A Low-Parametric Rhombic Microstructure Family for Irregular Lattices

Abstract

An increasingly common approach to creating spatially varying materials is to partition a shape into cells and use a parametric family of small-scale geometric structures with known effective properties to fill the cells. We propose a new approach to solving this problem for extruded, planar microstructures. We introduce cell decompositions consisting of (nearly) rhombic cells. These meshes have far greater flexibility than those with square cells in terms of approximating arbitrary shapes, and, at the same time, have a number of properties simplifying small-scale structure construction. Our main contributions include a new family of 2D cell geometry structures, explicitly parameterized by their effective Young’s moduli, Poisson’s ratios, and rhombic angle with the geometry parameters expressed directly as smooth spline functions. This family leads to smooth transitions between the tiles and can handle a broad range of rhombic cell shapes. We introduce a complete material design pipeline based on this microstructure family, composed of an algorithm to generate rhombic tessellation from quadrilateral meshes and an algorithm to synthesize the microstructure geometry. We fabricated a number of models and experimentally demonstrated how our method, in combination with material optimization, can be used to achieve the desired deformation behavior.