Multiscale Simulation Framework Research Articles

Wide and ultrawide-bandgap semiconductor surfaces: A full multiscale model

Germanium, gallium, nitrogen, and oxygen deposition on both GaN(0001) and GaN(0001̄) surfaces were investigated. A multiscale simulation framework was implemented. The DFT simulations were employed to reveal the interactions among the species and GaN surface. Energy diffusion barriers were obtained by the Nudged Elastic Band approach. A Poisson–Nernst–Planck model was implemented to calculate the concentration of each atomic species near GaN surface. The kinetic and unimolecular collision gas theories were incorporated to determine adsorption rates. These outcomes were integrated into a nanoscale kinetic Monte Carlo model. This model allowed to generate data on the surface diffusion and clustering of adsorbed atoms on GaN surfaces. As a result, an enhanced understanding of the deposition and agglomeration mechanisms was achieved. In particular, of the roles played by germanium and oxygen. Due to the relatively high diffusion energy barriers, germanium atoms act as pins around to which gallium atoms tend to cluster. The results align with both experimental observations and existing simulation literature. To the best of our knowledge, no previous DFT simulation results on germanium deposition on GaN have been reported.

Ion–surface interactions in plasma-facing material design

A multi-scale simulation framework for ion–solid interactions in plasma-exposed materials provides crucial insight into advancing fusion energy and space electric propulsion. Leveraging binary-collision approximation (BCA) simulations, the framework uniquely predicts sputter yields and analyzes material transport within volumetrically complex materials. This approach, grounded in the validated BCA code TRI3DYN, addresses key limitations in existing models by accurately capturing ion–solid interaction physics. A case study is presented, highlighting the framework’s ability to replicate experimental sputter yield results, underscoring its reliability and potential for designing durable materials in harsh plasma environments. Insights into sputtering transport phenomenology mark a significant advancement in material optimization for improved resilience in plasma-facing applications.

Personalized coronary and myocardial blood flow models incorporating CT perfusion imaging and synthetic vascular trees

Computational simulations of coronary artery blood flow, using anatomical models based on clinical imaging, are an emerging non-invasive tool for personalized treatment planning. However, current simulations contend with two related challenges – incomplete anatomies in image-based models due to the exclusion of arteries smaller than the imaging resolution, and the lack of personalized flow distributions informed by patient-specific imaging. We introduce a data-enabled, personalized and multi-scale flow simulation framework spanning large coronary arteries to myocardial microvasculature. It includes image-based coronary anatomies combined with synthetic vasculature for arteries below the imaging resolution, myocardial blood flow simulated using Darcy models, and systemic circulation represented as lumped-parameter networks. We propose an optimization-based method to personalize multiscale coronary flow simulations by assimilating clinical CT myocardial perfusion imaging and cardiac function measurements to yield patient-specific flow distributions and model parameters. Using this proof-of-concept study on a cohort of six patients, we reveal substantial differences in flow distributions and clinical diagnosis metrics between the proposed personalized framework and empirical methods based purely on anatomy; these errors cannot be predicted a priori. This suggests virtual treatment planning tools would benefit from increased personalization informed by emerging imaging methods.

Multiscale modeling of dislocation-mediated plasticity of refractory high entropy alloys

Refractory high entropy alloys (RHEAs) have drawn growing attention due to their remarkable strength retention at high temperatures. Understanding dislocation mobility is vital for optimizing high-temperature properties and ambient temperature ductility of RHEAs. Nevertheless, fundamental questions persist regarding the variability of dislocation motion in the rugged energy landscape and the effective activation barrier for specific mechanisms, such as kink-pair nucleation and kink migration. Here we perform systematic atomistic simulations and conduct statistical analysis to obtain the effective activation barriers for the mechanisms underlying various types of dislocation motion in a typical RHEA, NbMoTaW. Moreover, a stochastic line tension model is developed to calculate the activation barrier with substantially reduced computational costs. By incorporating the effective activation barriers into the crystal plasticity model, a multiscale simulation framework for predicting the mechanical properties of RHEAs is established. The ambient temperature yield strength of NbMoTaW is well-predicted by the kink-pair nucleation mechanism of screw dislocations, while the strengthening originating from screw dislocations does not predominate at high temperatures. Our work provides a robust foundation for atomistic studies of effective dislocation behaviors in random solution solids, elucidating the intricate relationship between microscopic mechanisms and macroscopic properties.

Exploring protein conformational paths using machine learning–generated structures coupled to a multiscale simulation framework showcased for RAS-RAF activation

Exploring protein conformational paths using machine learning–generated structures coupled to a multiscale simulation framework showcased for RAS-RAF activation

Knowledge-based modeling of simulation behavior for Bayesian optimization

Numerical simulations consist of many components that affect the simulation accuracy and the required computational resources. However, finding an optimal combination of components and their parameters under constraints can be a difficult, time-consuming and often manual process. Classical adaptivity does not fully solve the problem, as it comes with significant implementation cost and is difficult to expand to multi-dimensional parameter spaces. Also, many existing data-based optimization approaches treat the optimization problem as a black-box, thus requiring a large amount of data. We present a constrained, model-based Bayesian optimization approach that avoids black-box models by leveraging existing knowledge about the simulation components and properties of the simulation behavior. The main focus of this paper is on the stochastic modeling ansatz for simulation error and run time as optimization objective and constraint, respectively. To account for data covering multiple orders of magnitude, our approach operates on a logarithmic scale. The models use a priori knowledge of the simulation components such as convergence orders and run time estimates. Together with suitable priors for the model parameters, the model is able to make accurate predictions of the simulation behavior. Reliably modeling the simulation behavior yields a fast optimization procedure because it enables the optimizer to quickly indicate promising parameter values. We test our approach experimentally using the multi-scale muscle simulation framework OpenDiHu and show that we successfully optimize the time step widths in a time splitting approach in terms of minimizing the overall error under run time constraints.

A multiscale spatial modeling framework for the germinal center response.

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymphoid organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events, including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanistic and applied research questions on the adaptive humoral immune response in the future.

Multiscale modeling of functionally graded shell lattice metamaterials for additive manufacturing

In this work, an experimentally validated multiscale modeling framework for additively manufactured shell lattice structures with graded parameters is introduced. It is exemplified in application to the Schwarz primitive triply periodic minimal surface microstructure and 3D printing using masked stereolithography of a photopolymer material. The systematic procedure starts with the characterization of a hyperelastic material model for the 3D printed material. This constitutive model is then employed in the finite element simulation of shell lattices at finite deformations. The computational model is validated with experimental compression tests of printed lattice structures. In this way, the numerical convergence behavior and size dependence of the model are assessed, and the range in which it is reasonable to assume linear elastic behavior is determined. Then, representative volume elements subject to periodic boundary conditions are simulated to homogenize the mechanical behavior of Schwarz primitives with varying aspect ratios and shell thicknesses. Subsequently, the parameterized effective linear elasticity tensor of the metamaterial is represented by a physics-augmented neural network model. With this constitutive model, functionally graded shell lattice structures with varying microstructural parameters are simulated as macroscale continua using finite element and differential quadrature methods. The accuracy, reliability and effectiveness of this multiscale simulation approach are investigated and discussed. Overall, it is shown that this experimentally validated multiscale simulation framework, which is likewise applicable to other shell-like metamaterials, facilitates the design of functionally graded structures through additive manufacturing.Graphical

A simple machine learning-based framework for faster multi-scale simulations of path-independent materials at large strains

Coupled multi-scale finite element analyses have gained traction over the last years due to the increasing available computational resources. Nevertheless, in the pursuit of accurate results within a reasonable time frame, replacing these high-fidelity micromechanical simulations with reduced-order data-driven models has been explored recently by the modelling community. In this work, two classes of machine learning models are trained for a porous hyperelastic microstructure to predict (i) whether the microscopic equilibrium problem is likely to fail and (ii) the stress–strain response. The former may be used to identify critical macroscopic points where one may fall back to the high-fidelity analysis and possibly apply convergence bowl-widening techniques. For the latter, both a linear regression with polynomial features and artificial Neural Networks have been used, and the required stress–strain derivatives for solving the equilibrium problem have been derived analytically. A weight regularisation is introduced to stabilise the tangent operator and several strategies are discussed for imposing null stresses in undeformed configurations for both regression models. The regression techniques, here analysed exclusively in the context of porous hyperelastic materials, evidence very promising prospects to accelerate multi-scale analyses of solids under large deformation.

Multiscale thermomechanical assessment of silicon carbide-based nanocomposites in solar energy harvesting applications

Increasing the operating temperature of concentrating solar power plants beyond 650 °C is crucial for increasing their efficiency and energy storage capability, and thus pushing their market penetration. However, one of the main drawbacks that arise with an increase in temperature is material degradation. Ceramic materials are an interesting alternative to nickel–chromium superalloys due to their high thermal resistance and low expansion capabilities. In this work, we characterize the thermomechanical behavior of a silicon carbide-based ceramic material for receiver tubes up to 750 °C. For this purpose, we develop a multiscale simulation framework, combining studies at different scales of observation (i.e., material, and component) using different simulation tools. At the material scale, we generate virtual microstructures that are subject to thermomechanical tests using the lattice model. The material properties obtained at this scale of observation are subsequently used at component level simulations, which are carried out by means of the finite element method. This allows the exploration of new materials designed in silico and the prediction of their performance in solar energy applications. In this work, we use our methodology to assess the thermoelastic behavior of SiSiC tubes at high temperatures and obtain temperature-dependent material properties. At the material level, we report elastic moduli in the range of 250–500 MPa and coefficients of thermal expansion in the range of 6–12·10−6 1/°C, under operation conditions. Regarding the component, we found that SiSiC tubes with a thickness-to-diameter ratio of 0.15 or larger are safe at operating temperatures up to 750 °C.

Second-order homogenisation of crystal plasticity and martensitic transformation

Second-order computational homogenisation is combined with constitutive modelling of crystal plasticity and martensitic transformation to analyse the influence of strain gradients on the multi-scale response of polycrystalline materials and the kind of size effects that can be captured. The impact of the length of the Representative Volume Element (RVE) model and the size of the grains is analysed independently, resorting to parametric studies with several random realisations. It is observed that the captured size effects are due to the RVE length, while the size of the grains, which is related to the number of grains in the RVE, is mainly associated with the representativeness of the homogenised response. Macroscopic deformation states are extracted from a plate subjected to bending to guarantee the physical admissibility of the strain gradients and deformation gradients applied to the RVE. It is also found that the influence of the RVE length on the multi-scale response of polycrystals is also dependent on the relationship between the magnitude of the first and second-order deformations. The TRIP effect is also studied by performing these analyses with and without martensitic transformation.To quantify the differences between the results obtained with first- and second-order homogenisation, analytical expressions that take into consideration the macroscopic deformation measures and the RVE length are identified to approximate numerical observations. Finally, an adaptive framework for multi-scale simulation accounting for strain gradients is proposed, where these expressions can be employed in a criterion for the transition from first- to second-order homogenisation.

Theoretical study of the impact of alloy disorder on carrier transport and recombination processes in deep UV (Al,Ga)N light emitters

Aluminum gallium nitride [(Al,Ga)N] has gained significant attention in recent years due to its potential for highly efficient light emitters operating in the deep ultra-violet (UV) range (<280 nm). However, given that current devices exhibit extremely low efficiencies, understanding the fundamental properties of (Al,Ga)N-based systems is of key importance. Here, using a multi-scale simulation framework, we study the impact of alloy disorder on carrier transport, radiative and non-radiative recombination processes in a c-plane Al0.7Ga0.3N/Al0.8Ga0.2N quantum well embedded in a p–n junction. Our calculations reveal that alloy fluctuations can open “percolative” pathways that promote transport for the electrons and holes into the quantum well region. Such an effect is neglected in conventional and widely used transport simulations. Moreover, we find that the resulting increased carrier density and alloy induced carrier localization effects significantly increase non-radiative Auger–Meitner recombination in comparison to the radiative process. Thus, to suppress such non-radiative process and potentially related material degradation, a careful design (wider well, multi-quantum wells) of the active region is required to improve the efficiency of deep UV light emitters.

A hybrid CFD-RMD multiscale coupling framework for interfacial heat and mass simulation under hyperthermal ablative conditions

Under hypersonic flow conditions, the heat and mass transfer at the gas-solid interface of thermal protection material becomes highly complicated due to the strong chemical and thermal non-equilibrium phenomena, associated with the real gas effect, the high temperature effect and various heterogeneous reactions occurring at the interface or inside the TPM. Interfacial heat and mass transfer is strongly coupled with non-linear reactions at different spatiotemporal scales. Based on the traditional macroscopic Computational Fluid Dynamics (CFD) and microscopic Reactive Molecular Dynamics (RMD) methods, a hybrid CFD-RMD multiscale simulation framework is established in this work to improve the accuracy of aerothermal prediction by considering the heat and mass transfer at the gas-solid interface under hyperthermal non-equilibrium conditions. To validate the proposed multiscale framework, phenolic resin composite is investigated in this work with particular interest in the pyrolysis gas injection effects. Benchmarking ablation studies are conducted under three representative altitudes of 40, 60 and 80 km, respectively, and the recession rates of 7.47 × 10−4, 1.53 × 10−3 and 1.08 × 10−3 mm/s are obtained which are comparable with the experimental results. Much higher computational efficiency of the hybrid CFD-RMD multiscale framework is achieved comparing to a full RMD simulation method at the same spatial and temporal level. Not only to the pyrolysis study, the established framework can also potentially be extended to other gas-solid interfacial reaction situations, which is of great help in improving the mechanism understanding of various physics-derived microscopic models for macroscopic predication of hypersonic aerothermal characteristics.

Additive manufacturing of cellular structures: Multiscale simulation and optimization

This paper introduces a multiscale and multi-purpose simulation framework to investigate selective beam melting processes for metallic cellular structures along the complete process chain, up to the topology optimization of components made of cellular materials. Process simulation methods on various length scales are introduced to analyze the relation of process strategies and resulting properties of the cellular materials, as e. g. warpage, residual stresses, material grain structure and surface roughness. Numerical homogenization methods are applied to investigate the influence of the grain structure and the topology of the cellular materials on their mechanical properties. Based on these process-dependent mechanical properties, a two-scale optimization of components made of cellular material is performed, aiming in particular on optimizing the buckling resistance of the structures. The interfaces between the different simulation tools are specified and illustrate the flexibility of the numerical framework. It is shown that consistent simulations of additive manufacturing of cellular materials – from the manufacturing process to the optimized component – provide important insights into process–structure interactions and enable tailored additive manufacturing processes.

A Physics‐Aware Deep Learning Model for Energy Localization in Multiscale Shock‐To‐Detonation Simulations of Heterogeneous Energetic Materials

AbstractPredictive simulations of the shock‐to‐detonation transition (SDT) in heterogeneous energetic materials (EM) are vital to the design and control of their energy release and sensitivity. Due to the complexity of the thermo‐mechanics of EM during the SDT, both macro‐scale response and sub‐grid mesoscale energy localization must be captured accurately. This work proposes an efficient and accurate multiscale framework for SDT simulations of EM. We introduce a new approach for SDT simulation by using deep learning to model the mesoscale energy localization of shock‐initiated EM microstructures. The proposed multiscale modeling framework is divided into two stages. First, a physics‐aware recurrent convolutional neural network (PARC) is used to model the mesoscale energy localization of shock‐initiated heterogeneous EM microstructures. PARC is trained using direct numerical simulations (DNS) of hotspot ignition and growth within microstructures of pressed HMX material subjected to different input shock strengths. After training, PARC is employed to supply hotspot ignition and growth rates for macroscale SDT simulations. We show that PARC can play the role of a surrogate model in a multiscale simulation framework, while drastically reducing the computation cost and providing improved representations of the sub‐grid physics. The proposed multiscale modeling approach will provide a new tool for material scientists in designing high‐performance and safer energetic materials.

Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network

The reaction-diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction-diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls (p2), and the average width of the walls (p3). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in p2 and p3 for test data having 10% deviation from the training data were within 7% of the average magnitude of p2 and p3. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework.

CCCs off-axial orientation sensitivity analysis in hole pin-bearing failure via hierarchical multiscale simulation framework

In current investigation, a sequential multiscale modelling strategy together with corresponding experimental validation aimed to evaluate the influence of off-axial orientation on three-dimensional orthogonal woven carbon/carbon composites (3DOWCCCs) pin-bearing failure behavior. A hierarchical numerical simulation methodology at micro−/meso−/macroscales was developed to obtain the predictions. With the intention of acquiring precise mechanical responses of unnotched 3DOWCCCs, fiber and void stochastic arrangements in micro-level representative volume elements (RVEs) were generated using Random Sequential Adsorption (RSA) algorithm, meanwhile the geometrical reconstruction of meso-level RVE was accomplished via X-ray computed tomography (X-CT). Moreover, off-axial angle sensitivity analysis was presented through the comparison between macroscale modelling and testing results. The stress interaction and coupling impacts were embedded in material constitutive laws, which combined Murakami-Ohno theory for yarn based on continuum damage mechanics, and exponential damage rule for carbon matrix, incorporating trilinear cohesive zone model (CZM) for interface, and the achieved predictions agreed reasonably well with the experimental results. It is concluded that, for on-axial specimen, the warp yarns fracture and material out-of-plane swelling were the primary damage mechanism, while the material out-of-plane swelling in conjunction with yarns in-plane rotation dominated the structural failure under off-axial cases.

A Generic Framework for Multiscale Simulation of High and Low Enthalpy Fractured Geothermal Reservoirs under Varying Thermodynamic Conditions

We develop a multiscale simulation strategy, namely, algebraic dynamic multilevel (ADM) method, for simulation of fluid flow and heat transfer in fractured geothermal reservoirs under varying thermodynamic conditions. Fractures with varying conductivities are modeled using the projection-based embedded discrete fracture model (pEDFM) in an explicit manner. The developed ADM method allows the fine-scale system to be mapped to a discrete domain with an adaptive grid resolution via the use of the restriction and prolongation operators. The developed framework is used (a) to investigate the impacts of formulations with different primary variables on the simulation results, and (b) to assess the performance of ADM in a high-enthalpy reservoir by comparing the simulation results against those obtained from fine-scale grids. Results show that the two formulations produce similar results in the case of single-phase flow, which indicates that the molar formulation is a favorable option that can be applied to varying thermodynamic conditions. Moreover, the ADM can provide accurate solutions with only a fraction of fine-scale grids, e.g., for the studied case, the maximum error is by average 1.3 with only 42% of active cells, thereby improving the computational efficiency. This is promising for applying the developed method to field-scale geothermal systems.

Machine learning coarse-grained models of dissolutive wetting: a droplet on soluble surfaces.

Dissolutive wetting is not only a key problem in application fields such as energy, medicine, micro-devices and etc., but also a frontier issue of academic research. As an important tool for exploring the micro-mechanisms of dissolutive wetting, molecular dynamics simulations are limited by simulation scale and force field parameters. Thus, artificial intelligence is introduced into the multi-scale simulation framework to tackle such challenges. By combining density functional theory, molecular dynamics simulations and experiments, we obtain a coarse-grained model of the glucose-water dissolution pair. Furthermore, the structure of the solid molecules and the hydration shell near the solute particles are calculated by quantum mechanics/molecular mechanics to verify the accuracy of the model. Finally, the applicability of the coarse-grained model in dissolutive wetting is proven by experimental results. We believe our machine learning method not only lays a foundation for exploring the micro-mechanisms of dissolutive wetting, but also provides a general approach for obtaining the force field parameters of different systems.

Squishing Skyrmions: Symmetry-Guided Dynamic Transformation of Polar Topologies Under Compression.

Mechanical controllability of recently discovered topological defects (e.g., skyrmions) in ferroelectric materials is of interest for the development of ultralow-power mechano-electronics that are protected against thermal noise. However, fundamental understanding is hindered by the "multiscale quantum challenge" to describe topological switching encompassing large spatiotemporal scales with quantum mechanical accuracy. Here, we overcome this challenge by developing a machine-learning-based multiscale simulation framework─a hybrid neural network quantum molecular dynamics (NNQMD) and molecular mechanics (MM) method. For nanostructures composed of SrTiO3 and PbTiO3, we find how the symmetry of mechanical loading essentially controls polar topological switching. We find under symmetry-breaking uniaxial compression a squishing-to-annihilation pathway versus formation of a topological composite named skyrmionium under symmetry-preserving isotropic compression. The distinct pathways are explained in terms of the underlying materials' elasticity and symmetry, as well as the Landau-Lifshitz-Kittel scaling law. Such rational control of ferroelectric topologies will likely facilitate exploration of the rich ferroelectric "topotronics" design space.