High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies – comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.

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Current deep neural networks (DNNs) are overparameterized and use most of their neuronal connections during inference for each task. The human brain, however, developed specialized regions for different tasks and performs inference with a small fraction of its neuronal connections. We propose an iterative pruning strategy introducing a simple importance-score metric that deactivates unimportant connections, tackling overparameterization in DNNs and modulating the firing patterns. The aim is to find the smallest number of connections that is still capable of solving a given task with comparable accuracy, i.e. a simpler subnetwork. We achieve comparable performance for LeNet architectures on MNIST, and significantly higher parameter compression than state-of-the-art algorithms for VGG and ResNet architectures on CIFAR-10/100 and Tiny-ImageNet. Our approach also performs well for the two different optimizers considered—Adam and SGD. The algorithm is not designed to minimize FLOPs when considering current hardware and software implementations, although it performs reasonably when compared to the state of the art.

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We introduce a new continual (or lifelong) learning algorithm called LDA-CP &S that performs segmentation tasks without undergoing catastrophic forgetting. The method is applied to two different surface defect segmentation problems that are learned incrementally, i.e., providing data about one type of defect at a time, while still being capable of predicting every defect that was seen previously. Our method creates a defect-related subnetwork for each defect type via iterative pruning and trains a classifier based on linear discriminant analysis (LDA). At the inference stage, we first predict the defect type with LDA and then predict the surface defects using the selected subnetwork. We compare our method with other continual learning methods showing a significant improvement – mean Intersection over Union better by a factor of two when compared to existing methods on both datasets. Importantly, our approach shows comparable results with joint training when all the training data (all defects) are seen simultaneously.

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The building construction industry is the largest anthropogenic source of pollution, with massive energy consumption and substantial CO2 emissions. Lightweight tension structures allow the simultaneous implementation of several sustainable strategies by using recyclable low-carbon structural membranes offering a greener alternative to glass and other cladding materials. Their efficient structural load-bearing mechanisms result in significant weight savings in buildings and a drastic reduction of the environmental impact associated with material production, transportation, use, and disposal. A subgroup of lightweight materials, structural fabrics, and foils has been gaining popularity among designers and architects in recent years because of their desirable features such as high stiffness, strength, ductility, durability, and functional properties. While these structural membranes open new crucial perspectives for the clean energy transition and have been recently employed worldwide, their full potential is still limited by the lack of construction codes, advanced optimization tools, and comprehensive viscous-thermo-mechanical constitutive models. This chapter aims to foster the design of membrane structures by presenting their basic principles and recent advancements in the field. It covers the design approaches, employed materials and efforts in their characterization and modeling, implications on the sustainability of the built environment, current challenges, and future pathways from both academic research and engineering design viewpoints.@en

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that fulfill a PDE at the boundary and within the domain of interest can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, no incremental training procedure has been proposed for PINNs. As demonstrated herein, by developing incremental PINNs (iPINNs) we can effectively mitigate such training challenges and learn multiple tasks (equations) sequentially without additional parameters for new tasks. Interestingly, we show that this also improves performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE); and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction–diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field.

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For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 10⁸ at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

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Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained on a new one. This hinders cooperation because adapting an existing model for a new task affects the performance on a previous task trained by someone else. The authors developed a continual learning method that addresses this issue, applying it here for the first time to solid mechanics. In particular, the method is applied to recurrent neural networks to predict history-dependent plasticity behavior, although it can be used on any other architecture (feedforward, convolutional, etc.) and to predict other phenomena. This work intends to spawn future developments on continual learning that will foster cooperative strategies among the mechanics community to solve increasingly challenging problems. We show that the chosen continual learning strategy can sequentially learn several constitutive laws without forgetting them, using less data to achieve the same error as standard (non-cooperative) training of one law per model.

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The human brain is capable of learning tasks sequentially mostly without forgetting. However, deep neural networks (DNNs) suffer from catastrophic forgetting when learning one task after another. We address this challenge considering a class-incremental learning scenario where the DNN sees test data without knowing the task from which this data originates. During training, Continual Prune-and-Select (CP&S) finds a subnetwork within the DNN that is responsible for solving a given task. Then, during inference, CP&S selects the correct subnetwork to make predictions for that task. A new task is learned by training available neuronal connections of the DNN (previously untrained) to create a new subnetwork by pruning, which can include previously trained connections belonging to other subnetwork(s) because it does not update shared connections. This enables to eliminate catastrophic forgetting by creating specialized regions in the DNN that do not conflict with each other while still allowing knowledge transfer across them. The CP&S strategy is implemented with different subnetwork selection strategies, revealing superior performance to state-of-the-art continual learning methods tested on various datasets (CIFAR-100, CUB-200-2011, ImageNet-100 and ImageNet-1000). In particular, CP&S is capable of sequentially learning 10 tasks from ImageNet-1000 keeping an accuracy around 94% with negligible forgetting, a first-of-its-kind result in class-incremental learning. To the best of the authors’ knowledge, this represents an improvement in accuracy above 10% when compared to the best alternative method.

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Dynamic atomic force microscopy (AFM) is a key platform that enables topological and nanomechanical characterization of novel materials. This is achieved by linking the nanoscale forces that exist between the AFM tip and the sample to specific mathematical functions through modeling. However, the main challenge in dynamic AFM is to quantify these nanoscale forces without the use of complex models that are routinely used to explain the physics of tip–sample interaction. Here, we make use of machine learning and data science to characterize tip–sample forces purely from experimental data with sub-microsecond resolution. Our machine learning approach is first trained on standard AFM models and then showcased experimentally on a polymer blend of polystyrene (PS) and low density polyethylene (LDPE) sample. Using this algorithm we probe the complex physics of tip–sample contact in polymers, estimate elasticity, and provide insight into energy dissipation during contact. Our study opens a new route in dynamic AFM characterization where machine learning can be combined with experimental methodologies to probe transient processes involved in phase transformation as well as complex chemical and biological phenomena in real-time.@en

Aeronautical industries are concerned about the cost effective generation of design allowables for composite laminates. Design allowables take into account the variabilities arising from different sources (material, manufacturing, defects etc.,) which are determined using expensive and time consuming experimental campaigns. For rapid certification and costs reduction, it is of high interest for the aeronautical industries to use high fidelity numerical models to compliment the testing. In this work, we use a high fidelity numerical model to simulate open hole tension (OHT) of composite laminate, followed by an efficient global sensitivity analysis and uncertainty quantification and management framework to generate design allowables. In a first step, Morris sensitivity analysis is used to screen the sensitive input material properties that affect the OHT strength. In the second step, machine learning technique is used to create a surrogate model, which is used to obtain the B basis design allowable on the OHT strength. @en

This article introduces adaptivity in Clustering-based Reduced Order Models (ACROMs). The strategy is demonstrated for a particular CROM called Self-Consistent Clustering Analysis (SCA), extending it into the Adaptive Self-Consistent Clustering Analysis (ASCA) method. This is shown to improve predictions of Representative Volume Elements (RVEs) of materials exhibiting history-dependent localization phenomena such as plasticity, damage and fracture. The overall approach is composed of three main building blocks: target clusters selection criterion, adaptive cluster analysis, and computation of cluster interaction tensors. In addition, an adaptive clustering solution rewinding procedure and a dynamic adaptivity split factor strategy are suggested to further enhance the adaptive process. The ASCA method is shown to perform better than its static counterpart when capturing the multi-scale elasto-plastic behavior of a particle–matrix composite and predicting the associated fracture and toughness. The proposed adaptivity strategy can be followed in other CROMs to extend them into ACROMs, opening new avenues to explore adaptivity in this context.

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Gaussian processes are well-established Bayesian machine learning algorithms with significant merits, despite a strong limitation: lack of scalability. Clever solutions address this issue by inducing sparsity through low-rank approximations, often based on the Nystrom method. Here, we propose a different method to achieve better scalability and higher accuracy using quantum computing, outperforming classical Bayesian neural networks for large datasets significantly. Unlike other approaches to quantum machine learning, the computationally expensive linear algebra operations are not just replaced with their quantum counterparts. Instead, we start from a recent study that proposed a quantum circuit for implementing quantum Gaussian processes and then we use quantum phase estimation to induce a low-rank approximation analogous to that in classical sparse Gaussian processes. We provide evidence through numerical tests, mathematical error bound estimation, and complexity analysis that the method can address the “curse of dimensionality,” where each additional input parameter no longer leads to an exponential growth of the computational cost. This is also demonstrated by applying the algorithm in a practical setting and using it in the data-driven design of a recently proposed metamaterial. The algorithm, however, requires significant quantum computing hardware improvements before quantum advantage can be achieved.

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From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel “torsional soft-clamping” mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

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We introduce two essential building blocks with binary stiffness for mechanical digital machines. The large scale fully compliant mechanisms have rectilinear and rotational kinematics and use a new V-shaped negative stiffness structure to create two extreme states of stiffness by static balancing. The use of a mechanical bistable switch allows us to toggle between near-zero-stiffness and high-stiffness states, effectively turning off and on stiffness. A stiffness reduction of 98.8% and 99.9% is achieved for linear and rotary motion over a range of 13.3% (20mm) and 0.4rad (23∘) respectively. Stiffness states can be reversibly changed by toggling the mechanical switch, or irreversibly by actuating the main stage. These binary stiffness mechanisms could set the stage for a new type of mechanical logic, adaptive and programmable metamaterials and other types of digital mechanical devices. Practical mechanical digital machines and materials require miniaturized and easily micro-manufactured components. We have therefore carefully considered scalability by integrating all required structures into a planar and monolithic architecture. This allows miniaturization and fabrication with conventional surface-micro-machining and additive manufacturing such as photolithography, two-photon lithography and fused deposition modeling.

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Stiffness in compliant mechanisms can be dramatically altered and even eliminated entirely by using static balancing. This requires elastic energy to be inserted before operation, which is most often done with an additional device or preloading assembly. Adding such devices contrasts starkly with primary motivations for using compliant mechanisms, such as part count reduction, increased precision, and miniaturization. However, statically balanced compliant mechanisms with a fully monolithic architecture are scarce. In this article, we introduce two novel statically balanced compliant mechanisms with linear and rotary kinematics that do not require preloading assembly, enabling miniaturization. Static balance is achieved by the principle of opposing constant force and extended to a rotational device by using opposing constant torque mechanisms for the first time. A constant force mechanism based on existing work is used and inspired a novel constant torque mechanism. A single-piece device is obtained by monolithically integrating a bistable switch for preloading, which allows static balance to be turned on and off. The linear device reduces stiffness by 98.5% over 10 mm, has significantly reduced device complexity and has doubled relative range of motion from 3.3% to 6.6% compared to the state of the art. The rotary device reduces stiffness by 90.5% over 0.35 rad.

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This work represents the first step towards the application of machine learning techniques in the prediction of statistical design allowables of composite laminates. Building on data generated analytically, four machine algorithms (XGBoost, Random Forests, Gaussian Processes and Artificial Neural Networks) are used to predict the notched strength of composite laminates and their statistical distribution, associated to the uncertainty related to the material properties and geometrical features. This work focuses not only on the so-called Legacy Quad Laminates (0°/90°/±45°), typically used in the design of composite aerostructures, but also on the newer concept of double-double (or double-angle ply) laminates. Very good representations of the design space, translating in low generalization relative errors of around ±10%, and very accurate representations of the distributions of notched strengths around single design points and corresponding B-basis allowables are obtained. All machine learning algorithms, with the exception of the Random Forests, show very good performances, with Gaussian Processes outperforming the others for very small number of data points while Artificial Neural Networks have better performance for larger training sets. This work serves as basis for the prediction of first-ply failure, ultimate strength and failure mode of composite specimens based on non-linear finite element simulations, providing further reduction of the computational time required to virtually obtain the design allowables for composite laminates.

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A micromechanics framework for modelling the longitudinal failure of unidirectional fibre composites, in both tension and compression, is presented. Appropriate constitutive models are used for the different constituents (i.e., fibre and matrix) and interfaces. An algorithm for the generation of the fibre misalignment is reported. It combines a stochastic process with an optimization procedure in order to match the numerical and experimental misalignment angle distributions. Two alternative strategies could be used for the optimization procedure, based on the minimization of the standard error of the likelihood or probability, respectively, whose pros and cons are discussed. Finally, micromechanical modelling in tension and compression are reported, and the influence of the fibre misalignment angle distribution is assessed.

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To simplify the analysis and characterisation of composite laminates, an invariant-based approach to stiffness that takes the trace of the plane stress stiffness matrix as a material property was recently proposed. In the present work, a study based on micro-mechanical models brings new insight to this invariant-based approach. The Rule of Mixtures and the Halpin-Tsai models are used to establish the relations between the fibre volume fraction, the fibre/matrix stiffness ratios, and the trace-normalised engineering constants of unidirectional laminae and multidirectional laminates. For sufficiently high longitudinal fibre/matrix stiffness ratios and for fibre volume fractions between 50% and 70%, typical of advanced CFRPs, the variation of the trace-normalised longitudinal Young's modulus is within 6% for unidirectional laminae and within 1% for multidirectional laminates, supporting the definition of an invariant-based approach to stiffness based on a Master Ply concept and laminate factors derived thereof, defining clearly a domain of applicability of the invariant theory and confirming the empirical observations of the past.

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Designing future-proof materials goes beyond a quest for the best. The next generation of materials needs to be adaptive, multipurpose, and tunable. This is not possible by following the traditional experimentally guided trial-and-error process, as this limits the search for untapped regions of the solution space. Here, a computational data-driven approach is followed for exploring a new metamaterial concept and adapting it to different target properties, choice of base materials, length scales, and manufacturing processes. Guided by Bayesian machine learning, two designs are fabricated at different length scales that transform brittle polymers into lightweight, recoverable, and supercompressible metamaterials. The macroscale design is tuned for maximum compressibility, achieving strains beyond 94% and recoverable strengths around 0.1 kPa, while the microscale design reaches recoverable strengths beyond 100 kPa and strains around 80%. The data-driven code is available to facilitate future design and analysis of metamaterials and structures (https://github.com/mabessa/F3DAS).

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Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress-strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.

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