Compressive properties of parametrically optimised mechanical metamaterials based on 3D projections of 4D geometries

Tensile Properties of 3D‐Projected 4‐Polytopes: A New Class of Mechanical Metamaterial

“…Parametric design variables for 5-, 8-, 16-, and 24-cell designs as illustrated in Figure 4, adapted from ref. [40]. bottom of the unit cell (location of the encastre boundary condition (BC) in Figure 9).…”

“…Summary of the parameters used in genetic algorithm setup, adapted from ref. [40]. q is the number of parametric design variables (genes).…”

“…[7,31] Such approaches include evolutionary algorithms, [33,34] as well as Bayesian optimization, [20,32,35] gradientdescent, [36][37][38] and neural-network-powered techniques. [7,31,39] Following from our previous work, [40] this paper focuses on 3D-projected 4D polytopes (4-polytopes) that have inherently similar fractal substructures with superior mechanical properties. [41][42][43][44] The 3D-projected 4-polytopes have geometrical features which are self-repeating and hierarchical, benefiting from multiple symmetry planes within the polytope, and as such show great potential in applications where high global stiffness and lightweightness are required.…”

“…[41][42][43][44] The 3D-projected 4-polytopes have geometrical features which are self-repeating and hierarchical, benefiting from multiple symmetry planes within the polytope, and as such show great potential in applications where high global stiffness and lightweightness are required. [41,44,45] While our previous work [40] considered the effects of compression on parametrically optimized 3D-projected 4D polytopes, this paper will apply an optimization framework powered by a single objective evolutionary algorithm to enhance their specific tensile stiffnesses. In addition, we discuss how maximizing the specific tensile stiffness affects other mechanical properties of these metamaterials.…”

Improved mechanical performance of quasi-cubic lattice metamaterials with asymmetric joints

“…In the present paper, we focus on the strut-based artificial cellular structures -hereafter referred to as lattice metamaterials 4 . Modern 3d-printing technologies allow to produce the lattice metamaterials with complex geometry of the unit cells that provides their unique mechanical properties such as the ultra-high and tailorable specific stiffness and strength 5,6 , high impact strength [7][8][9] and wide band gaps in the dynamic response [10][11][12] , negative Poisson's ratio, thermal expansion or stiffness [13][14][15] , pronounced non-classical Cosserat-type and Mindlin-type macroscale behavoir [16][17][18][19] , etc. The design of the unit cells in the lattice structures are usually defines the position, size and orientation of the struts to provide some desired topology and related macroscopic response such that the stretch-dominated behavior [20][21][22] , the quasi-isotropic averaged properties 23,24 , the prescribed anisotropy and the symmetric groups 25,26 or the functionally graded structure 27,28 .…”