A computational method for determining the linear elastic properties of 2D aperiodic lattice structures

Abstract

This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.

Mechanical characterisation of novel aperiodic lattice structures

“…Homogenized properties are then derived for the extended domain by iterative fashion. For details on the strategy, the reader is referred to earlier work by Imediegwu et al [32]. The following sections show results of this investigation with subsequent deductions.…”

“…Aperiodically-ordered lattice structures are then derived as ordered planar networks connecting the vertices for each pattern. By exploiting the numerical strategy presented by Imediegwu et al [32] for determining the effective properties of aperiodic structures, we present the direction-dependent properties of these aperiodic lattices in comparison to the well-known hexagonal lattice structure. We demonstrate that even though the feature of high rotational symmetries supports near-isotropic material behavior, the geometry of underlying prototiles constituting the lattice play a significant role in the effective moduli of the lattices.…”

A Data-Driven Constitutive Model for 3D Lattice-Structured Material Utilising an Artificial Neural Network

“…These outstanding properties include tailorable mechanical strength and stiffness [1,2], a lightweight property [3,4], excellent energy absorption ability [5,6] and impact absorption [7,8]. Therefore, lattice-structured materials have been nominated for several potential industrial applications within the aerospace, personal protective equipment, sports equipment, packaging, military and defence, and medical equipment sectors [9][10][11][12]. This makes lattice-structured material an interesting and promising area of research for material scientists and engineers, as well as product designers.…”