Data-Driven and Diversity-Enhanced Design of Heterogeneous Multiscale Structures

Chan, Yu-Chin

doi:https://doi.org/10.21985/n2-9p0v-bz53

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Data-Driven and Diversity-Enhanced Design of Heterogeneous Multiscale Structures

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The advent of metamaterials—hierarchical structures that manifest properties beyond those found in nature through geometry rather than material composition—inspired new possibilities and research in many fields. In mechanics, periodic metamaterials exhibit behaviors ranging from unprecedented compressibility to extreme stiffness. Numerous geometric classes of metamaterials with these properties have been discovered, such as re-entrant structures, chiral patterns, trusses, and isosurfaces. Nevertheless, periodic mechanical metamaterials are limited in scope and application. Instead, aperiodic systems, or heterogeneous multiscale structures wherein microstructural topologies differ from neighbor-to-neighbor, can achieve fine control over spatially varying properties, leading to even more extraordinary functionalities such as programmable deformation and crashworthiness. However, the challenges of designing these heterogeneous structures grows alongside their geometrical and behavioral complexities. Computational methods like topology optimization have risen to meet some of the hurdles, but they are restricted by the computational costs of multiscale simulations, searching through vast combinatorial design spaces, and resolving disconnected neighboring microstructures. Recent attention is now shifting to data-driven design, which utilizes datasets of unit cells, usually from only one geometric class, and their pre-computed homogenized properties to alleviate much of the computational burden. While powerful, this new paradigm is held back by often-ignored questions pertaining to the adverse effect that the diversity and quality of a dataset can have on data-driven design representation and synthesis. We propose a suite of methods that take steps toward releasing the full potential of data-driven methods, improving the diversity of metamaterials datasets to enhance the design of complex heterogeneous multiscale structures. The methods focus on a core hypothesis: that diverse subsets of unit cells, including those from different geometric classes, form the basis of scalable and general data-driven synthesis frameworks. To this end, we create an automated data selection method, METASET, that uses similarity metrics and probabilistic Determinantal Point Processes to distill subsets that are jointly diverse in shapes and properties. For the first time in metamaterials design, we validate that by eliminating redundant or biased samples, small yet diverse subsets can boost the connectivity, design performance, and scalability of data-driven search algorithms. Leveraging the ability of a diverse subset to concisely encompass a wide design space, we then create two data-driven frameworks, which utilize diverse unit cell ``basis" classes to seed low dimensional design representations, transforming the design of functionally graded structures into highly efficient and effective approaches. Unlike typical methods, ours require neither pre-defined sets of compatible basis classes nor connectivity constraints to achieve a well-connected design. In the first framework, we propose a new multiclass shape blending scheme, which generates novel microstructures as a blend of diverse basis classes. By taking the blending parameters as low dimensional design variables and optimizing their distribution throughout the global structure, we can guarantee well-connected, functionally graded designs that attain high performance across compliance minimization and programmable shape matching problems, even with a small handful of diverse basis classes. Finally, we propose a generative deep learning-based framework to expand the design freedom, generality, and efficiency even further. Data from truss and isosurface classes, traditionally expressed through very different design variables, are incorporated into a single pipeline, from the simultaneous acquisition of a diverse and high quality multiclass dataset, to the training of a multiclass Wasserstein Generative Adversarial Network that compresses the classes into a unified, 10-dimensional latent representation. With the latent variables as design variables, our framework can optimize and synthesize exceptionally smooth grading between trusses and isosurfaces while achieving lower maximum stress. Thus, we can automate, with high efficiency and generality, the decision of whether to use trusses, isosurfaces, or hybrids of both, in a design. Although our proposed methods, METASET and data-driven synthesis, are demonstrated with linear elastic mechanical applications, they are general in order to welcome the potential of future extensions to additional domains.

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