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.