Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices

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Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, background): “With regard to this modelling issue, there is a large interest in the literature for strain-gradient homogenization of heterogeneous structures [12,25,23,24,61,60,51].”
Linear pantographic sheets: Asymptotic micro-macro models identification (2017, methodology): “This paper, differently to what done in [83], considers the case of extensible fibers and gives a more solid foundation to and generalizes the heuristic results presented in [82], based on an accurate analysis of the different and relative order of magnitude of involved physical phenomena.”