Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors. (September 2022)

• Record Type: Journal Article
• Authors: McMahan, Connor; Akerson, Andrew; Celli, Paolo; Audoly, Basile; Daraio, Chiara
• Is Part Of: Journal of the mechanics and physics of solids. Volume 166(2022)
• Publication Date: 2022-09
• Subjects: Effective continuum models -- Elastic stability -- Plate buckling -- Compliant structures -- Architected solids; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.104934
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: In this work, we construct an effective continuum model for architected sheets that are composed of bulky tiles connected by slender elastic joints. Due to their mesostructure, these sheets feature quasi-mechanisms — low-energy local kinematic modes that are strongly favored over other deformations. In sheets with non-uniform mesostructure, kinematic incompatibilities arise between neighboring regions, causing out-of-plane buckling. The effective continuum model is based on a geometric analysis of the sheets' unit cells and their energetically favorable modes of deformation. Its major feature is the construction of a strain energy that penalizes deviations from these preferred modes of deformation. The effect of non-periodicity is entirely described through the use of spatially varying geometric parameters in the model. Our simulations capture the out-of-plane buckling that occurs in non-periodic specimens and show good agreement with experiments. While we only consider one class of quasi-mechanisms, our modeling approach could be applied to a diverse set of shape-morphing systems that are of interest to the mechanics community.