LatticeMech: A discrete mechanics code to compute the effective static properties of 2D metamaterial structures

Abstract In the current work, we provide a Bernoulli beam-mechanics based code for the computation of the effective static properties of two-dimensional, metamaterial lattice structures. The software makes use of the asymptotic expansion form of the inner kinematic and static variables of the lattice structure, exploiting its spatial periodicity. As such, it makes use of the smallest repetitive material unit, substantially reducing the cost of full-scale computations. For the identification of the basic cell’s parameters, a dedicated Graphical User Interface (GUI) is provided. The Python code computes the complete linear elasticity stiffness and compliance matrix based on Cauchy mechanics, providing access to all relevant material moduli. In particular, the normal, shear and bulk moduli, as well as the Poisson’s ratio and relative density values of the architectured material structure are elaborated. Its formulation favors the analysis of a wide range of lattice designs, establishing a fundamental link between micro- and macro-scale material properties.

[1]  Sergei Khakalo,et al.  Anisotropic strain gradient thermoelasticity for cellular structures: Plate models, homogenization and isogeometric analysis , 2020, Journal of the Mechanics and Physics of Solids.

[2]  J. Ganghoffer,et al.  Equivalent mechanical properties of auxetic lattices from discrete homogenization , 2012 .

[3]  Alessandro Reali,et al.  GeoPDEs: A research tool for Isogeometric Analysis of PDEs , 2011, Adv. Eng. Softw..

[4]  R. Lakes,et al.  Properties of a chiral honeycomb with a poisson's ratio of — 1 , 1997 .

[5]  Massimo Ruzzene,et al.  Analysis of in-plane wave propagation in hexagonal and re-entrant lattices , 2008 .

[6]  D. McDowell,et al.  Multifunctional design of two-dimensional cellular materials with tailored mesostructure , 2009 .

[7]  D. Fang,et al.  Mechanical Properties of two novel planar lattice structures , 2008 .

[8]  Y. Xie,et al.  Topological design of microstructures of cellular materials for maximum bulk or shear modulus , 2011 .

[9]  Thomas C. Hull,et al.  Using origami design principles to fold reprogrammable mechanical metamaterials , 2014, Science.

[10]  Yunan Prawoto,et al.  Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio , 2012 .

[11]  Andrea Bacigalupo,et al.  Auxetic anti-tetrachiral materials: Equivalent elastic properties and frequency band-gaps , 2015 .

[12]  N. Auffray,et al.  Continuum modelling of frequency dependent acoustic beam focussing and steering in hexagonal lattices , 2019, European Journal of Mechanics - A/Solids.

[13]  R. Lakes,et al.  Poisson's ratio and modern materials , 2011, Nature Materials.

[14]  J. Ganghoffer,et al.  The role of non-slender inner structural designs on the linear and non-linear wave propagation attributes of periodic, two-dimensional architectured materials , 2019, Journal of Sound and Vibration.

[15]  David R. Smith,et al.  Metamaterials: Theory, Design, and Applications , 2009 .

[16]  M. Ruzzene,et al.  Floquet–Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems ☆ , 2011 .

[17]  Xiang Zhang,et al.  Metamaterials: a new frontier of science and technology. , 2011, Chemical Society reviews.

[18]  A. Bacigalupo,et al.  Simplified modelling of chiral lattice materials with local resonators , 2015, 1508.01624.

[19]  Z. Ahmad,et al.  Analytical solution and finite element approach to the dense re-entrant unit cells of auxetic structures , 2019, Acta Mechanica.

[20]  Viacheslav Balobanov,et al.  Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics , 2018, International Journal of Engineering Science.

[21]  N. Karathanasopoulos,et al.  Wave propagation characteristics of periodic structures accounting for the effect of their higher order inner material kinematics , 2018, Journal of Sound and Vibration.

[22]  Hong Hu,et al.  A review on auxetic structures and polymeric materials , 2010 .

[23]  F. D. Reis,et al.  Computing the effective bulk and normal to shear properties of common two-dimensional architectured materials , 2018, Computational Materials Science.

[24]  Pierre Seppecher,et al.  Strain gradient and generalized continua obtained by homogenizing frame lattices , 2018, Mathematics and Mechanics of Complex Systems.

[25]  T. Tancogne-Dejean,et al.  Stiffness and Strength of Hexachiral Honeycomb-Like Metamaterials , 2019, Journal of Applied Mechanics.

[26]  Zheng-Dong Ma,et al.  Theoretical prediction of mechanical properties of 3D printed Kagome honeycombs and its experimental evaluation , 2019, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.