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Research Papers

A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties

[+] Author and Article Information
Enrui Zhang, Yuan Liu

Applied Mechanics Laboratory,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Yihui Zhang

Applied Mechanics Laboratory,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China;
Center for Flexible Electronics Technology,
Tsinghua University,
Beijing 100084, China
e-mail: yihuizhang@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 21, 2018; final manuscript received March 24, 2018; published online April 13, 2018. Editor: Yonggang Huang.

J. Appl. Mech 85(7), 071002 (Apr 13, 2018) (9 pages) Paper No: JAM-18-1162; doi: 10.1115/1.4039815 History: Received March 21, 2018; Revised March 24, 2018

Soft network materials constructed with horseshoe microstructures represent a class of bio-inspired synthetic materials that can be tailored precisely to match the nonlinear, J-shaped, stress–strain curves of human skins. Under a large level of stretching, the nonlinear deformations associated with the drastic changes of microstructure geometries can lead to an evident mechanical anisotropy, even for honeycomb and triangular lattices with a sixfold rotational symmetry. Such anisotropic mechanical responses are essential for certain targeted applications of these synthetic materials. By introducing appropriate periodic boundary conditions that apply to large deformations, this work presents an efficient computational model of soft network materials based on the analyses of representative unit cells. This model is validated through comparison of predicted deformed configurations with full-scale finite element analyses (FEA) for different loading angles and loading strains. Based on this model, the anisotropic mechanical responses, including the nonlinear stress–strain curves and Poisson's ratios, are systematically analyzed for three representative lattice topologies (square, triangular and honeycomb). An analytic solution of the geometry-based critical strain was found to show a good correspondence to the critical transition point of the calculated J-shaped stress–strain curve for different network geometries and loading angles. Furthermore, the nonlinear Poisson's ratio, which can be either negative or positive, was shown to depend highly on both the loading angle and the loading strain.

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Figures

Grahic Jump Location
Fig. 5

Results of the unit-cell FEA and full-scale FEA on the normalized distance and the direction of different cross sections with respect to the center point of the unit cell for three representative examples in Fig. 4: (a) square networks with θ = 0 deg, (b) honeycomb networks with θ = −15 deg, and (c) triangular networks with θ = 19 deg. Here, LOA and LOB are the distance between O and A, and that between O and B, as shown in Fig. 1.

Grahic Jump Location
Fig. 4

Deformed configurations based on the unit-cell FEA and full-scale FEA for the three lattice topologies: (a) square, (b) honeycomb, and (c) triangular, with various loading strains and loading angles

Grahic Jump Location
Fig. 3

Full-scale FEA results of the three respective examples under a uniaxial stretching (εxx = 60%): (a) square networks with θ = 27 deg, (b) honeycomb networks with θ = 19 deg, and (c) triangular networks with θ = 19 deg. The insets denote a magnified view of the central area of the large networks.

Grahic Jump Location
Fig. 2

Schematic illustration of the periodic boundary conditions for a unit cell of the square network materials

Grahic Jump Location
Fig. 1

Geometric construction of the soft network materials. Three different topologies are studied, including (a) square, (b) honeycomb, and (c) triangular lattices. The network materials are subject to a uniaxial loading along the horizontal direction (x-axis). Each horseshoe microstructure in the unit cells has the radius R, the arc angle γ, the width w, and the intersection angle β between OA and OB. The axis of symmetry of the unit cells has a tilted angle of θ relative to the x-axis (a, b) or y-axis (c).

Grahic Jump Location
Fig. 6

Unit-cell FEA results of (a)–(c) normalized stress–strain curves and (d)–(f) transverse–longitudinal strain curves for three lattice topologies: (a and d) square, (b and e) honeycomb, and (c and f) triangular network materials with a wide range of loading angles

Grahic Jump Location
Fig. 7

(a) Schematic illustration of the main bearing components (bold) based on the unit-cell FEA. As the applied strain reaches the mechanical critical strain, the main bearing components are almost fully unraveled. (b) Stress–strain curve and its derivative curve based on the unit-cell FEA. The points (i)–(iv) in (b) correspond to deformed states (i)–(iv) in (a). (ce) Geometry-based critical strains predicted by the analytic solutions, as compared to the mechanical critical strains based on the unit-cell FEA, for the square, honeycomb, and triangular topologies, respectively. The geometric parameters are γ = 180 deg, w/R = 0.2; and γ = 120 deg, w/R = 0.173. (fh) Unit-cell FEA results of the normalized stress of the three lattice topologies, wherein each curve shows the stress response of the same loading strain from different loading directions normalized by the stress value of a special direction.

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