Materials Design Problems Research Articles

Accelerated materials design using batch Bayesian optimization: A case study for solving the inverse problem from materials microstructure to process specification

Microstructure-based process design is one of the main ingredients for materials design, under the integrated computational materials engineering paradigm, which relies on inverting process-structure–property linkages. The specific inverse problem connecting microstructure to processing conditions is exceedingly difficult to solve, even in a computational setting. The difficulty arises from the challenges associated with properly representing the microstructure space as well as the computational cost of the simulations used to connect process conditions to microstructure evolution. In this work, we attempt to invert a process-microstructure problem by implementing and deploying a search scheme based on multi-scale batch Bayesian optimization. We employ this framework to efficiently navigate the microstructure manifold in two examples involving phase-field simulations. In these examples, the volume fraction and characteristic length scale of phases resulting from spinodal decompositions are considered in different objective functions to find synthetic target microstructures. We show how this batch Bayesian optimization can be used to efficiently uncover process-microstructure connections through optimal parallel querying of the process space, providing a new pathway for solving inverse problems in materials design.

Comparison of conceptually different multi-objective Bayesian optimization methods for material design problems

For real-world applications, material properties must usually meet multiple requirements, and researchers often spend considerable time designing such materials by trial and error. Multi-objective Bayesian optimization (MOBO) constitutes a promising data-driven solution to accelerate such design problems. As things stand, conceptually different MOBO methods exist for material design problems, such as scalarization- and hypervolume-based methods. However, no standard approach exists to compare how these methods perform and the appropriate choice of MOBO method in each case remains unclear. Herein, a benchmark protocol to compare how conceptually different MOBO methods perform was introduced, based on which the performances of MOBO methods were comprehensively compared using multiple design problems and performance metrics. The benchmark results showed that there was no method that performed best for all combinations of design problems and performance metrics. Moreover, when multiple MOBO methods were compared, the opportunity cost of using each method emerged and it was shown that an inappropriately chosen method can hinder MOBO efficiency. The benchmark results shown here highlight the importance of choosing the right MOBO method and provide guidelines for how this can be done.

Setting the Free Material Design problem through the methods of optimal mass distribution

The paper deals with the Free Material Design {(text {FMD})} problem aimed at constructing the least compliant structures from an elastic material, the constitutive field of which plays the role of design variable in the form of a tensor valued measure lambda supported in the design domain. Point-wise the constitutive tensor is referred to a given anisotropy class mathscr {H}, while the integral of a cost c(lambda ) is bounded from above. The convex p-homogeneous elastic potential j is parameterized by the constitutive tensor. The work puts forward the existence result and shows that the original problem can be reduced to the Linear Constrained Problem (mathrm {LCP}) known from the theory of optimal mass distribution by G. Bouchitté and G. Buttazzo. A theorem linking solutions of {(text {FMD})} and (mathrm {LCP}) allows to effectively solve the original problem. The developed theory encompasses several optimal anisotropy design problems known in the literature as well as it unlocks new ones. By employing the derived optimality conditions we give several analytical examples of optimal designs.

Publisher's Note: “How to pose material design problems for flow through porous media applications? Sensitivity of dissipation rate to medium's permeability holds the key” [Phys. Fluids 34, 023103 (2022)

Publisher's Note: “How to pose material design problems for flow through porous media applications? Sensitivity of dissipation rate to medium's permeability holds the key” [Phys. Fluids <b>34</b>, 023103 (2022)

Multi-reward Reinforcement Learning Based Bond-Order Potential to Study Strain-Assisted Phase Transitions in Phosphorene.

We introduce a multi-reward reinforcement learning (RL) approach to train a flexible bond-order potential (BOP) for 2D phosphorene based on ab initio training data sets. Our approach is based on a continuous action space Monte Carlo tree search algorithm that is general and scalable and presents an efficient multiobjective optimization scheme for high-dimensional materials design problems. As a proof-of-concept, we deploy this scheme to parametrize multiple structural and dynamical properties of 2D phosphorene polymorphs. Our RL-trained BOP model adequately captures the structure, energetics, transformation barriers, equation of state, elastic constants, and phonon dispersions of various 2D P polymorphs. We use this model to probe the impact of temperature and strain rate on the phase transition from black (α-P) to blue phosphorene (β-P) through molecular dynamics simulations. A decrease in critical strain for this phase transition with increase in temperature is observed, and the underlying atomistic mechanisms are discussed.

How to pose material design problems for flow through porous media applications? Sensitivity of dissipation rate to medium's permeability holds the key

Recent studies have advocated using the total dissipation rate under topology optimization to realize material designs involving the flow of fluids through porous media. However, these studies decided how to pose the design problem, such as maximizing the total dissipation rate for some situations while minimizing for others, by solving one-dimensional problems and justifying their choices using numerical experiments. This approach lacks rigor—a bottleneck for further scientific advancements to computational material design. This paper provides the missing theoretical justification. We identify four classes of boundary value problems using the adjoint state method and analytically calculate the sensitivity of the total dissipation rate to the permeability field. For two of those classes in which the flow of fluids is pressure-driven, the sensitivity is positive—the total dissipation rate increases if the medium's permeability increases. While for the other two classes, in which the flow is velocity-driven, the trend is the opposite. These sensitivities provide rigorous answers to the central question: how to pose a material design problem for flow through porous media applications. The impact of our work is multifold. First, this study further elevates the role of the dissipation rate in posing well-posed material design problems using topology optimization. Second, besides the theoretical significance, the results benefit computational scientists and practitioners to realize optimal designs. Third, given their simplicity yet far-reaching impact, both the approach and results possess immense pedagogical value.

Inverse deep learning methods and benchmarks for artificial electromagnetic material design.

In this work we investigate the use of deep inverse models (DIMs) for designing artificial electromagnetic materials (AEMs) - such as metamaterials, photonic crystals, and plasmonics - to achieve some desired scattering properties (e.g., transmission or reflection spectrum). DIMs are deep neural networks (i.e., deep learning models) that are specially-designed to solve ill-posed inverse problems. There has recently been tremendous growth in the use of DIMs for solving AEM design problems however there has been little comparison of these approaches to examine their absolute and relative performance capabilities. In this work we compare eight state-of-the-art DIMs on three unique AEM design problems, including two models that are novel to the AEM community. Our results indicate that DIMs can rapidly produce accurate designs to achieve a custom desired scattering on all three problems. Although no single model always performs best, the Neural-Adjoint approach achieves the best overall performance across all problem settings. As a final contribution we show that not all AEM design problems are ill-posed, and in such cases a conventional deep neural network can perform better than DIMs. We recommend that a deep neural network is always employed as a simple baseline approach when addressing AEM design problems. We publish python code for our AEM simulators and our DIMs to enable easy replication of our results, and benchmarking of new DIMs by the AEM community.

Dimensions of Smart Additive Manufacturing

Dimensions of Smart Additive Manufacturing

A deep learning augmented genetic algorithm approach to polycrystalline 2D material fracture discovery and design

The gestalt of computational methods including physics-based molecular dynamics simulations, data-driven machine learning (ML) models, and biologically-inspired genetic algorithms affords a powerful toolbox for tackling materials mechanism discovery and design problems. Here, we leverage these methods to investigate the complex multidimensional problem of polycrystalline 2D material fracture. We focus first on graphene and in doing so, demonstrate a practical workflow for exploring the structural dependencies of fracture energy. Despite training our ML model on exclusively single crystal fracture in increments of 10° orientations, we can identify a crack branching mechanism responsible for high bicrystal toughness centered at initial crystal orientation angles of 19° and 41°. These high peaks span only a few degrees in range and are completely overlooked by a search with stride 10°. Furthermore, we can discover qualitative physical phenomena such as collective fracture branch termination and extract quantitative trends relating angular dispersion and mis-orientation angles of crystal grains to fracture energy. None of these complex polycrystalline behaviors were presented in the training data, and the predictive power of the model ultimately allows us to expeditiously generate polycrystalline graphene structures with bespoke fracture paths, a task with great implications in industrial design applications and mechanism discovery. Furthermore, the approach is not limited to graphene specifically, as we demonstrate by retraining the model for another more complex 2D material—MoS2—and achieve polycrystalline fracture predictions of comparable accuracy.

Design and development of multilayer cotton masks via machine learning

With the ongoing COVID-19 pandemic, reusable high-performance cloth masks are recommended for the public to minimize virus spread and alleviate the demand for disposable surgical masks. However, the approach to design a high-performance cotton mask is still unclear. In this study, we aimed to find out the relationship between fabric properties and mask performance via experimental design and machine learning. Our work is the first reported work of employing machine learning to develop protective face masks. Here, we analyzed the characteristics of Egyptian cotton (EC) fabrics with different thread counts and measured the efficacy of triple-layered masks with different layer combinations and stacking orders. The filtration efficiencies of the triple-layered masks were related to the cotton properties and the layer combination. Stacking EC fabrics in the order of thread count 100-300-100 provides the best particle filtration efficiency (45.4%) and bacterial filtration efficiency (98.1%). Furthermore, these key performance metrics were correctly predicted using machine-learning models based on the physical characteristics of the constituent EC layers using Lasso and XGBoost machine-learning models. Our work showed that the machine learning-based prediction approach can be generalized to other material design problems to improve the efficiency of product development.

Encoding and exploring latent design space of optimal material structures via a VAE-LSTM model

Variational autoencoders (VAE) are machine learning models that can extract low dimensional representations of data from datasets of high complexity and volume. Importantly, they can be used for generative purposes to reconstruct complex data, such as images, from a low dimensional encoding of only a few variables. Long short-term memory (LSTM) neural networks are well suited to learning logical trajectory relationships within datasets. Using these two models in concert, we develop a VAE-LSTM approach to learn a classic mechanical materials design problem. Here, we focus on the compliance optimization of cantilever design, using a VAE to encode cantilever structures into a 2D latent space and a LSTM to learn trajectories in that latent space corresponding to the optimization process. Ultimately, we are able to clearly visualize the space of cantilever design, generate new design with extremely low density beyond the original dataset, and obtain optimal cantilever structures inspired by nature. We also demonstrate how the resulting designs can be manufactured using 3D printing, offering a rapid pathway from concept to prototype. The method we developed here can be generalized to other image-based datasets encapsulating changes from multiple factors. The ability offered by our approach to interpret complex behavior, via representations in simplified space, has great potential for application in the intelligent design and manufacturing of materials structure problems.

Inverse homogenization using the topological derivative

PurposeThe purpose of this study is to solve the inverse homogenization problem, or so-called material design problem, using the topological derivative concept.Design/methodology/approachThe optimal topology is obtained through a relaxed formulation of the problem by replacing the characteristic function with a continuous design variable, so-called density variable. The constitutive tensor is then parametrized with the density variable through an analytical interpolation scheme that is based on the topological derivative concept. The intermediate values that may appear in the optimal topologies are removed by penalizing the perimeter functional.FindingsThe optimization process benefits from the intermediate values that provide the proposed method reaching to solutions that the topological derivative had not been able to find before. In addition, the presented theory opens the path to propose a new framework of research where the topological derivative uses classical optimization algorithms.Originality/valueThe proposed methodology allows us to use the topological derivative concept for solving the inverse homogenization problem and to fulfil the optimality conditions of the problem with the use of classical optimization algorithms. The authors solved several material design examples through a projected gradient algorithm to show the advantages of the proposed method.

Materials selection criteria weighting method using analytic hierarchy process (AHP) with simplest questionnaire and modifying method of inconsistent pairwise comparison matrix

The analytic hierarchy process has been widely used to determine subjective weights of materials selection criteria in materials selection using multi-criteria decision-making. However, the analytic hierarchy process has some drawbacks: it is difficult to construct a pairwise comparison matrix and meet the consistency requirement. First, we propose a new simplest questionnaire to perform the pairwise comparison without confusion, conventionally and easily. Next, we propose an improved modifying method for inconsistent pairwise comparison matrix according to the following principles: (1) the elements of the reconstructed pairwise comparison matrix should be nine-point scales, (2) the number and modifying the amount of the modified elements should be as small as possible and (3) the deviation between the original and reconstructed pairwise comparison matrixes should be as small as possible. The outline of the proposed modifying method is as follows: (1) calculate the consistency ration decrements of all the pairwise comparison matrixes reconstructed by modifying every element of the original pairwise comparison matrix to the lower and upper adjacent nine-point scales and (2) find the element with the maximum consistency ratio decrement and modify it to the lower or upper adjacent scale. To illustrate the effectiveness, we apply the proposed methods to determine the criteria weights for selecting the best phase change material used in a solar domestic hot water system, and apply the proposed modifying method to some examples from the published papers, and compare the performances with some previous methods. The simplest questionnaire and improved modifying method help materials designers and engineers to apply the analytic hierarchy process method in materials design and optimization problems, much more actively.

Adaptive active subspace-based efficient multifidelity materials design

Materials design calls for an optimal exploration and exploitation of the process-structure-property (PSP) relationships to produce materials with targeted properties. Recently, we developed and deployed a closed-loop multi-information source fusion (multi-fidelity) Bayesian Optimization (BO) framework to optimize the mechanical performance of a dual-phase material by adjusting the material composition and processing parameters. While promising, BO frameworks tend to underperform as the dimensionality of the problem increases. Herein, we employ an adaptive active subspace method to efficiently handle the large dimensionality of the design space of a typical PSP-based material design problem within our multi-fidelity BO framework. Our adaptive active subspace method significantly accelerates the design process by prioritizing searches in the important regions of the high-dimensional design space. A detailed discussion of the various components and demonstration of three approaches to implementing the adaptive active subspace method within the multi-fidelity BO framework is presented.

MODERN STRUCTURAL STEELS WITH TRIP-EFFECT

Purpose. The aim of this work is to analyze the latest literature data on current state of the issue in the development of the chemical composition and heat treatment modes of steels that implement the TRIP effect under loading. Due to the deformation martensitic transformation of retained austenite, these steels have increased mechanical and operational properties with cost-saving alloying. Methodology. The information published over a long period of time in scientific literature, including domestic sources and high-rating foreign publications are used in this work. The information is systematized by the main TRIP-steels’ types and relates to their chemical composition and heat treatment technology. Findings. The article presents a retrospective of the research progress on the development of structural TRIP effect added steels namely: high-alloy single-phase metastable austenitic steels, as well as low-alloy multiphase TRIP-assisted steels, in which the TRIP effect plays an supporting role, as an additional strengthening and providing increased plasticity mechanism. The latter group of steels includes low alloy TRIP-assisted steels, δ-TRIP steels and maraging TRIP steels. The typical alloying schemes and applied heat treatment modes that make it possible to achieve the optimal phase-structural components ratio, the volume fraction and stability of retained austenite to deformation martensitic transformation in steels and, as a result, to provide an increased mechanical and operational properties were described. The key role of the carbide-free structure formation is noted, which is achieved by alloying with silicon and/or aluminum in providing high properties of steel. The prospects of using modern structural TRIP steels in the automotive and in the machine-building industry are shown. Recommendations for further research directions in this area are made. Originality. The article provides an analysis and systematization of relevant literature data on the development of technologies for the production of multiphase structural steels with retained metastable austenite, realizing the TRIP effect. Practical value. The results of the research can be used as reference materials in solving material design problems, as well as for educational purposes in the preparation of specialized professionals in engineering specialties.

Bayesian optimization for goal-oriented multi-objective inverse material design

SummaryBayesian optimization (BO) can accelerate material design requiring time-consuming experiments. However, although most material designs require tuning of multiple properties, the efficiency of multi-objective (MO) BO in time-consuming experimental material design remains unclear, due to the complexity of handling multiple objectives. This study introduces MO BO method that efficiently achieves predefined goals and shows that by focusing on achieving the goals, BO can efficiently accelerate realistic MO design problems with small efforts. Benchmarks showed that the proposed BO method dramatically reduced the number of experiments needed to achieve goals relative to a baseline method. Virtual MO inverse design experiments with realistic material design problems were also performed, during which the proposed method could achieve goals within only around ten experiments in average and showed over 1000-fold acceleration relative to the random sampling for the most difficult case. The introduction of goal-oriented BO will precede real-world application of BO.

Simplifying inverse materials design problems for fixed lattices with alchemical chirality.

Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting "alchemical" enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.

Hybrid Data-Driven and Mechanistic Modeling Approaches for Multiscale Material and Process Design

The world’s increasing population requires the process industry to produce food, fuels, chemicals, and consumer products in a more efficient and sustainable way. Functional process materials lie at the heart of this challenge. Traditionally, new advanced materials are found empirically or through trial-and-error approaches. As theoretical methods and associated tools are being continuously improved and computer power has reached a high level, it is now efficient and popular to use computational methods to guide material selection and design. Due to the strong interaction between material selection and the operation of the process in which the material is used, it is essential to perform material and process design simultaneously. Despite this significant connection, the solution of the integrated material and process design problem is not easy because multiple models at different scales are usually required. Hybrid modeling provides a promising option to tackle such complex design problems. In hybrid modeling, the material properties, which are computationally expensive to obtain, are described by data-driven models, while the well-known process-related principles are represented by mechanistic models. This article highlights the significance of hybrid modeling in multiscale material and process design. The generic design methodology is first introduced. Six important application areas are then selected: four from the chemical engineering field and two from the energy systems engineering domain. For each selected area, state-of-the-art work using hybrid modeling for multiscale material and process design is discussed. Concluding remarks are provided at the end, and current limitations and future opportunities are pointed out.

Reinforcement learning in discrete action space applied to inverse defect design

Reinforcement learning (RL) algorithms that include Monte Carlo Tree Search (MCTS) have found tremendous success in computer games such as Go, Shiga and Chess. Such learning algorithms have demonstrated super-human capabilities in navigating through an exhaustive discrete action search space. Motivated by their success in computer games, we demonstrate that RL can be applied to inverse materials design problems. We deploy RL for a representative case of the optimal atomic scale inverse design of extended defects via rearrangement of chalcogen (e.g. S) vacancies in 2D transition metal dichalcogenides (e.g. MoS2). These defect rearrangements and their dynamics are important from the perspective of tunable phase transition in 2D materials i.e. 2H (semi-conducting) to 1T (metallic) in MoS2. We demonstrate the ability of MCTS interfaced with a reactive molecular dynamics simulator to efficiently sample the defect phase space and perform inverse design—starting from randomly distributed S vacancies, the optimal defect rearrangement of defects corresponds a line defect of S vacancies. We compare MCTS performance with evolutionary optimization i.e. genetic algorithms and show that MCTS converges to a better optimal solution (lower objective) and in fewer evaluations compared to GA. We also comprehensively evaluate and discuss the effect of MCTS hyperparameters on the convergence to solution. Overall, our study demonstrates the effectives of using RL approaches that operate in discrete action space for inverse defect design problems.

Tailoring composite materials for nonlinear viscoelastic properties using artificial neural networks

Polymer matrix composites exhibit nonlinear viscoelastic behavior over a wide range of temperatures and loading frequencies, which requires an elaborate experimental characterization campaign. Methods are now available to accelerate the characterization process and recover elastic modulus from storage modulus ( E′). However, these methods are limited to the linear viscoelastic region and need to be expanded to nonlinear viscoelastic problems to enable materials design. The present work aims to build a general machine learning based architecture to accelerate the characterization and materials design process for nonlinear viscoelastic materials using the E′ results. To expand outside the linear viscoelastic region, general relations of viscoelasticity are first developed so the master relation of E′ considering nonlinear viscoelasticity can be transformed to time domain relaxation function. The transform starts with building the master relation by optimizing the artificial neural network (ANN) formulation using Kriging model and genetic algorithm. Then the master relation is transformed to a relaxation function, which can be used to predict the stress response with a given strain history and to further extract the elastic modulus. The transform is tested on high density polyethylene matrix syntactic foams and the accuracy is found by comparing the predicted materials properties with those obtained from tensile tests. The good agreements indicate the transform can predict the elastic modulus under a wide range of temperatures and strain rates for any composition of the composite and can be used for material design problems.