The biphasic plate, manufactured by 41 medical in Bettlach, Switzerland, represents a deliberate departure from decades of orthopedic philosophy. Early plate fixation pursued absolute stability after anatomic reduction, exploiting direct bone healing. Later designs, such as the Limited Contact Dynamic Compression Plate introduced by Gautier and Perren, minimized soft-tissue damage, while bridging plates allowed secondary healing through callus formation. Systems like the Less Invasive Stabilization System and retrograde nailing reduced complication rates, and dual plating has shown promise in complex distal femur fractures, although a systematic review by Tripathy and colleagues found no significant functional advantage over single plating and longer procedure times. The recurring problem is that very stiff constructs, often used in osteoporotic bone to permit early weight bearing, can shield the fracture from the mechanical stimulation that callus formation requires.

The biphasic concept answers this dilemma by building the flexibility into the plate body itself. The implant is thicker than a conventional locking plate, raising its overall stiffness and fatigue strength, but an integrated meander-shaped recess locally reduces stiffness and permits a controlled degree of elastic movement with mechanical amplitude limitation. Previous work by Hofmann-Fliri and colleagues, who adapted the plate to the ovine tibia in an animal model, demonstrated rapid and robust callus formation and improved construct strength compared with conventional locking plates, especially at higher weight-bearing levels. Epari and colleagues, testing the plate on bone substitute material with a 20-millimeter fracture gap under axial loads from 0 to 1000 newtons, found a bilinear stiffness response that delivered more consistent interfragmentary movement and greater implant strength, properties particularly relevant for distal femur fractures.

What remained missing was a bridge between these controlled characterizations and the conditions an actual patient experiences. The Saarland team closed that gap with a three-part methodology. In the laboratory arm, they obtained a cadaveric femur from a 75-year-old female body donor, created a 30-degree osteotomy mimicking an OTA/AO type 33A2 distal femur fracture, and fixed it with the biphasic plate using nine head-locking screws. The specimen was clamped in a custom-designed testing rig validated in earlier work, and a spindle-driven linear actuator applied axial compression in six steps of 0.25 millimeters each at a quasi-static rate of 0.25 millimeters per second.

Two measurement technologies made the experiment unusually informative. A camera system documented the state of the plate’s meander structure, showing it open during the flexible phase and closed once the rigid phase engaged. Meanwhile, an implantable strain sensor known as the AO Fracture Monitor, developed by the AO Foundation in Davos, was mounted directly on the plate with two screws tightened to 1.5 newton-meters. This wireless device, originally built to track bone healing progression at 10 hertz via a strain gauge and transmit data to the cloud via Bluetooth, recorded the plate’s strain response throughout loading. At the final compression step the force reached 235 newtons, at which point the meander closed and the plate transitioned from its flexible to its rigid phase, a transition the authors note becomes apparent at roughly 200 newtons.

The computational arm of the study was built to reproduce exactly this experiment. The cadaveric specimen was scanned with a Siemens Somatom Definition AS64 CT scanner at 120 kVp and 0.6-millimeter slice thickness, together with a calibration phantom, and metal artifact reduction was applied to the images. After segmenting cortical and cancellous bone in consultation with treating physicians, the team generated a finite element model using ten-node tetrahedral C3D10 elements in Abaqus. Bone material properties were derived from CT gray values through density-modulus relationships, producing 25 material classes ranging from 100 to 22,000 megapascals, while the stainless steel plate and bolts were assigned a Young’s modulus of 200 gigapascals and a Poisson’s ratio of 0.3. The meander gap was modeled with frictionless tangential and hard normal contact, and six simulation steps applied the experimental forces across the proximal femur.

Validation proceeded on two fronts. First, the simulated relative strain change across the six loading steps closely followed the smoothed curve recorded by the AO Fracture Monitor, with only minor deviations attributed to differences in force application, clamping, bone alignment, and node selection. Second, the team replicated the benchmark scenario of Epari and colleagues, applying axial loads from 0 to 1000 newtons and confirming the characteristic nonlinear load-interfragmentary movement response. In the near cortex the load rose steadily and then steepened beyond 0.2 millimeters of interfragmentary movement; in the far cortex the pronounced load increase occurred mainly beyond 1 millimeter. The von Mises stress distribution at 1000 newtons, spanning 0 to 850 megapascals, concentrated in specific plate regions and matched the earlier study’s findings, confirming that the model captured the biphasic mechanism itself.

The most striking results came from the in vivo arm. Four patient-specific models were generated from clinical CT data, incorporating each patient’s anthropometry, fracture situation, plate position, screw configuration, and individualized material properties. For one patient, sensor insoles and a motion capture system were used two days after surgery to record real gait under recommended weight-bearing conditions, and a musculoskeletal simulation in AnyBody derived the hip joint reaction force over time. The other patients’ loading profiles were drawn from the OrthoLoad database according to body weight and fracture side. Crucially, these load cases contained force components in all three anatomical planes, not just axial compression, and physiological proximal-distal forces during gait can reach approximately 2500 newtons, far exceeding the 1000-newton benchmark.

Under these realistic conditions, the stress picture inverted. Whereas axial loading distributed stresses centrally over the meander region, all four patient simulations placed maximum von Mises stresses along the lateral edge of the plate. The medial-lateral and anterior-posterior force components, together with the lever arm introduced by force transmission through the femoral head, superimpose bending and shear on axial compression, exactly as classical biomechanics described by Pauwels would predict. The authors emphasize that standardized axial test setups remain useful for implant characterization but cannot fully represent the multi-planar loading that governs implant behavior during walking, and that overly simplified in vitro or in silico setups risk missing clinically relevant stress concentrations.

The implications reach toward smarter, more individualized fracture care. Patient-specific simulations could identify implant regions exposed to elevated stresses during daily activities, informing future geometry optimization, working-length selection, and fixation strategies before clinical application. Combined with implantable sensors that continuously report plate strain as a surrogate for callus maturation, the approach points toward rehabilitation plans tailored to each patient’s actual loading environment. The team is candid about limitations: a single cadaver specimen, quasi-static axial loading capped at 1000 newtons, no biological or healing simulation, and possible segmentation errors mean the patient results should be read as model-based predictions rather than validated clinical outcomes. Even so, the study delivers what the authors identify as its key outcomes, validation and reproducibility, and demonstrates that only by integrating in vivo, in vitro, and in silico methods can the true mechanical life of a fracture implant be understood.

Subject of Research: Biomechanical evaluation of the distal femur biphasic plate using in vivo, in vitro, and in silico methodologies

Article Title: Integrated Study of the Distal Femur Biphasic Plate: Exploring In Vivo, In Vitro, and In Silico Methodologies

Article References: Integrated Study of the Distal Femur Biphasic Plate: Exploring In Vivo, In Vitro, and In Silico Methodologies. (n.d.). https://doi.org/10.1007/s10439-026-04357-6

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04357-6

Keywords: biphasic plate, distal femur fracture, finite element simulation, AO Fracture Monitor, interfragmentary movement, patient-specific modeling, bone healing, osteosynthesis, biomechanics, cadaveric testing, gait loading, smart implants

Sandwich structures work much like an I-beam stretched into a panel: two stiff outer skins take bending stresses while a lightweight core holds them apart and resists shear. In civil engineering, this architecture promises high strength-to-weight ratios, built-in thermal insulation, and excellent energy absorption. Fiber-reinforced polymer face sheets add corrosion resistance, cutting maintenance and life-cycle costs compared with steel or reinforced concrete. Curved versions of these panels open additional design freedom for architecturally ambitious roofs and facades, yet their static bending behavior has remained surprisingly underexplored, with most prior research focused on vibration and aerospace applications.

The research team fabricated singly curved panels using vacuum infusion molding, a process that begins by cutting foam into an arc, wrapping it with a layer of ±45° glass-fiber fabric, and then sequentially assembling the bottom face sheet, internal web cores, and outer face sheet on a curved wooden mold before resin infusion. After eight hours of curing, the panels were demolded and trimmed. Three core configurations were compared: conventional polyurethane foam, grid-scored recycled PET foam, and recycled PET foam reinforced with a continuous lattice of glass fiber webs. Each panel had a span of 400 millimeters, a width of 200 millimeters, a 25-millimeter-thick core, and five ring webs spaced 200 millimeters apart horizontally.

Curvature proved to be a decisive variable. Panels were tested at three radii of 300, 580, and 1150 millimeters, corresponding to central angles of 60, 30, and 15 degrees. For the polyurethane foam series, the panel with the largest radius failed at 7.49 kilonewtons through brittle compressive fracture of the upper face sheet beneath the loading plate. Reducing the radius to 300 millimeters cut the ultimate load to 5.29 kilonewtons and the bending stiffness to 0.73 kilonewtons per millimeter, a 29.4 percent loss in capacity and a 26.3 percent loss in stiffness. Tighter curvature intensified membrane-bending coupling and radial compression, triggering premature debonding between face sheet and core before the panel could fully mobilize its bending resistance.

The grid-scored PET foam panels, in which load transfer relies on discontinuous resin-rich channels, fared worse under the same conditions. Their initial stiffness values of 0.66 and 0.77 kilonewtons per millimeter lagged well behind the lattice-reinforced equivalents, and stress concentrations at the resin columns, the foam-resin interface, and the face-core boundary interacted destructively during loading. At the smallest radius, interfacial delamination began at only 3.49 kilonewtons, and the panel ultimately failed at 4.37 kilonewtons before collapsing to 1.50 kilonewtons as shear cracks spread through the foam. The discrete grid could not bridge cracks or redistribute stress once local damage started, so degradation was rapid and brittle.

By contrast, the lattice-reinforced recycled PET foam panels delivered the best performance across every curvature. The largest-radius specimen reached an initial bending stiffness of 1.09 kilonewtons per millimeter and a peak load of 12.4 kilonewtons, while the moderate-radius panel achieved the highest ultimate load of the entire experimental campaign at 13.3 kilonewtons. Even the tightest-radius panel sustained 11.0 kilonewtons. Crucially, after the upper face sheet fractured in compression, the loads did not collapse entirely; they dropped only partially and then recovered, for example from 13.3 to 11.5 kilonewtons, because the continuous lattice webs acted as internal bridges that kept transferring load between the separated face sheets. Compared with the grid-scored design, ultimate loads rose by 71.5 to 151.7 percent.

Digital image correlation provided a strain-map view of these mechanisms in real time. In large-radius panels, strain concentrated in the upper face sheet under the loading plate, confirming compression-dominated failure. As radius shrank, shear strain localization migrated into the foam core near the load point and the face-core interface, signaling the shift toward debonding and core shear failure. The lattice-reinforced panels showed markedly more continuous strain distributions along the curved section than their grid-scored counterparts, evidence that the internal webs diffused stress, restrained local deformation, and delayed unstable crack propagation through the thickness of the core.

To go beyond what experiments alone could reveal, the team built a three-dimensional finite element model in ABAQUS incorporating Hashin damage criteria for the composite laminates, a crushable foam plasticity model with volumetric hardening for the PET core, and a bilinear cohesive zone model for the face-core interface. The simulations reproduced the measured stiffness and peak loads with errors below 10 percent, and predicted failure modes matched the laboratory observations, including interfacial debonding captured through cohesive damage variables. Deflection fields at a 4.0 kilonewton load level also agreed closely with the DIC measurements, validating the model as a trustworthy design tool.

The parametric study then isolated the levers that matter most. Raising the PET foam density from 80 to 150 kilograms per cubic meter increased ultimate load by 29.2 percent but bending stiffness by only 18.9 percent, because global stiffness is governed mainly by the axial stiffness and separation of the face sheets rather than the core. Fiber layup orientation strongly affected initial stiffness, with a (0°,90°) laminate reaching 2.15 kilonewtons per millimeter against 0.85 for an all ±45° stack, yet ultimate loads stayed within a narrow band around 13.7 to 14.1 kilonewtons. Lattice geometry emerged as the most powerful knob: thickening the longitudinal webs from 1.2 to 3.6 millimeters lifted ultimate load from 13.69 to 15.00 kilonewtons, and tightening longitudinal web spacing raised peak load to 16.43 kilonewtons, a gain of roughly half over the baseline configuration.

Across all variations, the dominant failure sequence remained interfacial delamination followed by compressive failure of the upper face sheet, but the lattice consistently delayed that sequence and preserved residual capacity afterward. The findings carry practical weight for sustainable construction: recycled PET foam diverts plastic waste, requires less production energy than traditional core materials, and adds thermal insulation, while GFRP skins resist corrosion and reduce reinforcement demands on existing structures. By demonstrating that a simple internal lattice transforms a recycled-core curved panel from brittle and debonding-prone into a progressively damage-tolerant structural element, the study offers designers a clear, simulation-backed recipe for lighter, greener, and more resilient civil infrastructure.

Subject of Research: Experimental and numerical investigation of the bending behavior, failure modes, and design parameters of curved GFRP sandwich panels with recycled PET foam cores and internal lattice reinforcement

Article Title: Bending behavior of curved sandwich panels comprising GFRP face sheets and recycled PET foam cores: Experimental investigation and numerical simulation

Article References: Xie, H., Man, J., Zhang, Z., Fang, H., Wang, Z., & He, P. (2026). Bending behavior of curved sandwich panels comprising GFRP face sheets and recycled PET foam cores: Experimental investigation and numerical simulation. Case Studies in Construction Materials, 25, Article e06525. https://doi.org/10.1016/j.cscm.2026.e06525

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06525

Keywords: GFRP, recycled PET foam, curved sandwich panels, lattice reinforcement, bending behavior, face-core debonding, finite element simulation, Hashin damage criteria, digital image correlation, sustainable construction, foam core density, civil infrastructure

The research, led by Xue Liang and Marc-Philipp H. Schmid as co-first authors, with senior authorship shared by Bradley G. Leshnower of Emory University School of Medicine and Hai Dong of Emory University and the Georgia Institute of Technology, set out to build a patient-specific computational framework capable of predicting aortic geometry and diameter growth in uncomplicated type B aortic dissection. The team included investigators from Georgia Tech, Texas Tech University, Emory University, and the Aortic Institute at Yale-New Haven Hospital, where John A. Elefteriades, one of the world’s foremost aortic surgeons, contributed his clinical expertise. What makes their approach remarkable is its reliance on data that clinicians already collect in routine practice: standard CT imaging and blood pressure measurements. No experimental tissue testing, no specialized imaging protocols, and no extra procedures were required.

At the heart of the framework lies a sophisticated description of aortic wall mechanics known as the unified fiber distribution, or UFD, model. The wall of the aorta is not a simple balloon-like membrane; it is a layered, fiber-reinforced composite in which networks of collagen and elastin bear load in different directions. Traditional constitutive models often assume discrete fiber families, which can struggle to capture the full diversity of fiber orientations found in real arterial tissue. The UFD model, developed previously by Dong and colleagues, treats fibers as distributed continuously across orientations within the plane of the vessel wall, providing a unified mathematical description that bridges different regimes of fiber recruitment under load. This planar distributed-fiber formulation also accounts for a so-called second kind of Poisson effect, a distinctive feature of thin, fiber-reinforced membranes. Implemented as a user-defined material subroutine in the commercial finite-element software Abaqus, the model allowed the researchers to represent the mechanical behavior of each patient’s dissected aortic wall with a high degree of physiological realism.

The second key innovation was geometric. In a dissection, the aortic wall splits into two channels, a true lumen and a false lumen, separated by an intimal flap, creating an enormously complex three-dimensional architecture. To track how this living structure grows over time, the researchers needed a way to map material points of the aortic tissue consistently across serial scans. They developed a novel centerline-based algorithm that determines the local material coordinates of aortic tissues by anchoring them to the curved central axis of the vessel. This algorithm, written in MATLAB, assigns each element of the finite-element mesh a local coordinate frame that follows the tortuous, patient-specific anatomy, enabling the model to distinguish local circumferential and longitudinal directions and to apply growth laws in the correct anatomical orientation.

The workflow the team devised is elegantly symmetrical, combining inverse and forward analyses. For each of seven type B aortic dissection patients, the researchers obtained three serial CT scans captured at different time points, along with blood pressure data. Using the geometries from the first two scans, they performed an inverse finite-element analysis: rather than predicting forward from known parameters, they worked backward from the observed second geometry to calibrate the patient-specific growth parameters that must have driven the enlargement seen between the first and second scans. Because the wall stress-driven growth framework posits that the aorta remodels in response to the mechanical stresses it experiences, this inverse step effectively reads out each patient’s individual biological propensity for enlargement, encoded in personalized growth coefficients. Once calibrated, these parameters were fed into a forward growth simulation to predict the aortic geometry at the third time point, a moment never shown to the model during calibration.

The results were striking. When the predicted geometries were compared against the actual CT measurements at the third time point, the model’s forecasts proved remarkably accurate. Across all seven patients, the absolute percent error in the predicted maximum aortic diameter was less than 3.5 percent, and the error in the predicted mean diameter across all anatomical locations was under 4 percent. Given that clinically meaningful aortic growth is often measured in single millimeters, this level of accuracy suggests the framework captured genuine biomechanical information rather than simply averaging away individual variation. The proof-of-concept validation demonstrates that aortic enlargement in dissection is not an inscrutable biological lottery but, at least in part, a mechanically governed process that can be quantified from clinical data.

The significance of this work becomes clearer when viewed against the stubborn uncertainties of current clinical practice. Decades of outcome studies have shown that risk factors for failure of medical management in type B dissection include anatomic features, false lumen patency, and aortic dimensions, yet diameter alone remains an imperfect predictor, and growth rates vary enormously between patients. Previous computational efforts have used computational fluid dynamics and fluid-structure interaction analysis to probe hemodynamic predictors such as false lumen pressure and wall shear stress, often requiring specialized 4D flow MRI data. The new framework complements this body of work by shifting attention to the solid mechanics of the wall itself and by demanding nothing more than the imaging and pressure data that every dissection patient already generates during surveillance.

If validated at larger scale, the implications for patient care could be substantial. A calibrated digital twin of a patient’s aorta could, in principle, support individualized surveillance intervals, identifying early on which patients are destined for rapid enlargement and warranting closer monitoring or earlier thoracic endovascular repair, while sparing stable patients unnecessary anxiety and intervention. It could also help surgeons time intervention for maximal benefit, converting an evidence-based but reactive strategy into a proactive, predictive one. The researchers are careful to frame this as a proof of concept: seven patients is a modest cohort, and the growth parameters are calibrated from observed enlargement rather than true out-of-sample prediction over entirely unseen futures. Larger, multi-center validation studies will be needed before such simulations can inform clinical guidelines, which are currently codified in the 2022 ACC/AHA aortic disease guideline.

Nevertheless, the study represents a compelling convergence of biomechanics, imaging, and cardiothoracic surgery. By extending a stress-driven growth framework, embedding the unified fiber distribution model into patient-specific finite-element simulations, and inventing a centerline-based method to track tissue coordinates through serial scans, the Emory-Georgia Tech-Yale team has shown that the future geometry of a dissected aorta can be computed with clinically useful precision. The MATLAB code for the coordinate-assignment algorithm and the Abaqus implementation of the UFD model are available from the corresponding authors upon reasonable request, and the study was supported by the National Heart, Lung, and Blood Institute through grant R01HL155537 and by the Carlyle Fraser Heart Center. For the hundreds of thousands of patients worldwide living under the watchful uncertainty of a dissected aorta, the prospect of a simulation that reveals tomorrow’s anatomy from today’s scan is a vision of predictive medicine that has moved measurably closer to reality.

Subject of Research: Patient-specific finite-element prediction of aortic growth in type B aortic dissection using the unified fiber distribution model

Article Title: Patient-Specific Aortic Growth Prediction in Type B Aortic Dissection Using Finite-Element Simulation Based on the Unified Fiber Distribution (UFD) Model

Article References: Liang, X., Schmid, M.-P. H., Liu, M., Cebull, H. L., Zhang, M., Xu, S., Naeem, M., Oshinski, J. N., Elefteriades, J. A., Gleason, R. L., Jr., Leshnower, B. G., & Dong, H. (2026). Patient-Specific Aortic Growth Prediction in Type B Aortic Dissection Using Finite-Element Simulation Based on the Unified Fiber Distribution (UFD) Model. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04379-0

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04379-0

Keywords: type B aortic dissection, aortic growth prediction, finite-element simulation, unified fiber distribution model, wall stress-driven growth, inverse finite-element analysis, patient-specific modeling, aortic aneurysm, optimal medical therapy, CT imaging, biomechanics, computational cardiology

The physical mechanism most widely invoked to explain particle adhesion is adiabatic shear instability. During impact, the periphery of the particle experiences extreme strain rates, often exceeding ten to the seventh per second. When thermal softening locally outpaces strain hardening, a narrow shear band forms, concentrating deformation and heat into a thin region at the particle-substrate interface. This localized softening promotes the formation of material jets and enables metallurgical bonding between surfaces that would otherwise rebound elastically. The Johnson-Cook constitutive model, which couples strain, strain-rate, and temperature effects into a single flow stress description, is the standard framework for capturing this behavior in finite element simulations, and its parameters directly shape how the response surface varies across the process parameter space.

Single-particle finite element models, such as the spherical particle on a cylindrical substrate configuration used in this study, have become the canonical tool for interrogating these mechanisms. The geometry chosen here, a forty-micrometer-radius aluminum particle striking an aluminum substrate of two hundred fifty micrometer radius and depth, reflects the typical scale of cold spray powder feedstock and allows the impact event to be resolved with sufficient mesh refinement to capture the deformation gradients near the contact zone. Normal incidence is assumed, which is a reasonable first approximation since most particles in a cold spray jet strike the substrate at or near perpendicular orientation, although oblique impacts and particle-particle interactions in real deposits introduce additional complexity that single-particle studies deliberately set aside.

The five output targets selected for prediction capture complementary aspects of the impact response. Maximum equivalent plastic strain quantifies the severity of deformation, which correlates with the extent of interfacial contact area development and hence with bonding likelihood. Average contact plastic strain provides a more spatially averaged measure of deformation at the interface. Maximum temperature indicates whether adiabatic heating approaches the softening regime necessary for jetting. Maximum von Mises stress characterizes the mechanical loading experienced by the material, relevant to residual stress development and potential substrate damage. The deformation ratio, finally, describes the geometric flattening of the particle, a quantity experimenters can measure directly in cross-sectioned deposits, making it a useful bridge between simulation and experimental validation.

The choice of particle velocity, particle temperature, and friction coefficient as the three input parameters reflects their dominant roles in governing impact outcomes. Velocity controls the kinetic energy available for plastic work and is widely regarded as the single most influential cold spray parameter, with critical velocities below which particles rebound and above which they bond. Particle temperature, set by the gas temperature in the spray nozzle, pre-softens the material and lowers the energy barrier for deformation. The friction coefficient at the interface, though harder to control experimentally, governs tangential restraint and energy dissipation during sliding contact, influencing jet formation and the distribution of plastic strain around the contact periphery.

The surrogate modeling strategy adopted in this work addresses a persistent bottleneck in process simulation. A single resolved finite element impact simulation can require substantial computational resources, and exploring a three-dimensional parameter space at useful resolution demands hundreds or thousands of such runs. Once trained, a surrogate model evaluates new process conditions in milliseconds, enabling optimization studies, sensitivity analyses, and inverse design tasks that would be intractable with direct simulation. The practical value of the surrogate, however, depends entirely on its accuracy across the operating envelope, which is precisely where the choice of machine learning architecture becomes consequential.

The central representational innovation of the study is the treatment of each simulation sample as a node in a k-nearest-neighbour graph constructed in feature space, rather than as an isolated feature vector. In conventional feedforward networks, each training example is processed independently, and any information about the similarity between neighboring process conditions is implicit only in the aggregate statistics of gradient descent. By contrast, graph neural networks explicitly pass messages along edges connecting similar samples, allowing each node’s prediction to be conditioned on the responses of its parametric neighbors. For a physical system like cold spray impact, where the response surface is smooth and continuous in the vicinity of any given operating point, this inductive bias aligns naturally with the structure of the underlying data-generating process.

The comparative results carry a clear message about which architectural assumptions suit this problem. GraphSAGE-style spatial aggregation and the geometric attention network both achieved coefficients of determination above 0.93 for most targets, with the attention model reaching 0.97 for maximum plastic strain. These architectures share a common principle: they aggregate information from spatially proximate neighbors in feature space, weighting that information either uniformly or through learned attention coefficients. The attention mechanism’s slight edge is physically sensible, since the velocity-dominated nature of the response means that neighbors at different velocities carry unequal informational value, and attention weights can adaptively emphasize the most relevant ones.

The comparatively poor performance of the Chebyshev spectral graph convolution network and the topologically augmented multilayer perceptron, including negative R-squared values on several targets, is instructive rather than merely negative. Spectral methods operate through polynomial approximations of the graph Laplacian, which excel at multi-scale feature extraction when the graph structure itself carries meaningful community or frequency information. For a k-nearest-neighbour graph built from a relatively smooth parametric dataset, the spectral structure may be too weak or too sensitive to the choice of graph construction to provide a useful signal. Similarly, persistent homology descriptors encode global topological features of the point cloud, such as connected components and loops across scales, which may be largely uninformative for a response surface governed by local parametric gradients rather than by global shape features.

Negative R-squared values deserve particular emphasis for readers less familiar with regression diagnostics. A negative coefficient of determination indicates that the model’s predictions are worse than simply predicting the mean of the training data for every input. This is not a marginal failure but a categorical one, signaling that the architecture has failed to extract any generalizable input-output relationship from the training set. In surrogate modeling applications, such failures typically arise from an inductive bias mismatched to the data structure, or from architectures whose capacity is poorly matched to the available training set size, rather than from noise in the underlying simulation data, which is deterministic in this case.

The velocity-dominated character of the input-output relationships, confirmed by the three-dimensional feature space visualizations and two-dimensional contour projections, is consistent with decades of experimental cold spray research. Deposition efficiency, critical velocity, and coating quality all vary steeply with particle velocity, while temperature and friction act as secondary modulators. A surrogate model that respects this hierarchy, as the attention-based spatial aggregation evidently does, can allocate its representational capacity where the response varies most sharply. This interpretability of model performance in terms of constitutive physics is one of the study’s more valuable contributions, since it transforms an empirical architecture comparison into a statement about the physics of the process itself.

Several limitations frame the scope of these findings. The dataset derives from a single material system, aluminum on aluminum, with a single particle size and normal impact geometry, so extrapolation to dissimilar material pairs, oblique impacts, or multi-particle interactions remains untested. The friction coefficient is treated as a fixed input parameter, whereas in reality interfacial friction evolves with temperature, pressure, and surface state during the impact itself. Furthermore, the surrogate learns from simulation data and inherits any idealizations embedded in the finite element model, including the constitutive parameters of the Johnson-Cook model and the assumed contact behavior. Experimental validation against measured deformation ratios or deposition efficiencies would strengthen confidence in the surrogate’s predictions beyond the simulation domain.

Nevertheless, the framework points toward practical applications in cold spray process development. A validated surrogate could accelerate the identification of operating windows that maximize interfacial plastic strain while keeping substrate stresses within acceptable limits, or support real-time process control where nozzle gas conditions are adjusted in response to measured particle velocities and temperatures. The graph-based representation could also be extended to incorporate additional parameters, such as particle size distributions, substrate preheating, or nozzle standoff distance, as further node features, provided the training dataset is expanded accordingly through continued automated simulation campaigns.

More broadly, the study contributes to a growing recognition in computational materials science that the structure imposed on training data can matter as much as the choice of model family. Where physical responses vary smoothly across a parametric space, encoding that continuity directly into the learning architecture, as graph-based neighborhood aggregation does, provides a form of physics-informed bias that improves both accuracy and data efficiency. For solid-state deposition processes, and potentially for other impact-dominated manufacturing problems with expensive simulations and smooth response surfaces, this representational insight may prove as consequential as the specific performance numbers reported.

Subject of Research: Application of geometric and topological deep learning to predict thermo-mechanical performance in cold spray deposition process modeling

Article Title: Geometric and topological deep learning for predicting thermo-mechanical performance in cold spray deposition process modeling

Article References: Mishra, A. (2026). Geometric and topological deep learning for predicting thermo-mechanical performance in cold spray deposition process modeling. Discover Informatics, 1(1), Article 13. https://doi.org/10.1007/s44564-026-00012-3

Image Credits: AI Generated

DOI: 10.1007/s44564-026-00012-3

Keywords: cold spray deposition, geometric deep learning, graph neural network, GraphSAGE, finite element simulation, Johnson-Cook model, topological data analysis, graph attention network, thermal spray coating, additive manufacturing, surrogate modeling, supersonic particle impact