Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization

Raphaël N. Glaesener, Erik A. Träff, Bastian Telgen, Renato M. Canonica, Dennis M. Kochmann*

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

    113 Downloads (Pure)

    Abstract

    Thanks to scale-bridging fabrication techniques, truss-based metamaterials have gained both popularity and complexity, ultimately resulting in structural networks whose description based on classical discrete numerical calculations becomes intractable. We here present a framework for the efficient and accurate simulation of large periodic three-dimensional (3D) truss networks undergoing nonlinear deformation (accounting for linear elastic beams undergoing finite rotations). Although the focus is on elastic beams, the method is sufficiently general to extend to inelastic material behavior. Our approach is based on a continuum representation of the truss (and its numerical implementation via finite elements) whose constitutive behavior is obtained from on-the-fly periodic homogenization at the microstructural unit cell level. We pursue a semi-analytical strategy (previously reported only in two dimensions) which admits the analytical calculation of consistent tangents for convergent implicit solution schemes; the extension to 3D – through the addition of torsional deformation modes and the handling of 3D rotations – results in a powerful tool for the prediction of the complex mechanical response of large structural networks. We validate the small-strain response by comparison to analytical solutions, followed by finite-strain benchmarks that compare simulation results to those of fully-resolved discrete calculations. The homogenization of beam unit cells results in a regularized macroscale model with an intrinsic length scale, which manifests especially when modeling bifurcations or localization. We finally apply our approach to macroscopic boundary value problems involving complex-shaped truss metamaterials (with truss unit cells near the body's boundary mapped onto a conformal surface), which reveal only an insignificant effect of boundary layers on the overall mechanical response, again supporting the applicability of our homogenization approach.

    Original languageEnglish
    JournalInternational Journal of Solids and Structures
    Volume206
    Pages (from-to)101-113
    ISSN0020-7683
    DOIs
    Publication statusPublished - 2020

    Keywords

    • Elasticity
    • Finite deformation
    • Finite element method
    • Homogenization
    • Metamaterial
    • Truss

    Fingerprint

    Dive into the research topics of 'Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization'. Together they form a unique fingerprint.

    Cite this