While the Discrete Element Method (DEM) provides high-fidelity insights into granular processes like high-energy ball milling, its computational cost can become prohibitive when exploring extensive parameter spaces required for scale-up. This limitation hinders the rapid design and optimization cycles crucial for emerging applications, like mechanochemistry. Surrogate modeling offers a promising path to overcome these computational barriers, yet existing approaches often struggle to accurately represent the complex, moving boundary conditions typical of milling equipment. In this work, we leverage a Signed Distance Function Graph Neural Network (SGN) surrogate tailored to the high-energy, moving-boundary regime of the Emax mill. Trained on DEM data, the SGN jointly predicts particle kinematics for recursive roll-out and a mechanochemistry-relevant global quantity, the global dissipated energy. The model exhibits strong generalization to unseen motion trajectories and moderate jar-shape edits without retraining, while operating with a timestep over 100x larger than required by DEM. In a CPU-only comparison, it achieves a minimum of 6.6× wall-clock speedup. This approach provides a powerful and promising technique for the simulation, analysis, and design optimization of high-energy ball milling equipment.

In blast furnace ironmaking, a mixture of iron ore pellets and sinter is charged in layers at the furnace top, with particle velocities reaching up to ∼10 m/s at the stock surface. The inherent differences in particle size, shape, and density between pellets and sinter pose challenges for maintaining a uniform mixture during this high-velocity charging, leading to segregation and uneven material distribution. This non-uniformity can negatively affect furnace efficiency and stability. Understanding segregation during charging is therefore crucial for optimizing the ironmaking process. The Discrete Element Method (DEM) can offer valuable insights, provided that the model parameters are calibrated and verified. This study presents a calibrated DEM model for a pellet–sinter mixture with a 50–50 mass ratio of both components. A novel high-velocity laboratory setup was used to simultaneously measure five different key performance indicators (KPIs) related to flow and packing behavior at various discharge heights, corresponding to different flow velocities. Calibration was performed at the highest flow velocity, representative of actual blast furnace conditions. The process involved creating response surface models for each KPI and using a multi-objective optimization approach with a desirability function to determine the model parameters. A step-wise calibration strategy was employed, first optimizing pellet and sinter interaction parameters individually, followed by calibration of the pellet–sinter interaction parameters. This approach proved effective, as the calibrated model accurately reproduced experimental data. Results also suggest that the calibration outcome is flow-invariant in this setup, with the model successfully predicting flow and packing behavior at lower discharge heights.

Micro-scale mechanisms, such as inter-particle and particle-fluid interactions, govern the behaviour of granular systems. While particle-scale simulations provide detailed insights into these interactions, their computational cost is often prohibitive. At a recent Lorentz Center Workshop on “Machine Learning for Discrete Granular Media”, researchers explored how machine learning approaches can aid the development of constitutive laws and efficient data-driven surrogates for granular materials while also addressing uncertainty quantification. Attended by researchers from both the granular materials (GM) and machine learning (ML) communities, the workshop brought the ML community up to date with GM challenges. This position paper emerged from the workshop discussions. In this position paper, we define granular materials and identify seven key challenges that characterise their distinctive behaviour across various scales and regimes–ranging from gas-like to fluid-like and solid-like. Addressing these challenges is essential for developing robust and efficient models for the digital twinning of granular systems in various industrial applications. To showcase the potential of ML to the GM community, we present classical and emerging machine/deep learning techniques that have been, or could be, applied to granular materials. We reviewed sequence-based learning models for path-dependent constitutive behaviour, followed by encoder-decoder type models for representing high-dimensional data in reduced spaces. We then explore graph neural networks and recent advances in neural operator learning. The latter captures the emerging field evolution of interacting particles via efficient latent space representation. Lastly, we discuss model-order reduction and probabilistic learning techniques for high-dimensional parameterised systems, both of which are crucial for quantifying and incorporating uncertainties arising from physics-based and data-driven models. We present a typical workflow aimed at unifying data structures and modelling pipelines and guiding readers through the selection, training, and deployment of ML surrogates for granular material simulations. Finally, we illustrate the workflow’s practical use with two representative examples, focusing on granular materials in solid-like and fluid-like regimes.

The International Maritime Organization aims to achieve full decarbonization by 2050 in response to climate change. This ambitious goal demands well-defined strategies guided by techno-economic assessments. The complexity of global shipping systems makes predicting long-term maritime trade patterns challenging, necessitating scenario-building rather than precise forecasts. Investigating shipping demand scenarios is crucial due to the uncertainty brought by the energy transition and its role as the primary driver of shipping emissions. This paper improves the representation of maritime shipping in Integrated Assessment Models (IAMs) by examining the impacts of climate targets on future shipping demand. A novel econometric model, grounded in advanced gravity theory and integrated with machine-learning algorithms, is proposed to estimate the elasticities of variables in bilateral seaborne trade. By coupling this model with the WITCH IAM, we explore various scenarios, providing deeper insights into trade patterns and their implications. The results show that stricter climate policies and higher carbon taxes reduce GDP due to higher abatement costs, higher fuel prices, and therefore reduced seaborne trade, especially for oil products and containerized cargo. Early adoption of carbon taxes in Europe may shift oil production and consumption patterns, temporarily boosting seaborne trade. Sub-Saharan Africa could experience significant demand growth due to economic and population increases.

In this study we investigate the mechanochemical regeneration of sodium borohydride (NaBH₄) from a system comprising hydrated sodium metaborate ( [Formula presented] ) and magnesium hydride (MgH₂). We explore the individual and joint impact of key operational parameters (rotational speed, milling time, ball-to-powder ratio (BPR), and molar ratio) on the regeneration yield. Furthermore, a method for quantifying chemical conversion is introduced relying only on water and thus, offering environmental benefits. This approach additionally facilitates the production and storage of a “ready-to-use” NaBH₄ solution with minimal losses at room temperature. Notably, a yield of 90% is achieved, with a 20% reduction in rotational speed compared to prior literature. This research contributes to sustainable hydrogen storage and presents practical advancements in mechanochemical processes.

Monopiles are the dominant foundation type for offshore wind turbines, accounting for approximately 80% of the installed capacity. Installing offshore monopile foundations on seabeds susceptible to scour erosion requires monopiles to penetrate several pre-installed scour protection rock layers before securing them into the seabed. The accurate prediction of the pile penetration resistance is crucial to ensure successful monopile installations. To complement, and potentially reduce the dependence on the costly and labour-intensive experimental small-scale penetration tests, a numerical model has been developed using the Discrete Element Method (DEM) that captures the discrete nature of interactions between rocks and piles and predicts the resistance during the penetration process. The developed DEM model includes armour and filter rocks represented by multispheres and sand particles represented by spheres. A multistage calibration, verification and validation DEM modelling framework is proposed and examined with small-scale penetration tests conducted using plates and piles in a double-layer scour protection configuration. The sand material model is calibrated and verified using penetrometer tests and the rock material models are calibrated and verified using a plate penetration test. The DEM model with three verified materials predicts the penetration resistance well in small-scale pile penetration tests and proves the validity of the proposed framework. The DEM model presented in this paper facilitates the modelling in areas where traditional continuum-based numerical methods give less accurate predictions and provide insights that are difficult or nearly impossible to obtain through experimental methods.

The offshore wind industry has grown significantly over the past decade with the increasing demand for clean energy, and over 80% of offshore wind turbines have monopile foundations. The installation of these foundations requires monopiles to penetrate several pre-installed scour protection rock layers before reaching the required penetration depth. With the increasing sizes of both monopiles and the extent of scour protection layers, various challenges arise during the monopile’s driving and self-weight penetration process, such as misalignment and early pile refusal. Lab scale testing and empirical modelling are time-consuming and normally not general enough to be applied to different scenarios. Within the Optimising Pile Installation through Scour Protection (OPIS) project, the high fidelity discrete element method (DEM) has been deployed to consider both the discrete nature and shapes of the scour protection rocks. A double-layer (armour & filter) scour protection with a sand layer underneath was simulated using the DEM. Detailed rock dynamics and the armour rocks dragging down during penetration are revealed and particle-geometry rolling friction is identified as the dominant parameter. The effects of the sand layer thickness and pile wall thickness on penetration resistance are also addressed.

Mechanochemical synthesis faces reproducibility and scale-up challenges due to complex parameter interactions. This study employs machine learning (ML) to predict NaBH4 regeneration yield, integrating chemical experimental data and DEM (Discrete Element Method) derived invariant mechanical descriptors (Ēn, Ēt, fcol/nball). Various algorithms were evaluated, including a two-step modeling strategy to isolate the dominant effect of milling time in our process. Results demonstrate that a two-step Gaussian Process Regression (GPR) model achieves good predictive performance (R2 = 0.83), significantly outperforming single-stage models and providing valuable uncertainty estimates. Tree-based ensembles (XGBoost, RF) also benefit from the two-step approach and can enhance interpretability. This work establishes a framework for using ML to optimize mechanochemical processes, reducing experimental cost and offering a method to link mechanical milling conditions to chemical outcomes, thereby enabling predictive mechanochemistry.

Calibration of discrete element method (DEM) models is crucial for the realistic simulation of granular materials. However, it remains a challenging task, especially for multi-component mixtures due to their higher complexity and larger number of parameters involved. This study presents a systematic and computationally efficient calibration framework designed to address these challenges, focusing on pellet-sinter mixtures, as a representative case of two-component mixtures commonly used in blast furnace steelmaking. The framework integrates sensitivity analysis, machine learning-based surrogate modelling with adaptive sampling, and genetic algorithm-driven optimisation techniques to minimise the number of required DEM simulations. Using this approach, we achieved a high-accuracy surrogate model (R² = 0.95) for seven DEM parameters with only 110 data points, highlighting the efficiency and robustness of the framework. These parameters were successfully calibrated with a relative error of less than 2 %. Moreover, the calibrated parameters for the base case (i.e., 50–50 pellet-sinter mass ratio) remained valid across different mass ratios and layering orders, eliminating the need for recalibration. Overall, the proposed framework offers a reliable, cost-effective, and adaptable solution for DEM calibration of two-component mixtures. Its flexibility and efficiency make it a promising tool for extending to more complex systems, facilitating the development of DEM models for a wide range of industrial applications involving granular mixtures.

High-energy ball milling is a versatile method utilized in mechanochemical reactions and material transformations. Understanding and characterizing the relevant mechanical variables is crucial for the optimization and up-scaling of these processes. To achieve this, the present study delves into differentiating the contributions of normal and tangential interactions during high-energy collisions. Using Discrete Element Method (DEM) simulations, we characterize how operational parameters influence these energy dissipation modes, emphasizing the significance of tangential interactions. Our analysis also reveals how different operational parameters such as ball size, fill ratio, and rotational speed affect the mechanical action inside the milling jar giving rise to multiple operating zones where different modes of energy dissipation can thrive. Finally, we present master curves that generalize findings across a wide range of configurations, offering a tool for characterizing and predicting mechanochemical processes beyond the presented cases. These results provide a robust framework for improving mechanochemical reaction efficiency, and equipment design.

To reduce global emissions, hydrogen is increasingly considered as an energy carrier for renewable energy storage. However, traditional storage methods for hydrogen such as compression or liquefaction require high pressures, extremely low temperatures, and still result in a low volumetric energy density. As a solution, sodium borohydride (NaBH₄) is proposed as an alternative method to store hydrogen. NaBH₄ is a granular material that can be stored using ambient temperature and pressure, and has a relatively high volumetric and gravimetric energy density compared to traditional hydrogen storage. This paper explores the application of NaBH₄ as a fuel in the maritime industry, and elaborates on how the use of NaBH₄ leads to a circular bunkering (refuelling) process. By using hydrolysis to extract hydrogen from NaBH₄ during vessel operation, a so called spent fuel remains and needs to be stored on the vessel until next port call. Additionally, examples of various bunkering equipment that can be used to design the circular bunkering process of NaBH₄ are presented. Moreover, it explains how design of bunkering equipment depends on the mechanical characteristics of the fuel and spent fuel. The main finding of this work is that NaBH₄ is a promising solution for a sustainable future. Before NaBH₄ can be used as a fuel, vessels and ports need to be adapted to facilitate circular bunkering with such a novel solid-state energy carrier.

Mechanical metamaterials are architected structures with unique functionalities, such as negative Poisson's ratio and negative stiffness, which are widely employed for absorbing energy of quasi-static and impact loads, giving improved mechanical response. Acoustic/elastic metamaterials, their dynamic counterparts, rely on frequency-dependent properties of their microstructure elements, including mass density and bulk modulus, to control the propagation of waves. Although such metamaterials introduced significant contribution for solving independently static and dynamic problems, they were facing certain resistance to their use in real-world engineering problems, mainly because of a lack of integrated systems possessing both mechanical and vibration attenuation performance. Advances in manufacturing processes and material and computational science now enable the creation of hybrid mechanical metamaterials, offering multifunctionality in terms of simultaneous static and dynamic properties, giving them the ability of controlling waves while withstanding the applied loading conditions. Exploring towards this direction, this review paper introduces the hybrid mechanical metamaterials in terms of their design process and multifunctional properties. We emphasize the still remaining challenges and how they can be potentially implemented as engineering solutions.

The use of optimization procedures for designing acoustic/elastic metamaterials (A/E MMs) has gained significant interest since they enable the efficient attainment of unique functionalities often contradicting. When it comes to vibration attenuation caused by mechanical stress waves, such as impact loads, the dynamic properties of A/E MMs are optimized so that their wave-control ability is maximized. However, the mechanical performance of A/E MMs during the propagation of such waves is normally not evaluated into the design optimization stages. This may compromise not only the load-bearing capacity of MMs, but also their ability in attenuating vibrations. To prevent such effects, we propose a design strategy that incorporates the stress analysis in the early design phase of A/E MMs subjected to an impact load. The effective mass density approach is applied, from which the vibration attenuation is identified at frequency ranges where the resonator moves out-of-phase in relation to the applied excitation. Regarding to the A/E MM mechanical behavior, maximum von Mises stress is calculated through the transient analysis of a unit cell array subjected to a dynamic load. A Pareto front shows a trade-off behavior between the A/E MM functionalities. With that, we emphasize the importance of incorporating the mechanical performance into the design stage of A/E MMs for vibration attenuation of structures undergoing high impact loads, such as installation of foundations by impact hammering. This brings A/E MMs closer to real applications involving energy filtering at specific frequencies from transient loads, designed in an optimized and efficient way.