CAREER: Optimal Design of Robust Nonlinear Elastic Metamaterials

About This Grant

This project will develop computational tools for designing new classes of high-performance mechanical metamaterials. Mechanical metamaterials are elastic materials engineered at the microstructure level to exhibit unique properties not found in nature. They have the potential to unlock new levels of performance in application domains like soft robotics, deployable structures, athletic gear, and prosthetics. However, designing microstructure geometries to create desired material properties poses significant challenges, especially for applications where the structures can undergo substantial deformations and self contact. In these settings, computationally intensive nonlinear simulation models must be used, and designing materials with controlled properties over their full range of possible deformations is prohibitively expensive with existing algorithms. The core aim of this research is to develop computational techniques to dramatically accelerate the simulation and design process for elastic metamaterials, making it practical to solve this challenging and important design problem. The project will also develop techniques for ensuring that the optimized metamaterials are as durable as possible and can be reliably manufactured on consumer-level 3D printers. The project will furthermore enhance STEM education by integrating these cutting-edge research topics into classroom lectures and facilitating outreach events where high school, undergraduate, and graduate students gain hands-on experience with computational design, numerical modeling and fabrication. The project will build a new computational framework for (1) fast periodic homogenization of nonlinear elasticity and (2) optimal design of elastic metamaterials to exhibit target properties over large deformations (finite regions of strain space). The central technical contribution is a suite of novel data-driven acceleration techniques based on adaptive high-dimensional interpolation, smart sampling, and machine learning that will enable solving metamaterial characterization problems to controlled accuracy at practical computational expense. This fast characterization method will be wrapped within an inverse design algorithm that is formulated as a shape optimization over a rich design space of smooth parametric lattice geometries. The design algorithm will incorporate physics-based manufacturability constraints and stress minimization objectives to ensure that optimized parts are robust to forces experienced during fabrication and use. The design tool will be evaluated on the task of creating metamaterials to emulate existing material models as well as producing exotic material behaviors like multistability and jamming. The performance of generated metamaterials will be confirmed with physical experiments, and the proposed acceleration schemes will be assessed on large-scale benchmark datasets that will be created as part of the project. Finally, a basic multiscale design tool for creating compliant mechanisms composed of spatially graded lattices will be developed using the generated metamaterials. The research will deliver powerful and accessible open-source computational design software, fast solvers for nonconvex optimization and sparse linear systems, and benchmark datasets to foster evaluation of future metamaterial design work. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.