Nonlinear compressive stability of hyperelastic 2D lattices at finite volume fractions

Gore Lukas Bluhm*, Ole Sigmund, Fengwen Wang, Konstantinos Poulios

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A framework is introduced for benchmarking periodic microstructures in terms of their ability to maintain their stiffness under large deformations, accounting in a unified manner both for buckling and softening due to geometric and material nonlinearities. The proposed framework is applied to three classical 2D lattice microstructures at different volume fractions as well as to an optimized hierarchical microstructure from the literature. The high slenderness of the structure members, often assumed in analyses, is demonstrated not to be valid at volume fractions of 10% and above, with the infinitesimal volume fraction solutions underestimating the actual buckling resistance considerably. The performed analyses provide useful and quantitative insight regarding the compressive load carrying capacity of materials with a moderately dense periodic microstructure, in a rather universal and practical form.
Original languageEnglish
Article number103851
JournalJournal of the Mechanics and Physics of Solids
Volume137
Number of pages19
ISSN0022-5096
DOIs
Publication statusPublished - 2020

Keywords

  • Buckling interaction
  • Anisotropic material
  • Stability and bifurcation
  • Finite strain
  • Non-slender lattice structures

Cite this

@article{fb768e469a5e44a6a677bd23a6f4f986,
title = "Nonlinear compressive stability of hyperelastic 2D lattices at finite volume fractions",
abstract = "A framework is introduced for benchmarking periodic microstructures in terms of their ability to maintain their stiffness under large deformations, accounting in a unified manner both for buckling and softening due to geometric and material nonlinearities. The proposed framework is applied to three classical 2D lattice microstructures at different volume fractions as well as to an optimized hierarchical microstructure from the literature. The high slenderness of the structure members, often assumed in analyses, is demonstrated not to be valid at volume fractions of 10{\%} and above, with the infinitesimal volume fraction solutions underestimating the actual buckling resistance considerably. The performed analyses provide useful and quantitative insight regarding the compressive load carrying capacity of materials with a moderately dense periodic microstructure, in a rather universal and practical form.",
keywords = "Buckling interaction, Anisotropic material, Stability and bifurcation, Finite strain, Non-slender lattice structures",
author = "Bluhm, {Gore Lukas} and Ole Sigmund and Fengwen Wang and Konstantinos Poulios",
year = "2020",
doi = "10.1016/j.jmps.2019.103851",
language = "English",
volume = "137",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Pergamon Press",

}

TY - JOUR

T1 - Nonlinear compressive stability of hyperelastic 2D lattices at finite volume fractions

AU - Bluhm, Gore Lukas

AU - Sigmund, Ole

AU - Wang, Fengwen

AU - Poulios, Konstantinos

PY - 2020

Y1 - 2020

N2 - A framework is introduced for benchmarking periodic microstructures in terms of their ability to maintain their stiffness under large deformations, accounting in a unified manner both for buckling and softening due to geometric and material nonlinearities. The proposed framework is applied to three classical 2D lattice microstructures at different volume fractions as well as to an optimized hierarchical microstructure from the literature. The high slenderness of the structure members, often assumed in analyses, is demonstrated not to be valid at volume fractions of 10% and above, with the infinitesimal volume fraction solutions underestimating the actual buckling resistance considerably. The performed analyses provide useful and quantitative insight regarding the compressive load carrying capacity of materials with a moderately dense periodic microstructure, in a rather universal and practical form.

AB - A framework is introduced for benchmarking periodic microstructures in terms of their ability to maintain their stiffness under large deformations, accounting in a unified manner both for buckling and softening due to geometric and material nonlinearities. The proposed framework is applied to three classical 2D lattice microstructures at different volume fractions as well as to an optimized hierarchical microstructure from the literature. The high slenderness of the structure members, often assumed in analyses, is demonstrated not to be valid at volume fractions of 10% and above, with the infinitesimal volume fraction solutions underestimating the actual buckling resistance considerably. The performed analyses provide useful and quantitative insight regarding the compressive load carrying capacity of materials with a moderately dense periodic microstructure, in a rather universal and practical form.

KW - Buckling interaction

KW - Anisotropic material

KW - Stability and bifurcation

KW - Finite strain

KW - Non-slender lattice structures

U2 - 10.1016/j.jmps.2019.103851

DO - 10.1016/j.jmps.2019.103851

M3 - Journal article

VL - 137

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

M1 - 103851

ER -