The stakes are considerable. Scoliosis affects roughly two to three percent of the pre-adult population, but a particularly vulnerable subset of children develop spinal deformity before the age of ten, before most of their skeletal growth has occurred. These cases, driven by congenital, neuromuscular, or acquired conditions, do far more than impair posture and height. Early onset spine deformity contributes to genuine morbidity and mortality, in part because a distorted spine and rib cage restrict the space available for the lungs to develop, sometimes culminating in a life-threatening condition known as thoracic insufficiency syndrome.

Modern surgical philosophy has shifted away from fusing a child’s spine with metal rods, an approach that corrects the curve but stunts thoracic growth and compromises pulmonary function. Instead, surgeons increasingly favor growth-preserving devices that exploit a century-old biological principle known as the Hueter-Volkmann law: compression across a growth plate inhibits bone elongation, while tension stimulates it. By applying asymmetric forces to a still-growing spine, implants such as posterior tethers can theoretically slow growth on one side of the vertebral column while the other side continues to lengthen, gradually straightening the deformity from within the child’s own biology.

The problem is that no instrument can measure the tissue-level stresses inside a living vertebra. That is where finite element models come in. These computational structures divide a spine into thousands of small elements and calculate how forces distribute through bone, discs, and ligaments. Yet most existing models of the porcine spine either used generic parametric geometry, which sacrifices anatomical detail, or modeled only single motion segments without any growth at all. The new study, led by Christian R. D’Andrea and Sriram Balasubramanian of Drexel University together with collaborators at the University of Pennsylvania, Thomas Jefferson University, the University of Delaware, and Boston Children’s Hospital, closes that gap.

The experimental foundation came from three skeletally immature female Yorkshire pigs, aged eight to twelve weeks, in which surgeons implanted a spring-loaded posterolateral cable tether spanning the lower thoracic and lower lumbar spine. The 1.7-millimeter cobalt-chromium cable attached to pedicle screws via lateral offset connectors, and tensioning it to approximately 30 newtons produced a left lateral bending moment across the intercalated segments. Over the following sixteen weeks, each pig developed a clinically significant convex right kyphoscoliosis, with Cobb angles reaching between 49 and 61 degrees. Serial CT scans captured the deformity’s progression from before surgery through the full growth period.

Building the digital counterpart required considerable ingenuity. Rather than meshing each spine from scratch, the team adapted a published dual-kriging morphing technique to warp a validated human spine mesh onto porcine anatomy defined by fifteen landmark points per vertebra. The resulting hexahedral mesh matched the CT-derived surface geometry with a mean symmetric error of just 1.48 millimeters, and roughly 94 percent of elements met recommended quality criteria. The researchers then recreated the implant hardware in software, modeled costovertebral joints as spherical articulations, represented ligaments and intercostal membranes with tension-only springs, and simulated vertebral growth using a thermal expansion trick that allowed each of four quadrants per vertebral body to elongate independently.

The heart of the model is a linear growth-modulation equation in which each vertebral quadrant’s growth rate depends on a baseline growth rate, a stress sensitivity coefficient, and the difference between the local intervertebral disc stress and the average stress under normal loading. Because the exact values of these parameters were unknown, the team calibrated them against the real pigs’ CT-derived curve progression, using a 64-sample Gaussian sampling strategy and an objective function that weighted Cobb angle errors and three-dimensional landmark displacements equally. Calibration slashed the objective function value by 83 to 93 percent compared with literature-based parameters, with baseline growth rates landing between 0.33 and 0.35 millimeters per week and stress sensitivities between 0.61 and 0.80 per megapascal.

The calibrated simulations reproduced the dominant frontal-plane deformity with a mean absolute Cobb angle error of 4.6 to 8.5 degrees across the three pigs, and landmark correspondence errors of only 2.1 to 2.9 millimeters, well within the five-millimeter precision target. For one pig, agreement matched or exceeded a previously reported parametric model, with errors of 2.5 plus or minus 1.6 degrees versus roughly 2.0 plus or minus 2.4 degrees. Just as importantly, the models captured the mechanism: disc compression rose nearly fourfold over sixteen weeks, from about 0.5 to 1.9 megapascals on average, with apical discs showing a stark gradient from 3.8 megapascals on the concavity to 1.4 on the convexity. That gradient suppressed growth on the compressed concave side, and vertebral body wedging accounted for roughly 83 percent of the final simulated deformity, mirroring the biological sequence in which disc wedging appears first and bony wedging follows.

The model was less convincing in the sagittal and transverse planes, where kyphosis angle errors ranged from 10.6 to 22.6 degrees and apical axial rotation errors hovered around 11 degrees. The authors attribute this partly to variability in how pigs were positioned during CT imaging, and partly to deliberate simplifications: rigid, non-growing ribs, no modeled growth of posterior vertebral elements, a homogeneous disc without a distinct nucleus pulposus, and a lumped follower load standing in for muscles and gravity. Notably, the pre-tether disc stresses of about 0.43 to 0.46 megapascals closely match the 0.48 megapascal growth-plate stress previously reported for standing pigs under low muscle activation, lending credibility to the loading assumptions.

The team is candid that this is a proof of principle. Three animals, one of which yielded only eight weeks of data due to tether failure, cannot establish a generalizable porcine stress-growth law, and because the same pigs served for both calibration and assessment, the reported agreement reflects in-sample fit rather than true validation on unseen cases. Still, the framework scales: larger cohorts, standardized imaging, posture-specific loading, and validation on animals excluded from calibration could turn these models into virtual testing grounds where implant designs and surgical configurations are screened computationally before any animal or child is involved. In an era when digital twins are transforming cardiovascular devices and orthopedic implants alike, a spine that grows inside a computer may soon be the first patient every new scoliosis treatment meets.

Subject of Research: Finite element modeling of stress-modulated vertebral growth in a porcine model of mechanically induced scoliosis

Article Title: Scoliosis Induction in the Porcine Spine Using a Growth-Modulating Posterior Tether: Finite Element Model Development and Calibration

Article References: D’Andrea, C. R., Orbach, M. R., Fusco, A., Vresilovic, E. J., Snyder, B. D., Schaer, T. P., Cahill, P. J., & Balasubramanian, S. (2026). Scoliosis Induction in the Porcine Spine Using a Growth-Modulating Posterior Tether: Finite Element Model Development and Calibration. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04403-3

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04403-3

Keywords: scoliosis, finite element model, porcine spine, growth modulation, posterior tether, Hueter-Volkmann law, early onset scoliosis, spine biomechanics, intervertebral disc stress, vertebral growth, implant design, computational biomechanics

The study, published in the Bulletin of Earthquake Engineering, focused on the Guangyue Tower, a traditional hybrid pavilion-style timber structure located in Liaocheng, Shandong Province, in northern China. Led by Xian-Cai Ren of Xi’an University of Architecture and Technology, together with colleagues from Liaocheng University and Qingdao University of Technology, the research team fabricated a 1/4.5-scale model of the tower and mounted it on a shaking table, a laboratory platform capable of reproducing the ground motions of real earthquakes. Three ground motion records of increasing intensity were applied to the model, allowing the researchers to track how the structure’s behavior evolved from mild tremors to rare, severe shaking.

Shaking table tests are among the most demanding experiments in earthquake engineering. The platform must replicate not only the peak acceleration of a seismic event but also its frequency content and duration, all while the instrumented model records accelerations, displacements, and dynamic properties at every level. For heritage timber structures, the challenge is compounded by the need to faithfully reproduce traditional joinery. The Guangyue Tower model incorporated the characteristic features of Chinese pavilion-style construction, including mortise-tenon joints, dou-gong bracket sets, and column feet that rest on stone plinths without rigid anchorage. These connections are deliberately loose by modern standards, and that looseness turned out to be central to the structure’s survival strategy.

Under strong seismic excitation, the model displayed exactly the kind of damage that conservators might fear: significant loosening at the joints and visible cracking in members. Yet the structural consequences were remarkably contained. The fundamental frequency of the model, a measure of its stiffness, dropped by 22.8 percent as the joints worked loose and energy was absorbed through friction and slippage. At the same time, the corresponding damping ratio increased by 59.3 percent, meaning the structure became far more effective at dissipating vibrational energy. In effect, the damage itself acted as a protective mechanism, softening the building and damping its response before deformations could grow dangerous.

Perhaps the most striking finding concerned acceleration. At every story of the model, the acceleration amplification factor, the ratio of the acceleration at that level to the acceleration at the base, remained below 1.0, and the factors decreased as seismic intensity increased. In conventional stiff buildings, accelerations typically amplify toward the roof, imposing large inertial forces on upper levels. The Guangyue Tower model did the opposite: the ground shaking was largely filtered out before it reached the upper stories. This behavior stems from the sliding and rocking of column feet and the energy dissipation at semi-rigid joints, which decouple the superstructure from the most violent components of ground motion.

Deformation capacity proved equally impressive. Under the rarely met earthquake, the most severe shaking level considered, the maximum interstory drift, the relative horizontal displacement between adjacent floors normalized by story height, reached 1/29. For many modern structural systems, drift ratios of this magnitude would raise concerns about collapse or permanent damage. Yet the timber model showed no obvious residual inclination after the shaking stopped. The structure simply returned to its original plumb position, its joints re-seating themselves as the motion subsided. This self-centering behavior, driven by gravity acting on rocking columns and the elastic recovery of timber, is a hallmark of traditional Chinese timber construction and a property that modern engineers often struggle to replicate with rigid connections.

To extend the experimental findings beyond the laboratory, the team developed a simplified numerical model of the structure and validated it against the shaking table measurements. The finite element model reproduced the dynamic responses of the test specimen with good agreement, capturing the frequency shifts, damping changes, and story-level accelerations observed experimentally. With a trustworthy computational surrogate in hand, the researchers could then ask a question that no ethical test program could answer directly: what would happen if the column feet were rigidly fixed to their foundations instead of resting freely on stone plinths?

The numerical comparison delivered a clear verdict. A model with rigid ground-story column foot connections did reduce the maximum interstory drift, making the structure nominally stiffer and less deformable. But this apparent benefit came at a steep price: the roof acceleration response increased significantly, exposing the upper levels of the building to much larger inertial forces. In other words, fixing the columns would trade controlled flexibility for amplified shaking at the top of the tower, potentially overloading roofs, brackets, and upper-story joints. The flexible, sliding column foot, so often dismissed as primitive, is in fact a deliberate seismic fuse that protects the entire building above it.

The implications reach well beyond a single tower in Shandong. Thousands of multi-story traditional timber structures across China, Japan, and Korea face seismic risk, and many have already been damaged in recent events, including the Ms 6.0 Luxian earthquake of 2022, which harmed numerous cultural heritage buildings. Rehabilitation programs guided by modern strengthening instincts, such as anchoring columns or stiffening joints, could inadvertently destroy the very mechanisms that have preserved these buildings for centuries. The study’s authors emphasize that their findings can serve as a reference for the rehabilitation of multi-story traditional hybrid pavilion-style timber structures, and the message for conservation engineers is unambiguous: preserve the flexible behavior of column foot connections if seismic resilience is the goal.

The work also adds to a growing body of experimental evidence on traditional timber engineering, from shaking table studies of Forbidden City palaces and Japanese pagodas to laboratory investigations of dou-gong brackets and mortise-tenon joints. Together, these studies sketch a coherent picture of an ancient building system that achieves earthquake resistance through energy dissipation, joint loosening, rocking, and self-centering rather than through the strength and stiffness that dominate modern codes. As China continues to invest in the protection of its timber heritage, validated numerical models like the one developed in this study offer a practical tool: they allow engineers to test rehabilitation strategies computationally, predict how a real tower will respond to future earthquakes, and ensure that interventions enhance rather than undermine the ingenious flexibility that has kept these wooden giants upright through the centuries.

Subject of Research: Seismic performance of multi-story traditional Chinese pavilion-style timber structures evaluated through shaking table tests and numerical modeling

Article Title: Seismic performance of multi-story traditional hybrid pavilion-style timber structures: shaking table tests and numerical analysis

Article References: Ren, X.-C., Meng, Z.-B., Wang, S.-W., & Cao, Y. (2026). Seismic performance of multi-story traditional hybrid pavilion-style timber structures: shaking table tests and numerical analysis. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02643-1

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02643-1

Keywords: timber structures, seismic performance, shaking table test, Guangyue Tower, mortise-tenon joints, dou-gong brackets, column foot connections, interstory drift, damping ratio, finite element model, heritage conservation, earthquake engineering

The research, led by Kwong Ming Tse of Swinburne University of Technology and the University of Melbourne, together with Dale Robinson, Melanie Franklyn of Australia’s Defence Science and Technology Group, and Peter Vee Sin Lee of the University of Melbourne, tackled a problem that has long frustrated injury biomechanics researchers. Most existing spinal injury criteria were derived from tests on entire spinal columns or large spinal sections, which provide useful system-level tolerance estimates but reveal little about which individual vertebra is most likely to fail. Earlier work had hinted at the importance of this question. Studies of vertical accelerations simulating aircraft ejection showed that as acceleration increases, injuries migrate from the thoracolumbar junction down toward the lower lumbar spine. Sled experiments simulating underbelly blast found that longer-duration seat pulses of 55 milliseconds reduced spinal responses by 68 to 78 percent compared with shorter 10-millisecond pulses, producing fewer pelvic and spinal injuries. But none of these approaches could isolate the vulnerability of each lumbar level.

To fill this gap, the team took an unusual two-pronged approach. They obtained five cadaveric lumbar spine specimens, each free of severe abnormalities as confirmed by radiography and visual inspection, and used dual-energy X-ray absorptiometry to verify that all specimens had areal bone mineral density values within the normal range reported for young adult males aged 17 to 25 years, despite the donors being under 62 years of age. From each spine they isolated a three-vertebra segment — a central vertebra flanked by its neighbours and two intervertebral discs — with the outer vertebrae partially embedded in dental plaster potting fixtures and the middle vertebra deliberately left exposed. Each segment was then compressed at approximately one metre per second on a mechanical testing machine, a rate chosen to bridge conventional quasi-static testing and the more severe blast-level conditions, where reported vehicle floor velocities in live-fire blast events range from 2.2 to 12.8 metres per second. The researchers note that the velocity actually experienced by the lumbar spine is lower than the floor velocity because the seat, pelvis, and surrounding soft tissues attenuate the load.

Alongside the physical tests, the team built specimen-specific finite element models of each three-vertebra segment from high-resolution computed tomography scans with a pixel size of just 0.098 millimetres. The models were anatomically meticulous: vertebral bodies were discretised with roughly 145,000 tetrahedral elements each, cortical shells were divided into seven regions with distinct properties, intervertebral discs comprised ten annulus layers surrounding a nucleus pulposus modelled with hyperelastic material laws, and all seven major spinal ligaments were represented as membrane elements. Crucially, the CT data were used to assign bone material properties element by element, using a calibration phantom to convert Hounsfield units to bone density and a power-law regression to derive Young’s modulus for the trabecular bone. When the models were run in an explicit finite element solver replicating the compression experiments, they reproduced the measured force–displacement responses with coefficients of determination between 0.93 and 0.98, and predicted fracture loads within 10 to 34 percent of the experimental values. The models also captured the observed failure patterns, including coronal split fractures of the vertebral body, impaction fractures of the superior endplate, and isolated trabecular fractures — morphologies consistent with those reported clinically in underbelly blast casualties.

With the models validated, the researchers unleashed them on a series of parametric simulations that would be impossible to perform experimentally. They varied spinal posture by adding 10 degrees of flexion or extension, mimicking the range of sagittal intervertebral rotation during maximal seated trunk movement, and added 10 degrees of lateral bending comparable to voluntary side-bending. They scaled vertebral height and cross-sectional area by plus or minus 10 percent, reflecting anthropometric variation across a military population. And they swept areal bone mineral density across a physiologically relevant range of 0.8 to 1.4 grams per square centimetre, corresponding to young healthy soldiers. The results revealed a striking level-dependence that no whole-column experiment could have exposed.

Posture emerged as a powerful, level-specific modulator of fracture risk. At L1, L2, and L4, flexion generally reduced the likelihood of injury, shifting the fracture probability curves rightward, while extension increased the risk. At L3 the trend reversed, and at L5 both flexion and extension reduced fracture tolerance — a unique behaviour the authors attribute to the biomechanical complexity of the lowest lumbar vertebra, including its adjacency to the sacrum and its altered facet joint geometry. Lateral bending increased fracture susceptibility at the lower lumbar levels, particularly L5, where the decreased fracture load coincided with a marked increase in vertebral body loading. The stiffness analysis added another layer of nuance: at the L4–L5–S1 segment, flexion cut the compressive load at 5 millimetres of displacement from 6,545 newtons to 2,499 newtons, a 62 percent reduction. Importantly, changes in axial stiffness did not consistently translate into changes in fracture load, underscoring that stiffness and strength are distinct metrics that both matter when assessing injury tolerance.

Geometry and bone quality told a more consistent story. Increasing vertebral height reduced axial stiffness and fracture load at all levels except L5, where the opposite trend appeared — a finding that contrasts with earlier ex vivo work reporting a positive correlation between vertebral height and strength, and one the authors suggest may reflect biological factors such as bone mineral density and trabecular connectivity not captured in the models. Larger cross-sectional area, by contrast, consistently enhanced mechanical resistance at every level. Areal bone mineral density proved to be a strong and reliable positive predictor of compressive fracture tolerance across the entire lumbar spine, with higher density producing systematic increases in both stiffness and failure load. Yet the analysis produced a surprise: a measure called axial rigidity, derived from CT-based geometry and material properties, actually outperformed bone mineral density as a predictor of injury risk, yielding injury curves with narrow confidence intervals that converged toward a single vertebra-independent relationship.

The practical implications reach well beyond the laboratory. Fracture tolerance generally increased from L1 to L4, tracking the increasing size and strength of the vertebrae, but L5 consistently bucked the trend, remaining highly vulnerable despite its larger dimensions. This persistent weakness identifies the lower lumbar spine as a critical target for injury mitigation — a finding that could guide the design of vehicle seats, armour, and blast-attenuating flooring. The injury prediction curves, generated using parametric survival analysis with a Weibull distribution, also align closely with injury corridors previously developed for whole lumbar spine segments, lending credibility to the modelling approach. The authors caution that their fracture tolerance values should be read as vertebral-level injury metrics rather than direct operational thresholds, since the experiments isolated axial compression and did not replicate the full combined-loading environment of a real blast, and the experimental component involved one specimen per lumbar level owing to the scarcity of suitable cadaveric material.

Even with those limitations, the study marks a genuine milestone. By integrating spinal posture, vertebral geometry, and bone quality into validated, specimen-specific finite element models, the researchers have created tools for injury prediction that are both anatomically specific and clinically relevant. The framework extends naturally beyond the battlefield: the same biomechanics governs spinal loading in aviation ejections, helicopter crashes, and occupational impact scenarios. And the finding that axial rigidity may be a more robust predictor of vertebral fragility than the bone density measurements routinely used in clinics hints at a future where fracture risk assessment becomes more precise — not just for soldiers facing blast threats, but for anyone whose spine must withstand the sudden, merciless forces of a high-rate impact.

Subject of Research: Level-specific biomechanical tolerance of lumbar vertebrae to high-rate vertical compression relevant to underbelly blast injury

Article Title: Level-Specific Lumbar Spine Injury Tolerance Under High-Rate Vertical Loading Relevant to Underbelly Blast Environments: A Combined Cadaveric Experimental and Finite Element Study of Three-Vertebra Spinal Segments

Article References: Tse, K. M., Robinson, D., Franklyn, M., & Lee, P. V. S. (2026). Level-Specific Lumbar Spine Injury Tolerance Under High-Rate Vertical Loading Relevant to Underbelly Blast Environments: A Combined Cadaveric Experimental and Finite Element Study of Three-Vertebra Spinal Segments. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04347-8

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04347-8

Keywords: lumbar spine, underbelly blast, finite element model, cadaveric testing, fracture tolerance, bone mineral density, spinal posture, injury prediction curves, military biomechanics, burst fractures, vertebral geometry, axial rigidity

The research, led by Charlotte Mabbs with Lloyd Smith, both of Washington State University, addresses a gap that has persisted in sports ball mechanics for years. While the behavior of balls in head-on, or normal, impacts is routinely measured and modeled, oblique impacts are considerably more complicated. During such an impact, a ball can either slide across the surface — if it comes in at a shallow angle or the friction between ball and surface is low — or it can grip the surface, momentarily bringing its contact patch to a halt. When the ball grips, frictional forces stretch and shear the compliant cover and core, storing elastic energy that is later released as rotation. Capturing this transition between sliding and gripping has proven a stubborn challenge for previous simulations of tennis balls, soccer balls, and golf balls.

Earlier models typically relied on a constant coefficient of friction, treating the resistance between ball and surface as a single fixed value throughout the collision. Those models could reproduce sliding behavior or gripping behavior, but not both. A tennis ball study that achieved good agreement compared its simulation to only one impact condition, leaving its general validity uncertain. Other investigations varied the friction coefficient numerically under fixed conditions without experimental validation at all. The Washington State team took a different route: they implemented what they call a temporal friction model, in which the friction coefficient evolves during contact, transitioning between independently measured static and dynamic values depending on the relative sliding velocity between ball and surface.

To build the model, the researchers first needed to characterize the softball itself. They studied adult fastpitch softballs with a circumference of 306 millimeters and a mass of 0.2 kilograms, constructed with a rigid polyurethane foam core surrounded by a thin leather cover stitched with raised seams. Upon impact, a softball dissipates roughly 75 percent of its energy, so the material model had to capture severe energy loss. Using the explicit finite element solver LS-DYNA, the team employed a non-linear viscoelastic foam material model governed by a high-speed stress-strain loading curve, with parameters controlling hysteresis and energy dissipation tuned until simulated normal impacts at 21.4 and 30.6 meters per second matched measured stiffness and coefficient of restitution within 4 percent of laboratory results.

One of the study’s most striking findings concerns the ball’s moment of inertia — a measure of how its mass is distributed around its center. A homogeneous sphere, the standard simplification in sports ball modeling, underestimated the measured moment of inertia by 9.1 percent because the dense leather cover and seams push mass toward the outside of the ball. That seemingly small discrepancy had outsized consequences: the homogeneous model overpredicted the final angular velocity of a sliding impact by about 13 percent. By adding a thin shell of massless-stiffness elements to the ball’s radius and adjusting densities to match the measured inertia, the researchers brought the angular velocity error down to just 3 percent. For balls with seams — softballs, baseballs, cricket balls — the lesson is clear: assuming a uniform sphere is not good enough when rotation is at stake.

The experimental half of the study was equally ambitious. The team fired softballs from a pneumatic cannon at a steel plate across a wide envelope of conditions: speeds from 20.1 to 63.5 meters per second, spin rates up to 117 radians per second, and impact angles from 14 to 80 degrees. A triaxial load sensor recorded normal and shear forces during contact at 150 kilohertz, while high-speed cameras filming at up to 14,100 frames per second tracked the ball’s position and rotation through the roughly 1.5-millisecond collision. Ball rotation was computed by detecting and matching distinctive features on a randomly patterned leather cover frame by frame. Between every shot, the steel plate was cleaned with 1000-grit sandpaper to keep friction conditions consistent.

Friction measurements fed directly into the model. Sliding impacts — those in which the ball skids through contact — yielded a dynamic friction coefficient of 0.360, while an inclined plane test using a panel of leather removed from an actual softball gave a static coefficient of 0.625. The dynamic value carried a relatively large uncertainty of about 22 percent, consistent with the scatter reported in prior dynamic friction measurements on other balls. The static value aligned well with published engineering data for leather against metal, which typically cites values around 0.6. The temporal friction model blended these two values with an exponential decay governed by a transition parameter, tuned to match representative sliding and gripping impacts and then validated against the full range of angles and speeds.

The validation results were emphatic. Compared with a constant friction model using the dynamic coefficient, the temporal friction model reduced the mean normalized root-mean-square error in predicted angular velocity during contact by 29 percent, and by 81 percent compared with a constant friction model based on the static coefficient. Crucially, it was the first friction formulation for any sports ball to describe both sliding and gripping behavior simultaneously. In gripping impacts, the simulated friction coefficient lingered near the dynamic value for only about 10 percent of the contact duration before climbing rapidly to the static value as the ball’s contact patch came to rest; in sliding impacts, the coefficient stayed near the dynamic value for nearly half the impact. Predicted peak normal forces came within 2.5 percent of experiment, and tangential forces within 6.1 percent.

The model also reproduced the distinctive energy landscape of oblique impacts. As impact angle decreases from vertical, more of the ball’s incoming kinetic energy is converted into transverse motion and rotation, with rotational energy peaking at the shallowest angles at which the ball still grips the surface. The simulation correctly captured the inflection point — between 25 and 30 degrees — below which the ball slides through contact rather than gripping. Interestingly, the frictional force did not substantially reverse during contact, unlike the dramatic reversals seen in highly elastic superballs, a difference the researchers attribute to the softball’s prodigious energy dissipation. One residual discrepancy remained: the simulated frictional force peaked slightly earlier than measured, by roughly 0.1 to 0.16 milliseconds. Tests on a coverless ball, with the leather stripped away, largely eliminated the timing gap, suggesting the thin cover — only 10 percent of the ball’s volume — measurably influences shear response, perhaps through slip at the core-cover interface or the cover’s own compliance.

The implications extend beyond softball. Because softballs are simple in construction compared with the layered pills, yarn windings, and seams of baseballs and cricket balls, the inhomogeneity effects documented here are likely even more pronounced in those sports. The work also marks the first dynamic measurement of friction coefficients for a solid sports ball at speeds representative of actual play, and the first controlled laboratory experiments on softball oblique impacts of any kind — previous on-field studies of softball-bat collisions had reported lower tangential restitution values, consistent with the greater energy dissipation expected when a compliant, curved bat is involved. For governing bodies, equipment designers, and modelers of ball flight, the message is that both the velocity-dependent nature of friction and the true mass distribution of the ball must be respected. As the authors conclude, ball inhomogeneity and temporal friction are not refinements but necessities for accurately modeling how solid sports balls shear, grip, and spin when they meet the ground.

Subject of Research: Finite element modeling and experimental validation of oblique, frictional impacts of softballs

Article Title: Finite element modeling of oblique impacts of softballs

Article References: Mabbs, C., & Smith, L. (2026). Finite element modeling of oblique impacts of softballs. Sports Engineering, 29(2), Article 31. https://doi.org/10.1007/s12283-026-00564-5

Image Credits: AI Generated

DOI: 10.1007/s12283-026-00564-5

Keywords: softball, finite element model, oblique impact, friction, spin, sports engineering, coefficient of restitution, moment of inertia, LS-DYNA, sliding and gripping, shear deformation, sports biomechanics