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

• Published in: Journal of strain analysis for engineering design 2023-10, Vol.58 (7), p.590-602
• Main Authors: Imediegwu, Chikwesiri, Grimm, Uwe, Moat, Richard, Jowers, Iestyn
• Format: Article
• Language: English
• Subjects: Aerospace engineering; Aerospace industry; Bioengineering; Boundary conditions; Cellular structure; Elastic properties; Homogenization; Periodic structures; Unit cell
• ISSN: 0309-3247; 2041-3130
• DOI: 10.1177/03093247221150666

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.