Feedstock deformation during the robotic 3D printing of continuous fiber thermoplastic composites has long been a stubborn source of manufacturing defects, and a new open-access study in Advanced Modeling and Simulation in Engineering Sciences presents a hybrid modeling framework that combines established physics with machine learning to predict it. The work, led by Chady Ghnatios and Kazem Fayazbakhsh, targets the deformation of a single deposited tape of continuous carbon fiber reinforced with low-melt poly-aryl ether ketone, a problem the authors identify as critical for path planning and a main driver of defect generation during printing.

The researchers built their experimental foundation around a robotic 3D printing setup consisting of an ABB IRB 1200 robotic arm fitted with a custom-built printing head that includes a slotted nozzle. A 304.8 by 304.8 millimeter steel plate, 12.7 millimeters thick, served as the build platform, while a Programmable Logic Controller regulated nozzle and platform temperatures and an ABB IRC5 controller optimized robot movement. The feedstock itself was a continuous carbon fiber prepreg tape with a nominal width of 6.35 millimeters and a thickness of roughly 0.180 millimeters, combining high-strength HTS45 carbon fiber with the low-melt poly-aryl ether ketone matrix.

When a single tape was deposited under specific conditions, a nozzle temperature of 380 degrees Celsius, a build platform temperature of 160 degrees Celsius, a printing speed of 10 millimeters per second, and a layer height of 0.200 millimeters, its width shrank dramatically. Caliper measurements taken at multiple points showed the tape width varying between 5.10 and 5.50 millimeters, mainly around 5.30 millimeters, far below the pre-processed width of 6.35 millimeters. Because the tape dimensions change after deposition, the raw feedstock width cannot simply be used as the spacing between the centerlines of adjacent tapes, known as the Tape Raster Offset. Since producing high-quality parts without gaps and overlaps would otherwise require many experimental trials for every parameter combination, the authors argue that numerical modeling can predict tape width across all possible cases and significantly reduce time and cost.

To characterize the material, the team ran two thermal tests. A Differential Scanning Calorimetry instrument, following the ASTM D3418-21 standard, heated a 2.89 milligram specimen from 20 to 400 degrees Celsius at 10 degrees Celsius per minute with isothermal holds, then cooled it back down. From the first heating ramp they obtained a glass transition temperature of 147 degrees Celsius, taken as the inflection temperature, a crystallization peak temperature of 184 degrees Celsius, and an enthalpy of cold crystallization of 5.208 joules per gram. A Dynamic Mechanical Analyzer then measured dimensional change at two temperatures, 120 and 180 degrees Celsius, one below and one above the glass transition. Pieces of prepreg tape about 40 millimeters long were clamped in a film tension fixture with a negligible 0.01-newton force, and each experiment followed four iso-stress steps of heating and cooling at 0.5 degrees Celsius per minute with soak times of 60 and 180 minutes, chosen so the tape’s dimensional change stabilized before each subsequent ramp.

On the modeling side, the thermal simulation solved the heat transfer equation using the Proper Generalized Decomposition method, computing the solution in separated space-time form with a fine out-of-plane mesh of 21 nodes through the thickness. The result showed a homogeneous thermal distribution in the part during the experiments, meaning the thermal fields could be treated as functions of time alone. For the mechanical behavior, the experimental evidence pointed to viscoelasticity, since deformation differed between heating and cooling cycles, so the authors adopted a Kelvin-Voigt viscoelastic model in which stress is the sum of an elastic part and a viscous part. The stiffness tensor came from the manufacturer’s datasheet and Halpin-Tsai homogenization equations, with a fiber volume fraction of 0.6. Because no direct characterization of the viscous tensor exists for this specific material, the team assumed an orthotropic structure in which the fiber direction is purely elastic while transverse and coupling responses carry viscous terms, and fitted the resulting five parameters, two thermal expansion coefficients and three viscous parameters, to the 120-degree experiment using a custom MATLAB finite element code coupled to an optimizer.

The fitting procedure deliberately excluded the first heating stage, because that stage showed irreversible behavior attributed to drying and the release of residual stresses from the spooled prepreg. Instead, the discrepancy between the viscoelastic simulation and the measured strains during that first heating was used to quantify this initial strain release, which the authors define as the combined effect of moisture drying out of the thin, roughly 0.18-millimeter-thick tape and the relaxation of residual stresses introduced during spooling. This component was modeled with a stabilized form of a Neural Ordinary Differential Equation, a dynamic machine learning architecture that, unlike more classical models such as ResNet or LSTM networks, tends to preserve stability and predictability in time far beyond the training region. The network used two LSTM layers taking recent values of temperature, time, and the simulated strain, integrated forward with an Euler scheme, and was trained on the first 80 percent of the DMA-1 time sequence with the remaining 20 percent reserved for validation.

The results of that extrapolation are among the most striking in the study. The neural ODE achieved relative errors of 0.76 percent on the training set and 0.57 percent on the test set for the initial strain release, and, without any further refinement, it was applied to the second experiment where the maximum temperature was 60 degrees Celsius higher than anything seen during training. The network automatically learned to predict saturation of the strain release at higher temperatures, an effect the authors attribute to the stable form of the neural ODE. They also observed that the shrinking accelerated at around 100 degrees Celsius, the evaporation temperature of water, before reaching saturation. A separate stabilized neural ODE was trained to capture crystallization-induced strains above the glass transition temperature, achieving relative errors of 0.82 percent for the training set and 1.21 percent for the test set, with the final cooling stage of the experiment withheld entirely from training and used only for testing.

Combining all three components, the viscoelastic thermal strain model, the initial strain release model, and the crystallization strain model, the authors compared the total predicted strain against the measurements from the 180-degree experiment. The comparison showed that the release of initial strains was slightly overestimated, because that model was trained only on data reaching 120 degrees Celsius while predictions extended to 180 degrees. Although the neural ODE captured the saturation trend, the predicted saturation occurred at a higher temperature than the validation response suggested, and the authors note that additional training experiments at higher temperatures would be needed to better constrain the saturation behavior and reduce the extrapolation error. On the other hand, the framework successfully predicted the contribution of crystallization to strain generation as soon as the temperature rose beyond the glass transition.

The final validation came from the printing process itself. The team simulated a 280-millimeter-long tape with the measured boundary conditions, an imposed base temperature of 160 degrees Celsius, an incoming tape temperature of 380 degrees Celsius, ambient air at 20 degrees Celsius, and convection coefficients of 25 watts per square meter kelvin with the air and 60 with the base. The thermal simulation, solved with the Proper Generalized Decomposition method and a Streamline Upwind Petrov-Galerkin stabilization for the convective term, showed an equilibrium temperature of about 120 degrees Celsius and a through-thickness temperature variation of less than 0.3 degrees Celsius. The residual strain release model saturated at 0.06 percent strain, and crystallization strains were transferred to the deposition thermal history using the reaction enthalpy from the DSC measurements as an internal state variable, an assumption supported by the established relation between crystallinity and crystallization enthalpy. A tape was then deposited experimentally under the same operating conditions, and the comparison of simulated and measured lateral deformations showed the framework could evaluate the deformation of the printed tape with high fidelity, with remaining differences attributed to warping and caliper measurement errors on such a thin tape.

The authors position this work as a cornerstone for understanding feedstock deformation in robotic 3D printing of continuous fiber thermoplastic tapes and as a step toward a digital twin of the printing process. Because the model predicts final tape dimensions for given process parameters, it can be used to place tapes on a build platform according to their final dimensions, preventing defects like gaps and overlaps while significantly reducing the experimental trials otherwise required. The authors are careful to note the limitations: the experimental campaign covered only the LM PAEK carbon fiber material, the validation is described as preliminary, the simulation covered a straight deposition path, and future work will analyze variability using repeated measurements and laser line scanning to quantify prediction error and measurement uncertainty across process conditions and material parameters. Even so, the demonstration that a physics-anchored hybrid model trained at 120 degrees Celsius can remain stable and reasonably accurate when extrapolated to 180 degrees Celsius marks a meaningful advance for defect-free additive manufacturing of continuous fiber composites.

Subject of Research: Hybrid physics and machine learning modeling of feedstock deformation in robotic 3D printing of continuous fiber thermoplastic composites

Article Title: Hybrid machine learning and physical modeling of feedstock deformation during robotic 3D printing of continuous fiber thermoplastic composites

Article References: Ghnatios, C., & Fayazbakhsh, K. (2026). Hybrid machine learning and physical modeling of feedstock deformation during robotic 3D printing of continuous fiber thermoplastic composites. Advanced Modeling and Simulation in Engineering Sciences, 13(1), 16. https://doi.org/10.1186/s40323-026-00337-6

Image Credits: AI Generated

DOI: 10.1186/s40323-026-00337-6

Keywords: robotic 3D printing, continuous carbon fiber, thermoplastic composites, LM PAEK, neural ODE, Kelvin-Voigt viscoelasticity, crystallization, residual stress, DMA, DSC, prepreg tape deformation, digital twin