Session: 01-02-03: Phononic Crystals and Metamaterials

Paper Number: 147050

147050 - Accelerating Band Gap Predictions in Mechanical Metamaterials: A Novel Framework for Managing Geometrical Uncertainties 

The advent of additive manufacturing has revolutionized the field of material science, leading to the development of dynamic mechanical metamaterials with unique properties tailored for specific applications such as vibration isolation, wave propagation control, and energy absorption. One critical feature of these metamaterials is their ability to exhibit band gaps—frequency ranges where the dynamic response is attenuated. However, a prevailing challenge within the industry is managing manufacturing uncertainties which significantly impact the predictability and effectiveness of these band gaps.

This paper introduces a novel computational framework that expedites the prediction and assessment of band gaps in metamaterials considering geometric uncertainties inherent to the manufacturing process. The framework combines a perturbation method focusing on fixed-interface component eigenvalues with an advanced surrogate modeling technique based on Kriging. This combination offers a fast and accurate estimation of band gap changes due to variabilities in material geometry without necessitating a complete re-computation of the metamaterial's global mass and stiffness matrices involved in standard finite element methods.

The framework is equipped with a baseline model derived from nominal geometric parameters, taking advantage of standard Craig-Bampton reduction for substructure analysis. The developed surrogate model is then trained to predict subsequent fixed-interface eigenvalues for any new geometrical parameter sets. This predictive capability hinges on a perturbation scheme bolstered by an upgraded parametrization approach that addresses multiple model parameters concurrently. The explicit inclusion of geometrical uncertainties and their spatial correlations is a novel aspect of our methodology, enhancing the accuracy of band gap determinations under manufacturing tolerances.

Our approach is rigorously validated through three collected benchmark problems. The first of these benchmarks examines the response of one-dimensional metamaterials to the perturbation approach focusing on Bragg and sub-Bragg band gaps. Then, a plate-like metamaterial model (second Benchmark) serves the dual purpose of validating the combined perturbation and surrogate modeling framework while also demonstrating the method's proficiency in uncertainty propagation analysis. The final benchmark elevates the framework's application to a two-dimensional lattice metamaterial, employing the methodology for comprehensive uncertainty quantification in the context of geometrical imperfections.

The results underscore significant computational efficiencies, which have the potential to drastically enhance the reliability and optimization processes for metamaterial design and application. The potential benefits extend across various engineering domains, including civil, mechanical, and aerospace industries, where precision in band gap control is crucial. The benchmarks presented are compared with a high-definition model, where the performance in terms of precision and computational time are studied.

Presenting Author: Rafael Ruiz University of Michigan-Dearborn

Presenting Author Biography: Dr. Rafael O. Ruiz joined the Department of Mechanical Engineering at the University of Michigan-Dearborn in August 2022 as an Assistant Professor, following nearly six years at the University of Chile, where he was an Assistant Professor in the Department of Civil Engineering. Dr. Ruiz received a double Ph.D. in 2016 from the University of Notre Dame and the Pontificia Universidad Católica de Chile. At the University of Chile, Dr. Ruiz led the operation of the Uncertainty Quantification Group, emphasizing the development of strategies to support designing under uncertainty, risk-informed optimization, and system identification employing Bayesian paradigms.

Currently, his research focuses on the design/modeling/optimization of mechanical devices for vibration control based on multi-functional metamaterials and piezoelectric energy harvesters, incorporating advanced computational techniques based on surrogate models to account for uncertainties in the mechanical properties.

Authors:

Jesus Pereira University of Michigan-Dearborn
Rafael Ruiz University of Michigan-Dearborn