Applied Mathematics Colloquium - Linear elastic properties of 2D aperiodically-ordered lattice structures

Speaker: Chikwesiri Imediegwu (The Open University)

Abstract: Additive manufacturing has introduced new possibilities with respect to the types of shapes that are physically realizable. Material can be deposited only where it is needed and, taking cues from natural bone-like materials, components can be designed with internal structures that have material in place to support necessary forces, but empty space elsewhere. The focus of such research has been on cubic or hexagonal lattices; periodic structures which are well understood but give rise to undesirable mechanical anisotropy. Aperiodically-ordered structures (structures that exhibit order but without periodicity) offer a fascinating alternative. Such structures promise superior mechanical behavior because they can realise higher symmetries which are incompatible with periodic lattices. They could potentially expand the space of material properties whilst avoiding undesirable material anisotropies associated with lattice-periodic structures. However, there is little research to confirm the mechanical properties of aperiodically-ordered lattice structures.

In this work, the linear elastic properties of aperiodic lattice structures are investigated. Aperiodic structures are generated algorithmically on a structured mesh, by an element-based material assignment, using specific substitution strategies. An adaptation to Asymptotic Expansion Homogenisation (AEH) is implemented to derive the elasticity matrix for each aperiodic structure. 

The isotropic performance of the aperiodic structures is apparent in the analyses, and the derived framework as well as its results are validated by comparison to periodic structures with documented elastic properties. The rotation symmetries associated with a range of aperiodic structures are also verified. These investigations validate the existence of higher material symmetries in aperiodically-ordered lattice structures and supports their use as superior alternatives to periodic structures in aerospace and bio-engineering applications.

Experimental validation of numerical simulations of this work is well underway.