may obtain specic macro-
scale (or bulk) properties in the resulting architectured material by properly
designing the unit-cell. Typically, this is stated as an optimal design problem
in which the parameters describing the shape and mechanical properties of
the unit-cell are selected in order to produce the desired bulk characteristics.
This is especially pertinent due to the ease manufacturing of these complex
structures with 3D printers. The Proper Generalized Decomposition (PGD)
provides explicit parametic solutions of parametric PDEs. Here, the same ideas
are used to obtain parametric solutions of the algebraic equations arising from
lattice structural models. Once the explicit parametric solution is available, the
optimal design problem is a simple post-process. The same strategy is applied
in the numerical illustrations, rst to a unit-cell (and then homogenized with
periodicity conditions), and in a second phase to the complete structure of a
lattice material specimen.

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Bibtex:

@article{CM-SGAMD-18}
        Author = {Sibileau, A. and García-González, A. and Auricchio, F. and Morganti, S. and Díez, P.},
        Title = {Explicit parametric solutions of lattice structures with Proper Generalized Decomposition (PGD): Applications to the design of 3D-printed architectured materials},
         Fjournal = {Computational Mechanics},
        Journal = {Comput. Mech.},
        Volume = {62},
        Number = {4},
        Pages = {871–891},
        Year = {2018},
        Doi = {110.1007/s00466-017-1534-9},
}