Session: 13-19-01: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials I

Paper Number: 166246

Engineering Poisson’s Ratio in Periodic Two-Phase Mechanical Metamaterials via a Deep Learning Framework 

The Poisson’s ratio, a critical mechanical property defining a material’s bi-axial deformation behaviors under stress, plays a pivotal role in engineering applications ranging from aerospace to biomedical devices. Traditional methods for designing materials with tailored Poisson’s ratios often rely on mechanism-based approaches or trial-and-error experimentation or computationally expensive simulations, limiting efficiency and scalability. This study proposes a deep learning (DL)-driven framework to systematically explore and optimize the Poisson’s ratio of composite materials by integrating finite element analysis (FEA) with neural networks.

Specifically, the study focuses on one type of two-phase mechanical metamaterial composed of two phases with distinct Young’s moduli: phase A (high stiffness) and phase B (low stiffness). The spatial material distribution is governed by level-set designs of periodic structures with a set of periodic function controlled by tunable parameters, such as amplitude, frequency, and phase shift. By varying these parameters, diverse periodic microstructures are generated, and their effective Poisson’s ratios are systematically evaluated via FE simulations.

Then, a dual-component deep learning architecture is developed, comprising a forward model and an inverse model, to establish a bidirectional relationship between geometric parameters and Poisson’s ratio. The forward model, a convolutional neural network (CNN), maps the material distribution pattern to the corresponding Poisson’s ratio. Training data for this model is generated by coupling parametric variations of the periodic function with FE predictions. Once the forward model achieves sufficient accuracy (validated by low mean squared error loss), it is employed to rapidly synthesize additional virtual data points, augmenting the dataset for training the inverse model. The inverse model, designed as a generative adversarial network (GAN), accepts a target Poisson’s ratio as input and predicts the optimal periodic function parameters required to achieve it. This two-stage approach circumvents data scarcity and enhances the robustness of the inverse design process.

The trained forward model demonstrates high predictive accuracy (>99%) on test data for conventional Poisson’s ratios (e.g., 0.2–0.8), effectively reducing reliance on iterative FEA simulations. However, the inverse model currently generates parameter sets for target Poisson’s ratios within a limited range (0.2–0.8) due to the absence of auxetic configurations (negative Poisson’s ratio) in the training dataset. Analysis suggests this limitation stems from the initial parameter space of the periodic function, which prioritizes moderate amplitude and frequency combinations to ensure structural stability during FEA. The workflow validates the potential of deep learning in mapping parametric relationships for conventional composites, laying a foundation for future extensions to programmable metamaterials.

Presenting Author: Yunzheng Yang Nothrastern University

Presenting Author Biography: Completed a bachelor's degree at Sun Yat-sen University, obtained a master's degree at Northeastern University, and currently pursuing a Ph.D. at Northeastern University.

Authors:

Yunzheng Yang Nothrastern University
Yaning Li Northeastern University