Amplitude-tuned quasi-isotropy and programmable energy absorption in a 3D auxetic metamaterial

The practical application of auxetic metamaterials is often hampered by inherent anisotropy, a critical limitation that degrades performance under multidirectional loading. To address this challenge, we propose a three-dimensional (3D) auxetic metamaterial with prominent quasi-isotropic mechanical properties. Using sinusoidal elements as fundamental building blocks, its key innovation lies in the novel spatially symmetric 3D configuration of these elements and the identified amplitude-dependent tuning mechanism. When A exceeds 1.4 mm, the structure achieves quasi-isotropy, with plateau stresses of 2.84 MPa (in-plane) and 2.93 MPa (out-of-plane). Numerical impact simulations further confirm that amplitude (A) is a pivotal design parameter for regulating the directionality of energy absorption: at A = 0.6 mm, the specific energy absorption in the out-of-plane direction reaches 13.76 J/g, a 47.9% enhancement compared to that at A = 3.0 mm. These findings form the basis of the proposed amplitude–velocity–direction framework, which systematically decouples the design space for dynamic mechanical performance by coordinating amplitude (governing stiffness and deformation mode), impact velocity (controlling inertial and strain-rate effects), and loading direction. Overall, this work establishes a versatile design paradigm for programmable auxetic metamaterials, enabling tailored applications—from satellite mounts requiring isotropic mechanical responses to blast protection devices demanding directional energy absorption.