Data and scripts from: A Computational Framework to design 3D stiffness gradient acoustic metamaterials for impedance matching

The dataset consists of MATLAB .mat files containing matrices that define the geometry and material properties of acoustic metamaterial unit cells. These unit cells were generated using custom MATLAB code with COMSOL Multiphysics, as part of a computational framework for designing 3D stiffness-gradient acoustic metamaterials for impedance matching.

The data represent both periodic boundary-compatible and randomly formed unit cell geometries, with associated effective material properties. The files can be used to reproduce and further explore the designs reported in the manuscript.

Methodological Context

Software used: MATLAB (data generation and storage) and COMSOL Multiphysics (physics-based simulations).

Data type: Numerical matrices storing geometric parameters and effective acoustic properties of unit cells.

Purpose: Inputs for optimization and analysis of acoustic metamaterials with controlled impedance and stiffness gradients.

Reproducibility: The dataset is directly linked to the dual-algorithm design framework (GenUnit based on NSGA-II and MLMatch based on differentiable ML) described in the manuscript.

Abstract:
Acoustic waves play a crucial role in various applications, including medical imaging, non-destructive testing, and sonar systems. One of the significant challenges in these applications is impedance matching, which is essential for minimizing reflections and maximizing the transfer of acoustic energy between different media. Acoustic metamaterials offer a promising solution to this challenge. In addition to impedance control, gradient stiffness can enhance structural efficiency and enable spatial control of wave propagation, making it a valuable feature in acoustic metamaterial design. In this paper, we present our developed computational method to design 3D stiffness gradient acoustic metamaterials for impedance matching. The key steps in our approach include generating initial designs using a periodic covariance function to provide unit cells that are both periodic on the boundaries and randomly formed inside the unit cell. Furthermore, we integrated manufacturing constraints into the design process, ensuring that the structures are interconnected for fabrication. We propose two computational optimization algorithms: GenUnit, based on a non-dominated sorting genetic algorithm (NSGA-II), and MLMatch, which leverages differentiable machine learning. The two approaches are not separate contributions but complementary components of a unified framework. GenUnit requires no training data and directly interfaces with physics-based simulations, making it highly accurate but slower for large-scale exploration. In contrast, MLMatch is data-hungry during training but, once trained, enables near-instantaneous inference and broad design-space coverage. Together, they form a hybrid strategy: MLMatch rapidly explores the global design space, and GenUnit provides local refinement with high-fidelity accuracy. This balance between training cost, inference time, and precision is the motivation for including both methods in the same study. We applied this dual-algorithm framework to generate two steel-based metamaterial designs that match the acoustic impedance of water while exhibiting a controlled gradient in stiffness (from stiff to soft). The stiffness gradient is particularly advantageous in applications where one side of the structure must interface with soft or sensitive surfaces, such as human tissue or delicate components. This work paves the way for improved materials in various acoustic applications, particularly in ultrasound devices, by providing better impedance matching and thereby improving the efficiency of acoustic energy transfer.