A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

Qiang Ma, Huanyu Cheng, Kyung In Jang, Haiwen Luan, Keh Chih Hwang, John A. Rogers, Yonggang Huang, Yihui Zhang

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

Original languageEnglish (US)
Pages (from-to)179-202
Number of pages24
JournalJournal of the Mechanics and Physics of Solids
Volume90
DOIs
StatePublished - May 1 2016

Fingerprint

Stress-strain curves
Mechanics
microstructure
Microstructure
Topology
Poisson ratio
curves
topology
Skin
Biomimetic materials
Biological materials
Porosity
Elastic moduli
Mechanical properties
tangents
Geometry
compatibility
modulus of elasticity
arcs
mechanical properties

Keywords

  • Bio-inspired materials
  • Finite deformation
  • Hierarchical design
  • Horseshoe microstructure
  • Lattice materials
  • Stress-strain curves

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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title = "A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures",
abstract = "Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.",
keywords = "Bio-inspired materials, Finite deformation, Hierarchical design, Horseshoe microstructure, Lattice materials, Stress-strain curves",
author = "Qiang Ma and Huanyu Cheng and Jang, {Kyung In} and Haiwen Luan and Hwang, {Keh Chih} and Rogers, {John A.} and Yonggang Huang and Yihui Zhang",
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A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures. / Ma, Qiang; Cheng, Huanyu; Jang, Kyung In; Luan, Haiwen; Hwang, Keh Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui.

In: Journal of the Mechanics and Physics of Solids, Vol. 90, 01.05.2016, p. 179-202.

Research output: Contribution to journalArticle

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