Near-Isotropic, Extreme-Stiffness, Continuous 3D Mechanical Metamaterial Sequences Using Implicit Neural Representation

Abstract

Mechanical metamaterials represent a distinct category of engineered materials characterized by their tailored density distributions to have unique properties. It is challenging to create continuous density distributions to design a smooth mechanical metamaterial sequence in which each metamaterial possesses stiffness close to the theoretical limit in all directions. This study proposes three near-isotropic, extreme-stiffness, and continuous 3D mechanical metamaterial sequences by combining topology optimization and data-driven design. Through innovative structural design, the sequences achieve over 98% of the Hashin–Shtrikman upper bounds in the most unfavorable direction. This performance spans a relative density range of 0.2–1, surpassing previous designs, which fall short at medium and higher densities. Moreover, the metamaterial sequence is innovatively represented by the implicit neural function; thus, it is resolution-free to exhibit continuously varying densities. Experimental validation demonstrates the manufacturability and high stiffness of the three sequences.