Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium

By Francesco dell'Isola, Ivan Giorgio, Marek Pawlikowski, Nicola Rizzi. Proceedings of the Royal Society A, 2016

442 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1fd2f622eff82645fd3e8bb4126e41502a83be04

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Citations in the corpus

Linear pantographic sheets: Asymptotic micro-macro models identification (2017, methodology): “This procedure has been described in general already in the works by Piola [40] (he seems to us to be among the first scientists having introduced such a heuristic method of homogenization (see [36, 83])): however he applied it specifically only to the case of fluids.”
A Survey of Modeling of Lattice Structures Fabricated by Additive Manufacturing (2017, methodology): “To investigate the large deformations of extensible beams and lattice structures, a heuristic homogenization technique was proposed by considering a discrete spring model to formulate a continuum fully nonlinear beam model Corresponding author: Yaoyao Fiona Zhao 17 [75].”
Pantographic metamaterials: an example of mathematically driven design and of its technological challenges (2018, methodology): “14 Equilibrium shape and strain energy density when a shear displacement is prescribed [13] (color figure online)”
Mechanical metamaterials: a state of the art (2019, methodology): “and using Piola’s ansatz (see dell’Isola [124] for more details), we get the following continuum energy”
Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models (2016, methodology): “The metamaterial conceived in [2,5,9,40] has been designed to be governed, when considering macroscopic behavior, as a second gradient continuum and to have an enhanced extensional toughness: it has been actually synthesized exploiting the novel possibilities given by 3D printing technologies.”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, methodology): “Their most distinctive feature is that they do not enter the framework of Cauchy stress theory (the internal mechanical interactions are not described by a Cauchy stress tensor) [dell’Isola et al. 2015b; 2016b; 2017].”
Qualitative pivot damage analysis in aluminum printed pantographic sheets: Numerics and experiments (2017, methodology): “(2) will be remarkable with longer pivots and it will be negligible with shorter pivots (this case is, infact, the one considered in [5]).”