Deep generative spatiotemporal learning for integrating fracture mechanics in composite materials: inverse design, discovery, and optimization.

The trade-off between strength and toughness presents a fundamental challenge in engineering material design. Composite materials (CMs) can strategically arrange different materials to enhance both strength and toughness by optimizing the distribution of loads and increasing resistance to crack propagation. However, current data-driven computational modeling approaches for CM configuration optimization suffer from limitations of "substantial computational cost" and "poor predictive power over extrapolation spaces", making it difficult to integrate with global optimization algorithms, and ultimately limiting the discovery of materials with optimal tradeoffs. As a breakthrough, we propose a data-driven design framework with a multi-task DL architecture capable of accurately predicting local fields' spatiotemporal behavior, including stress evolution and crack propagation, alongside homogenized mechanical properties. Our model, trained on datasets generated from crack phase fields simulations of random configurations, demonstrated exceptional predictive performance even for unseen configurations with well organized patterns exploiting nature-inspired morphological features. Importantly, solely from composite material (CM) configurations, our model effectively predicts long-term spatiotemporal fields with an accuracy comparable to FEM but with a substantial reduction in computational time. By coupling the model's predictive power with genetic optimization algorithms, we demonstrated the framework's applicability in two representative inverse design tasks: devising CM configurations with mechanical properties beyond the training set and guiding desired crack pattern formation. Our research highlights the potential of artificial intelligence as a feasible alternative to conventional computational approaches for straightforward configurational and structural optimization.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials.

Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This article also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pretrained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pretraining.

Towards silent and efficient flight by combining bioinspired owl feather serrations with cicada wing geometry.

As natural predators, owls fly with astonishing stealth due to the serrated feather morphology that produces advantageous flow characteristics. Traditionally, these serrations are tailored for airfoil edges with simple two-dimensional patterns, limiting their effect on noise reduction while negotiating tradeoffs in aerodynamic performance. Conversely, the intricately structured wings of cicadas have evolved for effective flapping, presenting a potential blueprint for alleviating these aerodynamic limitations. In this study, we formulate a synergistic design strategy that harmonizes noise suppression with aerodynamic efficiency by integrating the geometrical attributes of owl feathers and cicada forewings, culminating in a three-dimensional sinusoidal serration propeller topology that facilitates both silent and efficient flight. Experimental results show that our design yields a reduction in overall sound pressure levels by up to 5.5 dB and an increase in propulsive efficiency by over 20% compared to the current industry benchmark. Computational fluid dynamics simulations validate the efficacy of the bioinspired design in augmenting surface vorticity and suppressing noise generation across various flow regimes. This topology can advance the multifunctionality of aerodynamic surfaces for the development of quieter and more energy-saving aerial vehicles.

Mechanical metamaterials as broadband electromagnetic wave absorbers: investigating relationships between geometrical parameters and electromagnetic response.

The utilization of low-density and robust mechanical metamaterials rises as a promising solution for multifunctional electromagnetic wave absorbers due to their structured porous structures, which facilitates impedance matching and structural absorption. However, the various geometrical parameters involved in constructing these metamaterials affect their electromagnetic response, necessitating a comprehensive understanding of underlying absorbing mechanisms. Through experimentally validated numerical analysis, this study delves into the influence of geometrical factors on the electromagnetic response of representative low-density, high strength mechanical metamaterials, namely octet-truss and octet-foam. By juxtaposing electromagnetic response under varying volume fractions, cell lengths, and multilayer configurations of octet-truss and octet-foam, distinct absorption mechanisms emerge as geometrical parameters evolve. These mechanisms encompass diminished reflection owing to porous structures, effective medium approximations within subwavelength limits, and transmission-driven or reflection-driven phenomena originating from the interplay of open- and closed-cell structures. Through analyses on these mechanical metamaterials, we demonstrate the viability of employing them as tunable yet scalable structures that are lightweight, robust, and broadband electromagnetic wave absorption.

Multifunctionality of Additively Manufactured Kelvin Foam for Electromagnetic Wave Absorption and Load Bearing.

Rationally engineered porous structures enable lightweight broadband electromagnetic (EM) wave absorbers for countering radar signals or mitigating EM interference between multiple components. However, the scalability of such structures has been hindered by their limited mechanical properties resulting from low density. Herein, an additively manufactured Kelvin foam-based EM wave absorber (KF-EMA) is reported that exhibits multifunctionality, namely EM wave absorption and light-weighted load-bearing structures with constant relative stiffness made possible using bending-dominated lattice structures. Based on tuning design parameters, such as the backbone structures and constituent materials, the proposed KF-EMA features a multilayered 3D-printed design with geometrically optimized KF structures made of carbon black-based backbone composites. The developed KF-EMA demonstrated an absorbance greater than 90% at frequencies ranging from 5.8 to 18 GHz (average EM wave absorption rates of 95.89% and maximum of 99.1% at 15.8 GHz), while the low-density structures of the absorber (≈200 kg m-3 ) still maintained a compression index between the stiffness and relative density (n = 2) under compression. The design strategy paves the way for using metamaterials as mechanically reinforced EM wave absorbers that enable multifunctionality by optimizing unit-cell parameters through a single and low-density structure.

Investigation of mechanical properties and structural integrity of graphene aerogels via molecular dynamics simulations.

Graphene aerogel (GA), a 3D carbon-based nanostructure built on 2D graphene sheets, is well known for being the lightest solid material ever synthesized. It also possesses many other exceptional properties, such as high specific surface area and large liquid absorption capacity, thanks to its ultra-high porosity. Computationally, the mechanical properties of GA have been studied by molecular dynamics (MD) simulations, which uncover nanoscale mechanisms beyond experimental observations. However, studies on how GA structures and properties evolve in response to simulation parameter changes, which provide valuable insights to experimentalists, have been lacking. In addition, the differences between the calculated properties via simulations and experimental measurements have rarely been discussed. To address the shortcomings mentioned above, in this study, we systematically study various mechanical properties and the structural integrity of GA as a function of a wide range of simulation parameters. Results show that during the in silico GA preparation, smaller and less spherical inclusions (mimicking the effect of water clusters in experiments) are conducive to strength and stiffness but may lead to brittleness. Additionally, it is revealed that a structurally valid GA in the MD simulation requires the number of bonds per atom to be at least 1.40, otherwise the GA building blocks are not fully interconnected. Finally, our calculation results are compared with experiments to showcase both the power and the limitations of the simulation technique. This work may shed light on the improvement of computational approaches for GA as well as other novel nanomaterials.

Physics-Informed Deep-Learning For Elasticity: Forward, Inverse, and Mixed Problems.

Elastography is a medical imaging technique used to measure the elasticity of tissues by comparing ultrasound signals before and after a light compression. The lateral resolution of ultrasound is much inferior to the axial resolution. Current elastography methods generally require both axial and lateral displacement components, making them less effective for clinical applications. Additionally, these methods often rely on the assumption of material incompressibility, which can lead to inaccurate elasticity reconstruction as no materials are truly incompressible. To address these challenges, a new physics-informed deep-learning method for elastography is proposed. This new method integrates a displacement network and an elasticity network to reconstruct the Young's modulus field of a heterogeneous object based on only a measured axial displacement field. It also allows for the removal of the assumption of material incompressibility, enabling the reconstruction of both Young's modulus and Poisson's ratio fields simultaneously. The authors demonstrate that using multiple measurements can mitigate the potential error introduced by the "eggshell" effect, in which the presence of stiff material prevents the generation of strain in soft material. These improvements make this new method a valuable tool for a wide range of applications in medical imaging, materials characterization, and beyond.

Deep Learning Accelerated Design of Mechanically Efficient Architected Materials.

Lattice structures are known to have high performance-to-weight ratios because of their highly efficient material distribution in a given volume. However, their inherently large void fraction leads to low mechanical properties compared to the base material, high anisotropy, and brittleness. Most works to date have focused on modifying the spatial arrangement of beam elements to overcome these limitations, but only simple beam geometries are adopted due to the infinitely large design space associated with probing and varying beam shapes. Herein, we present an approach to enhance the elastic modulus, strength, and toughness of lattice structures with minimal tradeoffs by optimizing the shape of beam elements for a suite of lattice structures. A generative deep learning-based approach is employed, which leverages the fast inference of neural networks to accelerate the optimization process. Our optimized lattice structures possess superior stiffness (+59%), strength (+49%), toughness (+106%), and isotropy (+645%) compared to benchmark lattices consisting of cylindrical beams. We fabricate our lattice designs using additive manufacturing to validate the optimization approach; experimental and simulation results show good agreement. Remarkable improvement in mechanical properties is shown to be the effect of distributed stress fields and deformation modes subject to beam shape and lattice type.

Quantum Informed Machine-Learning Potentials for Molecular Dynamics Simulations of CO2's Chemisorption and Diffusion in Mg-MOF-74.

Among various porous solids for gas separation and purification, metal-organic frameworks (MOFs) are promising materials that potentially combine high CO2 uptake and CO2/N2 selectivity. So far, within the hundreds of thousands of MOF structures known today, it remains a challenge to computationally identify the best suited species. First principle-based simulations of CO2 adsorption in MOFs would provide the necessary accuracy; however, they are impractical due to the high computational cost. Classical force field-based simulations would be computationally feasible; however, they do not provide sufficient accuracy. Thus, the entropy contribution that requires both accurate force fields and sufficiently long computing time for sampling is difficult to obtain in simulations. Here, we report quantum-informed machine-learning force fields (QMLFFs) for atomistic simulations of CO2 in MOFs. We demonstrate that the method has a much higher computational efficiency (∼1000×) than the first-principle one while maintaining the quantum-level accuracy. As a proof of concept, we show that the QMLFF-based molecular dynamics simulations of CO2 in Mg-MOF-74 can predict the binding free energy landscape and the diffusion coefficient close to experimental values. The combination of machine learning and atomistic simulation helps achieve more accurate and efficient in silico evaluations of the chemisorption and diffusion of gas molecules in MOFs.

Monitoring Anomalies in 3D Bioprinting with Deep Neural Networks.

Additive manufacturing technologies have progressed in the past decades, especially when used to print biofunctional structures such as scaffolds and vessels with living cells for tissue engineering applications. Part quality and reliability are essential to maintaining the biocompatibility and structural integrity needed for engineered tissue constructs. As a result, it is critical to detect for any anomalies that may occur in the 3D-bioprinting process that can cause a mismatch between the desired designs and printed shapes. However, challenges exist in detecting the imperfections within oftentimes transparent bioprinted and complex printing features accurately and efficiently. In this study, an anomaly detection system based on layer-by-layer sensor images and machine learning algorithms is developed to distinguish and classify imperfections for transparent hydrogel-based bioprinted materials. High anomaly detection accuracy is obtained by utilizing convolutional neural network methods as well as advanced image processing and augmentation techniques on extracted small image patches. Along with the prediction of various anomalies, the category of infill pattern and location information on the image patches can be accurately determined. It is envisioned that using our detection system to categorize and localize printing anomalies, real-time autonomous correction of process parameters can be realized to achieve high-quality tissue constructs in 3D-bioprinting processes.

Generative machine learning algorithm for lattice structures with superior mechanical properties.

Lattice structures are typically made up of a crisscross pattern of beam elements, allowing engineers to distribute material in a more structurally effective way. However, a main challenge in the design of lattice structures is a trade-off between the density and mechanical properties. Current studies have often assumed the cross-sectional area of the beam elements to be uniform for reducing the design complexity. This simplified approach limits the possibility of finding superior designs with optimized weight-to-performance ratios. Here, the optimized shape of the beam elements is investigated using a deep learning approach with high-order Bézier curves to explore the augmented design space. This is then combined with a hybrid neural network and genetic optimization (NN-GO) adaptive method for the generation of superior lattice structures. In our optimized design, the distribution of material is smartly shifted more towards the joint region, the weakest location of lattice structures, to achieve the highest modulus and strength. This design strikes to balance between two modes of deformation: axial and bending. Thus, the optimized design is efficient for load bearing and energy absorption. To validate our simulations, the optimized design is then fabricated by additive manufacturing and its mechanical properties are evaluated through compression testing. A good correlation between experiments and simulations is observed and the optimized design has outperformed benchmark ones in terms of modulus and strength. We show that the extra design flexibility from high-order Bézier curves allows for a smoother transition between the beam elements which reduces the overall stress concentration profile.

Modeling Bioinspired Fish Scale Designs via a Geometric and Numerical Approach.

Fish scales serve as a natural dermal armor with remarkable flexibility and puncture resistance. Through studying fish scales, researchers can replicate these properties and tune them by adjusting their design parameters to create biomimetic scales. Overlapping scales, as seen in elasmoid scales, can lead to complex interactions between each scale. These interactions are able to maintain the stiffness of the fish's structure with improved flexibility. Hence, it is important to understand these interactions in order to design biomimetic fish scales. Modeling the flexibility of fish scales, when subject to shear loading across a substrate, requires accounting for nonlinear relations. Current studies focus on characterizing these kinematic linear and nonlinear regions but fall short in modeling the kinematic phase shift. Here, we propose an approach that will predict when the linear-to-nonlinear transition will occur, allowing for more control of the overall behavior of the fish scale structure. Using a geometric analysis of the interacting scales, we can model the flexibility at the transition point where the scales start to engage in a nonlinear manner. The validity of these geometric predictions is investigated through finite element analysis. This investigation will allow for efficient optimization of scale-like designs and can be applied to various applications.

Scalable Graphene Defect Prediction Using Transferable Learning.

Notably known for its extraordinary thermal and mechanical properties, graphene is a favorable building block in various cutting-edge technologies such as flexible electronics and supercapacitors. However, the almost inevitable existence of defects severely compromises the properties of graphene, and defect prediction is a difficult, yet important, task. Emerging machine learning approaches offer opportunities to predict target properties such as defect distribution by exploiting readily available data, without incurring much experimental cost. Most previous machine learning techniques require the size of training data and predicted material systems of interest to be identical. This limits their broader application, because in practice a newly encountered material system may have a different size compared with the previously observed ones. In this paper, we develop a transferable learning approach for graphene defect prediction, which can be used on graphene with various sizes or shapes not seen in the training data. The proposed approach employs logistic regression and utilizes data on local vibrational energy distributions of small graphene from molecular dynamics simulations, in the hopes that vibrational energy distributions can reflect local structural anomalies. The results show that our machine learning model, trained only with data on smaller graphene, can achieve up to 80% prediction accuracy of defects in larger graphene under different practical metrics. The present research sheds light on scalable graphene defect prediction and opens doors for data-driven defect detection for a broad range of two-dimensional materials.

Mechanical Training-Driven Structural Remodeling: A Rational Route for Outstanding Highly Hydrated Silk Materials.

Highly hydrated silk materials (HHSMs) have been the focus of extensive research due to their usefulness in tissue engineering, regenerative medicine, and soft devices, among other fields. However, HHSMs have weak mechanical properties that limit their practical applications. Inspired by the mechanical training-driven structural remodeling strategy (MTDSRS) in biological tissues, herein, engineered MTDSRS is developed for self-reinforcement of HHSMs to improve their inherent mechanical properties and broaden potential utility. The MTDSRS consists of repetitive mechanical training and solvent-induced conformation transitions. Solvent-induced conformation transition enables the formation of ß-sheet physical crosslinks among the proteins, while the repetitive mechanical loading allows the rearrangement of physically crosslinked proteins along the loading direction. Such synergistic effects produce strong and stiff mechanically trained-HHSMs (MT-HHSMs). The fracture strength and Young's modulus of the resultant MT-HHSMs (water content of 43 ± 4%) reach 4.7 ± 0.9 and 21.3 ± 2.1 MPa, respectively, which are 8-fold stronger and 13-fold stiffer than those of the as-prepared HHSMs, as well as superior to most previously reported HHSMs with comparable water content. In addition, the animal silk-like highly oriented molecular crosslinking network structure also provides MT-HHSMs with fascinating physical and functional features, such as stress-birefringence responsibility, humidity-induced actuation, and repeatable self-folding deformation.

Learning hidden elasticity with deep neural networks.

Elastography is an imaging technique to reconstruct elasticity distributions of heterogeneous objects. Since cancerous tissues are stiffer than healthy ones, for decades, elastography has been applied to medical imaging for noninvasive cancer diagnosis. Although the conventional strain-based elastography has been deployed on ultrasound diagnostic-imaging devices, the results are prone to inaccuracies. Model-based elastography, which reconstructs elasticity distributions by solving an inverse problem in elasticity, may provide more accurate results but is often unreliable in practice due to the ill-posed nature of the inverse problem. We introduce ElastNet, a de novo elastography method combining the theory of elasticity with a deep-learning approach. With prior knowledge from the laws of physics, ElastNet can escape the performance ceiling imposed by labeled data. ElastNet uses backpropagation to learn the hidden elasticity of objects, resulting in rapid and accurate predictions. We show that ElastNet is robust when dealing with noisy or missing measurements. Moreover, it can learn probable elasticity distributions for areas even without measurements and generate elasticity images of arbitrary resolution. When both strain and elasticity distributions are given, the hidden physics in elasticity-the conditions for equilibrium-can be learned by ElastNet.

Ca2+-supplying black phosphorus-based scaffolds fabricated with microfluidic technology for osteogenesis.

Effective osteogenesis remains a challenge in the treatment of bone defects. The emergence of artificial bone scaffolds provides an attractive solution. In this work, a new biomineralization strategy is proposed to facilitate osteogenesis through sustaining supply of nutrients including phosphorus (P), calcium (Ca), and silicon (Si). We developed black phosphorus (BP)-based, three-dimensional nanocomposite fibrous scaffolds via microfluidic technology to provide a wealth of essential ions for bone defect treatment. The fibrous scaffolds were fabricated from 3D poly (l-lactic acid) (PLLA) nanofibers (3D NFs), BP nanosheets, and hydroxyapatite (HA)-porous SiO2 nanoparticles. The 3D BP@HA NFs possess three advantages: i) stably connected pores allow the easy entrance of bone marrow-derived mesenchymal stem cells (BMSCs) into the interior of the 3D fibrous scaffolds for bone repair and osteogenesis; ii) plentiful nutrients in the NFs strongly improve osteogenic differentiation in the bone repair area; iii) the photothermal effect of fibrous scaffolds promotes the release of elements necessary for bone formation, thus achieving accelerated osteogenesis. Both in vitro and in vivo results demonstrated that the 3D BP@HA NFs, with the assistance of NIR laser, exhibited good performance in promoting bone regeneration. Furthermore, microfluidic technology makes it possible to obtain high-quality 3D BP@HA NFs with low costs, rapid processing, high throughput and mass production, greatly improving the prospects for clinical application. This is also the first BP-based bone scaffold platform that can self-supply Ca2+, which may be the blessedness for older patients with bone defects or patients with damaged bones as a result of calcium loss.

Birefringent Silk Fibroin Hydrogel Constructed via Binary Solvent-Exchange-Induced Self-Assembly.

Birefringent hydrogels have a strong potential for applications in biomedicine and optics as they can modulate the optical and mechanical anisotropy in confined two-dimensional geometries. However, production of birefringent hydrogels with hierarchical structures, mechanical properties, and biorelated behavior that are analogous to biological tissues is still challenging. Starting from the silk fibroin (SF)-ionic liquid solution system, this study aimed to rationally design a "binary solvent-exchange-induced self-assembly (BSEISA)" strategy to produce birefringent SF hydrogels (SFHs). In this method, the conformational transition rate of SF can be effectively controlled by the exchange rate of the binary solvents. Therefore, this method provides the possibility of controlling the conformation and orientation of SF. Molecular simulations confirmed that methanol is more effective in driving ß-sheet formation than other often used solvents, such as formic acid and water. The formed ß-sheets act as the physical cross-links that connect disparate protein chains, thereby forming continuous and stable three-dimensional (3D) hydrogel networks. The resultant BSEISA-SFHs are transparent and birefringent with mechanical characteristics similar to those of soft biological tissues, such as lens and cartilage. Interestingly, our results revealed that the evolution of experimental birefringent fringes perfectly matched the changes in stress distribution predicted using finite element analysis. Owing to the unique birefringence of BSEISA-SFHs, together with the advantages in mechanical performance, these hydrogels are anticipated to act as good tissue surrogates for understanding the mechanical response of biological tissues.

Nano-topology optimization for materials design with atom-by-atom control.

Atoms are the building blocks of matter that make up the world. To create new materials to meet some of civilization's greatest needs, it is crucial to develop a technology to design materials on the atomic and molecular scales. However, there is currently no computational approach capable of designing materials atom-by-atom. In this study, we consider the possibility of direct manipulation of individual atoms to design materials at the nanoscale using a proposed method coined "Nano-Topology Optimization". Here, we apply the proposed method to design nanostructured materials to maximize elastic properties. Results show that the performance of our optimized designs not only surpasses that of the gyroid and other triply periodic minimal surface structures, but also exceeds the theoretical maximum (Hashin-Shtrikman upper bound). The significance of the proposed method lies in a platform that allows computers to design novel materials atom-by-atom without the need of a predetermined design.

Designing an Adhesive Pillar Shape with Deep Learning-Based Optimization.

Over the past decades, significant effort has been made to improve the adhesive properties of adhesive pillars, by searching for pillar shapes with optimized interfacial stress distribution. However, the shape optimizations in the previous studies are conducted by considering specific pillar forms with a few parameters, hence with limited design space. In this study, we present a framework to find a free-form optimized adhesive pillar shape out of extensive design space. We generate 200 000 different shapes of adhesive pillars based on the Bézier curve with a few control points by considering two distinct edge shapes, sharp and truncated edges, to account for the limitation in the realistic manufacturing resolution. The resulting interfacial stress distributions from numerical simulations are used to train deep neural networks for each edge type. Our deep learning model shows greater than 99% classification accuracy on a limited data set with orders of magnitude speedup in computation time compared to finite element analyses. On the basis of the trained neural network, we conduct genetic optimization by maximizing a fitness function that prefers the uniform interfacial stress distribution with neither stress peak nor singularity. The optimized adhesive pillar shape is composed of smoothly mixed convex and concave parts and shows improved uniformity in the interfacial stress distribution. Our study also demonstrates that the deep learning can be used for nonparametric curve optimization task with diverse fitness function.

Generative Deep Neural Networks for Inverse Materials Design Using Backpropagation and Active Learning.

In recent years, machine learning (ML) techniques are seen to be promising tools to discover and design novel materials. However, the lack of robust inverse design approaches to identify promising candidate materials without exploring the entire design space causes a fundamental bottleneck. A general-purpose inverse design approach is presented using generative inverse design networks. This ML-based inverse design approach uses backpropagation to calculate the analytical gradients of an objective function with respect to design variables. This inverse design approach is capable of overcoming local minima traps by using backpropagation to provide rapid calculations of gradient information and running millions of optimizations with different initial values. Furthermore, an active learning strategy is adopted in the inverse design approach to improve the performance of candidate materials and reduce the amount of training data needed to do so. Compared to passive learning, the active learning strategy is capable of generating better designs and reducing the amount of training data by at least an order-of-magnitude in the case study on composite materials. The inverse design approach is compared with conventional gradient-based topology optimization and gradient-free genetic algorithms and the pros and cons of each method are discussed when applied to materials discovery and design problems.