Thermodynamically consistent machine-learned internal state variable approach for data-driven modeling of path-dependent materials
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36 MATERIALS SCIENCE↗
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Active learning path-dependent properties using a cloud-based materials acceleration platform
Solid state materials are central to many modern technologies in which a given material may be exposed to a variety of environments. The material properties often vary with the sequence of environments in an irreversible manner, resulting in a quintessential path-dependency in experimental observables. While sequential learning techniques have been effectively deployed for accelerating learning of state properties of materials, they often use a consistent environment path in all experiments. To elevate such techniques for making optimal decisions in experimental investigations of path-dependent properties, we introduce an iterated expected information gain acquisition function that optimizes over entire experimental trajectories. This approach is implemented within a cloud-based Materials Acceleration Platform architecture utilizing an event-driven stateful broker coupled with remote HELAO (Hierarchical Experimental Laboratory Automation and Orchestration) instances and an AI science manager. The platform's efficacy was demonstrated through a case study optimizing multi-step spectro-electrochemical experiments to identify optically stable potential windows in (Co–Ni–Sb)O z metal oxides. The system successfully integrated AI-driven experiment design, remote laboratory automation, and cloud-based data infrastructure, validating the platform's capability for managing complex, adaptive, path-dependent workflows in materials discovery.
Guevarra, Dan [California Institute of Technology ↗
Modular machine learning-based elastoplasticity: Generalization in the context of limited data
The development of highly accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions and from the viewpoint of data availability, verification, and validation. Recently, data-driven modeling approaches have been proposed that aim to establish stress-evolution laws that avoid user-chosen functional forms by relying on machine learning representations and algorithms. However, these approaches not only require a significant amount of data but also need data that probes the full stress space with a variety of complex loading paths. Furthermore, they rarely enforce all necessary thermodynamic principles as hard constraints. Hence, they are in particular not suitable for low-data or limited-data regimes, where the first arises from the cost of obtaining the data and the latter from the experimental limitations of obtaining labeled data, which is commonly the case in engineering applications. In this work, we discuss a hybrid framework that can work on a variable amount of data by relying on the modularity of the elastoplasticity formulation where each component of the model can be chosen to be either a classical phenomenological or a data-driven model depending on the amount of available information and the complexity of the response. The method is tested on synthetic uniaxial data coming from simulations as well as cyclic experimental data for structural materials. The discovered material models are found to not only interpolate well but also allow for accurate extrapolation in a thermodynamically consistent manner far outside the domain of the training data. This ability to extrapolate from limited data was the main reason for the early and continued success of phenomenological models and the main shortcoming in machine learning-enabled constitutive modeling approaches. Training aspects and details of the implementation of these models into Finite Element simulations are discussed and analyzed.
42 ENGINEERING↗
Experimental/analytical characterization of composite tubes under combined loading
The paper outlines the results of an investigation performed to characterize the response of P75/934 graphite/epoxy tubes with a stacking sequence of (15/0/+,-10/0/-15)s under pure torsion and combined axial/torsion loading. The experimentally observed nonlinear response and path-dependent failure are discussed in terms of material nonlinearites at the ply level and first ply failure loads with the help of an analytical model.
Derstine, Mark S.↗
Machine-Learning-Based Multiscale Methods for 3D Modelling of Granular Materials by Incorporating History-Dependent State Variables
Over the past decades, the prevalence of machine learning (ML) methods has made the development of ML-based constitutive models for granular materials undoubtedly a popular subject. Numerous studies have been made to feature the loading path or history-dependent stress-strain response of granular media using neural networks. In this work, a novel finite element method (FEM)–ML multiscale approach was developed by incorporating internal variables to improve the simulation accuracy of 3D history-dependent granular materials for the first time. To this end, a surrogate constitutive model based on the single-step-based multi-layer perceptron (MLP) neural network was used to replace representative volume element (RVE) simulations conducted by the discrete element method (DEM) in the multiscale FEM–DEM approach. Although the prediction principle of the MLP aligns with the FEM algorithm, artificially added internal variables are required to differentiate the loading history. To address this issue, history variables associated with the Frobenius norm are proposed to be fed into the MLP coupled with the strain tensor to extract the history-dependent behaviour of granular assemblies. The developed FEM–ML approach was demonstrated in 3D conventional triaxial compression (CTC) simulations. Compared to the multiscale FEM–DEM approach, the proposed FEM–ML method exhibits a significantly improved computational efficiency.
granular materials↗
Development and Experimental Validation of a Path-Dependent Spin Forming Finite Element Model
Spin forming is an advanced manufacturing process widely used in the aerospace and defense sectors to produce lightweight, high-strength cylindrical components with tight dimensional tolerances. This study explores the applicability of the path-dependent Mechanical Threshold Stress (MTS) constitutive model by simulating the evolution of geometry, machining forces, and plastic deformation during the spin forming of a 10-mm thick 6061-O aluminum cylinder. While numerical modeling of spin forming has advanced substantially over the past decade, systematic verification and experimental validation of material models remain limited, particularly in predicting through-thickness process evolution. The MTS model, incorporating a Voce hardening rule, is employed for its ability to represent cyclic loading, rapidly varying temperature fields, and strain rates characteristic of spin forming. Numerical convergence analysis indicates discretization uncertainties between 0.3% and 9.2% for key quantities of interest. Experimental validation demonstrates that the MTS model, when implemented with a verified mesh, accurately reproduces both elastic and plastic behavior of 6061-O aluminum, predicting peak roller loads within 11–18% of measurements, geometric tolerances within 3%, and plastic strain distributions within 10% of experimental values. Collectively, these results establish a validated computational framework for predictive spin-forming simulations with quantified confidence, providing a foundation for extension to other alloys, geometries, and forming conditions.
Spin forming↗
Neural network kinetics for exploring diffusion multiplicity and chemical ordering in compositionally complex materials
Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. The inherent chemical complexity in compositionally complex materials poses challenges for modeling atomic diffusion and the resulting formation of chemically ordered structures. Here, we introduce a neural network kinetics (NNK) scheme that predicts and simulates diffusion-induced chemical and structural evolution in complex concentrated chemical environments. The framework is grounded on efficient on-lattice structure and chemistry representation combined with artificial neural networks, enabling precise prediction of all path-dependent migration barriers and individual atom jumps. To demonstrate the method, we study the temperature-dependent local chemical ordering in a refractory NbMoTa alloy and reveal a critical temperature at which the B2 order reaches a maximum. The atomic jump randomness map exhibits the highest diffusion heterogeneity (multiplicity) in the vicinity of this characteristic temperature, which is closely related to chemical ordering and B2 structure formation. The scalable NNK framework provides a promising new avenue to exploring diffusion-related properties in the vast compositional space within which extraordinary properties are hidden.
36 MATERIALS SCIENCE↗
Beyond Melting: Amorphous Bonding for Joining and Consolidation
Crystallization may be the hidden constraint in thermoplastic composite manufacturing. It requires tightly controlled cooling, induces residual stresses through shrinkage, and introduces path-dependent behavior that complicates predictive modeling yet remains essential for structural performance. This work asks: can bonding be achieved without relying on melt-driven crystallization? To address this, thin (5–20 μm) polyetherimide (PEI) interlayers are pre-healed to slow-cooled polyaryletherketone (PAEK) in two contexts. The first, Thermabond®, is sub-melt joining of low melt-PAEK laminates. Results show that bond quality is governed primarily by processing (i.e., adequate healing and film handling) rather than modest changes in interlayer thickness. This concept is then extended to laminate-scale manufacturing through an architecture known as OATMEAL (Out-of-autoclave Amorphous/semicrystalline Thermoplastic Material for Energy-efficient Aerospace-grade Laminates). PEI is healed to carbon fiber reinforced polyetheretherketone (PEEK) at the prepreg and excess PEI is then ablated from the surface. Crystallinity is developed off-line during prepreg fabrication, while subsequent consolidation occurs below the melt temperature to preserve it. Cross-ply warpage experiments show that, contrary to intuition, repeated amorphous interfaces reduce global curvature by lowering the effective stress lock-in temperature and eliminating crystallization shrinkage from the lamina response. Correspondingly, laminate behavior is accurately predicted using classical laminate theory (CLT) with a single effective stress-free temperature, whereas conventional CF/PEEK requires accounting for crystallization-driven effects. By decoupling interfacial healing from crystallization, OATMEAL enables sub-melt consolidation, reduces energy consumption by up to 75%, and increases manufacturing throughput by fivefold. These results demonstrate that amorphous bonding is not only a joining strategy, but a pathway to more predictable and scalable thermoplastic composite manufacturing.
solidification↗