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For over three decades, the materials tetrahedron has captured the essence of materials science and engineering with its interdependent elements of processing, structure, properties, and performance. As modern computational and statistical techniques usher in a new paradigm of data-intensive scientific research and discovery, the rate at which the field of materials science and engineering capitalizes on these advances hinges on collaboration between numerous stakeholders. Here, we provide a contemporary extension to the classic materials tetrahedron with a dual framework—adapted from the concept of a “digital twin”—which offers a nexus joining materials science and information science. We believe this high-level framework, the materials–information twin tetrahedra (MITT), will provide stakeholders with a platform to contextualize, translate, and direct efforts in the pursuit of propelling materials science and technology forward.

This article provides a contemporary reimagination of the classic materials tetrahedron by augmenting it with parallel notions from information science. Since the materials tetrahedron (processing, structure, properties, performance) made its first debut, advances in computational and informational tools have transformed the landscape and outlook of materials research and development. Drawing inspiration from the notion of a digital twin, the materials–information twin tetrahedra (MITT) framework captures a holistic perspective of materials science andmore »engineering in the presence of modern digital tools and infrastructures. This high-level framework incorporates sustainability and FAIR data principles (Findable, Accessible, Interoperable, Reusable)—factors that recognize how systems impact and interact with other systems—in addition to the data and information flows that play a pivotal role in knowledge generation. The goal of the MITT framework is to give stakeholders from academia, industry, and government a communication tool for focusing efforts around the design, development, and deployment of materials in the years ahead.

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Graph databases capture richly linked domain knowledge by integrating heterogeneous data and metadata into a unified representation. Here, we present the use of bespoke, interactive data graphics (bar charts, scatter plots, etc.) for visual exploration of a knowledge graph. By modeling a chart as a set of metadata that describes semantic context (SPARQL query) separately from visual context (Vega-Lite specification), we leverage the high-level, declarative nature of the SPARQL and Vega-Lite grammars to concisely specify web-based, interactive data graphics synchronized to a knowledge graph. Resources with dereferenceable URIs (uniform resource identifiers) can employ the hyperlink encoding channel or image marks in Vega-Lite to amplify the information content of a given data graphic, and published charts populate a browsable gallery of the database. We discuss design considerations that arise in relation to portability, persistence, and performance. Altogether, this pairing of SPARQL and Vega-Lite—demonstrated here in the domain of polymer nanocomposite materials science—offers an extensible approach to FAIR (findable, accessible, interoperable, reusable) scientific data visualization within a knowledge graph framework.

The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples revealmore »that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.

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A strategy for developing irregular materials can lead to a wide range of functional properties.

An object’s interior material properties, while invisible to the human eye, determine motion observed on its surface. We propose an approach that esti- mates heterogeneous material properties of an object directly from a monoc- ular video of its surface vibrations. Specifically, we estimate Young’s modulus and density throughout a 3D object with known geometry. Knowledge of how these values change across the object is useful for characterizing defects and simulating how the object will interact with different environments. Traditional non-destructive testing approaches, which generally estimate homogenized material properties or the presence of defects, are expensive and use specialized instruments. We propose an approach that leverages monocular video to (1) measure an object’s sub-pixel motion and decompose this motion into image-space modes, and (2) directly infer spatially-varying Young’s modulus and density values from the observed image-space modes. On both simulated and real videos, we demonstrate that our approach is able to image material properties simply by analyzing surface motion. In particular, our method allows us to identify unseen defects on a 2D drum head from real, high-speed video.

Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to design optical, thermal, and electric cloaks. However, they are not applicable in designing mechanical cloaks, since continuum-mechanics equations are not form invariant under general coordinate transformations. As a result, existing design methods for mechanical cloaks have so far been limited to a narrow selection of voids with simple shapes. To address this challenge, we present a systematic, data-driven design approach to create mechanical cloaks composed of aperiodic metamaterials using a large precomputed unit cell database. Our method is flexible to allow the design of cloaks with various boundary conditions, multiple loadings, different shapes and numbers of voids, and different homogeneous surroundings. It enables a concurrent optimization of both topology and properties distribution of the cloak. Compared to conventional fixed-shape solutions, this results in an overall better cloaking performance and offers unparalleled versatility. Experimental measurements on additively manufactured structures further confirm the validity of the proposed approach. Our research illustrates the benefits of data-driven approaches in quickly responding to new design scenarios and resolving the computational challenge associated with multiscale designs ofmore »functional structures. It could be generalized to accommodate other applications that require heterogeneous property distribution, such as soft robots and implants design.« less

Abstract Scientific and engineering problems often require the use of artificial intelligence to aid understanding and the search for promising designs. While Gaussian processes (GP) stand out as easy-to-use and interpretable learners, they have difficulties in accommodating big data sets, categorical inputs, and multiple responses, which has become a common challenge for a growing number of data-driven design applications. In this paper, we propose a GP model that utilizes latent variables and functions obtained through variational inference to address the aforementioned challenges simultaneously. The method is built upon the latent-variable Gaussian process (LVGP) model where categorical factors are mapped into a continuous latent space to enable GP modeling of mixed-variable data sets. By extending variational inference to LVGP models, the large training data set is replaced by a small set of inducing points to address the scalability issue. Output response vectors are represented by a linear combination of independent latent functions, forming a flexible kernel structure to handle multiple responses that might have distinct behaviors. Comparative studies demonstrate that the proposed method scales well for large data sets with over 104 data points, while outperforming state-of-the-art machine learning methods without requiring much hyperparameter tuning. In addition, an interpretable latent spacemore »is obtained to draw insights into the effect of categorical factors, such as those associated with “building blocks” of architectures and element choices in metamaterial and materials design. Our approach is demonstrated for machine learning of ternary oxide materials and topology optimization of a multiscale compliant mechanism with aperiodic microstructures and multiple materials.« less