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Study of architectural responses of 3D periodic cellular materials

Modelling and Simulation in Materials Science and Engineering, 2013

The functional properties of periodic cellular solids such as photonic and phononic crystals, nanocrystal superlattices and foams may be tuned by an applied inhomogeneous mechanical strain. A fundamental methodology to analyse the structure of periodic cellular materials is presented here and is compared directly with indentation experiments on three-dimensional microframed polymer photonic crystals. The application of single-continuumscale finite-element modelling (FEM) was impossible due to the numerous cells involved and the intricate continuum geometry within each cell. However, a method of dual-scale FEM was implemented to provide stress and displacement values on both scales by applying an upper scale continuum FEM with reference to the lower scale continuum FEM to provide coarse-grained stressstrain relationships. Architecture and orientation dependences of the periodic porous materials on the macro-/microscopic responses were investigated under different loading conditions. Our study revealed a computational tool for exploring elastic strain engineering of photonic crystals and, more broadly, may help the design of metamaterials with mechanical controllability.

Microarchitectured cellular solids - the hunt for statically determinate periodic trusses

ZAMM, 2005

The mechanical properties of open-cell metallic foams and periodic lattice materials are explained by a structural analysis of their parent pin-jointed truss structures. A matrix method of analysis is presented in order to elucidate whether a periodic truss structure can collapse by macroscopic strain producing mechanisms, or by periodic collapse mechanisms which induce zero macroscopic strain to first order. It is shown that the planar Kagome truss is of the latter type, and is consequently stiff. The in-plane stiffness of the 2D Kagome grid and the bending stiffness of the 3D Kagome double-layer grid (KDLG) are determined for elastic members. An alternative, statically determinate, double-layer grid is derived from the octet truss, and is referred to as the modified octet truss (MOT). This structure has faces comprising a hexagonal grid and a semi-regular triangular grid, and is much less stiff than the Kagome double-layer grid. Both structures have morphing capability due to their static and kinematic determinacy.

Pattern transformation induced by elastic instability of metallic porous structures

Computational Materials Science, 2019

Uniform pattern transformation can be observed in some structures with periodic arrays of pores at a critical compressive load because of buckling of the constituents of the structures. This pattern transformation can be exploited to design structures for various potential applications. Previous studies have focused on the instability of periodic porous structures of which the base materials were elastomers, and applications of these structures may be narrow because of the elastomer limitations of low melting temperature and stiffness. In addition, material failures such as plasticity and fracture were rarely discussed in previous studies. Here, we introduce metals as the base materials for some periodic metallic porous nanostructures (PMPNs). Our molecular dynamics simulation results show that PMPNs can exhibit pattern transformation at a critical strain because of buckling. In addition, we develop a simple formulation by incorporating the effect of surface on the Euler-Bernoulli beam theory to predict the critical load for the buckling of nanostructures. The prediction of our model is in good agreement with the molecular dynamics simulation results. When the applied strain is sufficiently large, the nanoscale metals experience dislocation-medicated plasticity. We also show that the pore shape of the PMPNs strongly affects the characteristics of the periodic metallic structures including the effective Young's modulus, critical strain for micro-buckling, and critical strain for plasticity.

Compliant cellular materials with compliant porous structures: A mechanism based materials design

International Journal of Solids and Structures, 2014

Cellular materials have two important properties: structures and mechanisms. These properties have important applications in materials design; in particular, they are used to determine the modulus and yield strain. The objective of this study is to gain a better understanding of these two properties and to explore the synthesis of compliant cellular materials (CCMs) with compliant porous structures (CPSes) generated from modified hexagonal honeycombs. An in-plane constitutive CCM model is constructed using the strain energy method, which uses the deformation of hinges around holes and the rotation of links. A finite element (FE) based simulation is conducted to validate the analytical model. The moduli and yield strains of the CCMs with an aluminum alloy are about 5.8 GPa and 0.57% in one direction and about 2.9 MPa and 20% in the other direction. CCMs have extremely high positive and negative Poisson's ratios (m à xy $ AE40) due to the large rotation of the link member in the transverse direction caused by an input displacement in the longitudinal direction. CCMs also show higher moduli after contact of slit edges at the center region of the CPSes. The synthesized CPSes can also be used to design a new CCM with a Poisson's ratio of zero using a puzzle-piece CPS assembly. This paper demonstrates that compliant mesostructures can be used for next generation materials design in tailoring mechanical properties such as moduli, strength, strain, and Poisson's ratios. The proposed mesostructures can also be easily manufactured using a conventional cutting method.

Shape Design of Periodic Cellular Materials Under Cyclic Loading

Volume 5: 37th Design Automation Conference, Parts A and B, 2011

A numerical method based on asymptotic homogenization theory is presented for the design of lattice materials against fatigue failure. The method is applied to study the effect of unit cell shape on the fatigue strength of hexagonal and square lattices. Cell shapes with regular and optimized geometry are examined. A unit cell is considered to possess a regular shape if the geometric primitives defining its inner boundaries are joined with an arc fillet, whose radius is 1% of the cell length. An optimized cell shape, on the other hand, is obtained by minimizing the curvature of its interior borders, which are conceived as continuous in curvature to smooth stress localization.