Linear pantographic sheets: Asymptotic micro-macro models identification

By C. Boutin, Francesco dell'Isola, Ivan Giorgio, Luca Placidi. 2017

190 citations recorded by the source corpus.

In this paper, we consider linear pantographic sheets which in their natural configuration are con- stituted by two orthogonal arrays of straight fibers interconnected by internal pivots. We introduce a continuous model by means of a micro-macro identification procedure based on the asymptotic homogenization method of discrete media. The rescaling of the mechanical properties and of the deformation measures is calibrated in order to complies with the specific kinematics imposed by the quasi-inextensibility of the fibers together with the large pantographic deformability. The ob- tained high order continuum model shows interesting and exotic features, related to its extreme anisotropy but also to the sub-coercivity of its deformation energy. Some first numerical simula- tions are presented, showing that the model can account for experimental uncommon phenomena occuring in pantographic sheets. The paper focuses on the precise analysis and the understanding of the effective behaviour based on a well-calibration of the extension and bending phenomena arising at the local scale. In an upcoming work the analysis will be extended to oblique arrays, to some analytical solutions to proposed equations and to some further applications.

Subfields: Control and Systems Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/397c40961cafa7596a8dea657f987b48c2de10c5

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In Control and Systems Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions (2017, methodology): “see also [12] for a direct derivation of this energy based on a homogenization procedure exploiting the micro-balance of force and momentum.”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, background): “Some discrete structures [6], [5], [20], [76], [21] lead to a more general second gradient energy.”
Pantographic metamaterials: an example of mathematically driven design and of its technological challenges (2018, methodology): “[50], numerical solutions using the strain energy density (42) are presented for a circular pantographic specimen and three exemplary problems: bias extension, shear, and rotation tests (Fig.”