Predictive strain-gradient homogenization of a pantographic material with compliant junctions

Baptiste Durand (1) , Arthur Lebée (1) , Pierre Seppecher (2) , Karam Sab (1)

1 NAVIER UMR 8205 - Laboratoire Navier
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

This paper presents an architectured material featuring significant strain-gradient effects and called pantographic material. It is easy to fabricate, being a plate made of a single and continuous linear elastic material containing voids. The pattern consists of triangles connected by thin junctions and arranged in such a way that two floppy strain modes are present. A homogenization scheme based on the two-scale asymptotic expansion is suggested, keeping only significant strain-gradient contributions in the homogenized energy through an adequate projection. The predictions from the homogenization scheme are validated against a full-scale simulation and yield very good L2 error estimates whereas the classical first-gradient homogenization fails. Furthermore, the relative position of the unit cell in the full-scale computation does not have a significant influence on the quality of the prediction. Finally, with an adequate choice of scalings between scale separation and junction thinness, it is possible to ensure that strains as well as displacements in compliant junctions remain bounded while preserving macroscopic strain-gradient effects.

Mots clés: Strain-gradient continuum; Higher-order homogenization; Metamaterial; Compliant mechanism

Domaines: Mécanique des matériaux [physics.class-ph]

Baptiste Durand, Arthur Lebée, Pierre Seppecher, Karam Sab. Predictive strain-gradient homogenization of a pantographic material with compliant junctions. Journal of the Mechanics and Physics of Solids, 2022, 160, ⟨10.1016/j.jmps.2021.104773⟩. ⟨hal-03529670⟩