Adhesively bonded joints are critical for the use of fiber-reinforced composite materials as structural elements. Even though they are critical, they are often not analyzed until further down in the design cycle because of the fine mesh required to represent the adhesive bond. In this work, we develop a macro finite element shell element which uses a 1D equilibrium solution to capture a fine field of adhesive stresses. This element can be seamlessly integrated into existing coarse finite element meshes to include adhesive stresses early on in the design of composite structural parts.

Ceramic materials are essential in aerospace, medical, automotive, energy, and semiconductor industries due to their exceptional mechanical, optical, electrical, and thermal properties. However, their fabrication is often time-consuming, particularly in binder-based systems where binder removal is a critical bottleneck. In this study, we explored strategies to accelerate the debinding process using additive manufacturing (AM) by tailoring particle size distribution to induce a capillary gradient from the core to the surface. Two microscale models with distinct particle arrangements were studied: Random and Gradient. The results show that the Gradient model debound 1.3x faster than the Random model due to enhanced capillary-driven binder transport. Particle motion affected binder migration pathways, increasing their tortuosity compared to models without particle movement. These findings demonstrate the role of spatially tailored particle distributions in meaningfully accelerating binder removal while expanding design possibilities for more complex, high-performance architectures in ceramic AM.

Composite microstructures are susceptible to localized stress concentrations between close or touching fibers where failure can initiate and propagate. Typically, representative volume elements are used to predict mechanical response by simulating random microstructure arrangements under different loading configurations. However, these simulations can be prohibitively expensive when considering large microstructures or closely packed fibers. The current work aims to provide a computationally efficient method for predicting homogenized and local properties of composite microstructures through a novel finite element mesh referred to as the fixed triangulation-mesh model. This triangulation-based meshing algorithm uses configured element sizes where the highest stresses occur and higher order elements to capture stress gradients between closely packed fibers. An efficient homogenization technique to fully characterize the stiffness matrix of the composite without the need for individual load perturbations or stress integration was derived and implemented. A progressive damage model using the smeared crack approach was implemented with higher order elements to simulate post-peak softening. The results for stiffness, transverse strength, and in-plane shear strength were verified against the high fidelity generalized method of cells for different microstructures of varying fiber volume fractions. Then, a comparison was made to a refined mesh finite element model with linear elements and a toughened matrix. The fixed triangulation-mesh model showed good agreement between the high fidelity generalized method of cells and linear element models, and computation time was reduced by approximately 104 times for the low-toughness matrix, and 55 times for the toughened matrix.

Helmets are designed to protect the wearer from impacts that may cause serious injuries or trauma. Standardized tests are conducted to ensure their blunt impact absorption performance. Small variations when mounting and positioning any helmet on the headform during the test lead to uncertainty on the maximum peak linear acceleration, a threshold used to assess bicycle, wheeled recreational devices, and combat helmets for their impact absorption. Such uncertainty may lead to fallacious results and, thus, incorrect approval for a helmet. In turn, the unqualified helmet can significantly increase injury risk calculated through the Abbreviated Injury Scale. This study quantifies the uncertainty of the helmet positioning and the other blunt impact test parameters on the peak linear acceleration. For this purpose, over 1400 variations of a helmet blunt impact computational model were considered. The uncertainty quantification analysis was conducted through Sobol Sensitivity Analysis and Shapely Additive Explanations obtained from a Light Gradient Boosting Machine model, a decision support model developed to assist the experimental blunt impact test for helmets. The results indicated that the helmet positioning parameters had the highest contribution to the uncertainty. Additionally, the proposed model successfully determined whether a helmet passed or failed the test. The accuracy level of these predictions was at 80.17% when the helmet positioning parameters vary from one test to the next, and at 98.89% when considering the helmet was positioned correctly.

Fiber-reinforced composites contain microscale features such as variations in local fiber volume fraction, fiber clusters, and resin-rich regions, which may impact mechanical properties. Microscale models need to be large enough to capture these features while maintaining high fidelity to capture the localized fiber-to-fiber interactions. This makes it difficult to efficiently model regions with equivalent fiber morphologies to as-manufactured scans and to perform large statistical studies to examine how these features drive mechanical performance. This study uses a novel microstructure generator and an efficient micromechanical model along with a characterization method that measures the geometry of these features to simulate a wide range of microstructures for strength and stiffness. After understanding how the mechanical properties are affected by morphology through correlation matrices, equivalent microstructures were generated to regions of an as-manufactured composite. The generation of microstructures based on different morphological descriptors allows for an understanding of which features are valuable when modeling these materials. In comparing microstructures with different equivalent descriptors to the case with all six descriptors, it was found that only using local fiber volume fraction median resulted in over predictions of strength and stiffness. Once two descriptors or more were introduced, such as local fiber volume fraction median and inter-quartile range, there was no significant difference in strength and stiffness. This suggests that at least two descriptors should be considered when generating equivalent microstructures for mechanical properties.

A multiscale repeating unit cell model of a single spherulite containing four disparate length scales was developed to predict the thermoelastic behavior of semicrystalline thermoplastic materials for composite aerospace applications. The continuum level scales were fully coupled and modeled using the generalized method of cells and the high-fidelity generalized method of cells micromechanics theories. Data from molecular dynamics simulations were used as inputs for the amorphous and crystalline constituents in the multiscale continuum models. Effective Young’s modulus, shear modulus, Poisson’s ratio, coefficient of thermal expansion, and thermal conductivity were predicted for polyether ether ketone and polyether ketone ketone, showing good agreement with the available experimental data from the open literature. Moreover, it is shown that predicted properties are fairly insensitive to the fidelity of the micromechanics model used at the highest continuum scale or the assumed shape of the spherulite.

Parachute suspension lines shed vortices during descent, and these vortices develop oscillating aerodynamic forces that can induce forced parasitic vibrations of the lines, which can have an adverse impact on the parachute system. Understanding the line’s mechanical behavior can assist in studying the vibrations experienced by the suspension lines. A well-calibrated structural model of the suspension line could be used to help to identify how the braid’s architecture contributes to its mechanical behavior and to explore if and how a suspension line can be designed to mitigate these parasitic vibrations. In the current study, a mesomechanical finite element model of a polyester braided parachute suspension line was constructed. The line geometry was built in the Virtual Textile Morphology Suite (VTMS), and a user material model (UMAT) was implemented in LS-DYNA® release 14 to describe the material behavior of the individual tows. The material properties were initially calibrated using experimental tension tests on individual tows, which exhibited an initial modulus of ~4100 MPa before transitioning to ~3200 MPa at a stress of 30 MPa. When these properties were applied to the full braid model, slight adjustments were made to account for geometric complexities in the braid structure, improving the correlation between the model and experimental tensile tests. The final calibrated model captured the bilinear tensile behavior of the braid, with an initial modulus of 2219 MPa and a secondary modulus of 1350 MPa, compared to experimental values of 2253 MPa and 1420 MPa, respectively, showing 2% and 5% differences. The calibrated model of the braided cord was then subjected to torsion, and the results showed good agreement with dynamic and static experimental torsion tests, with a difference of 8–19% for dynamic tests and 13–27% for static tests when compared to experimental values. The availability of virtual models of suspension lines can ultimately assist in the design of suspension lines that mitigate flow-induced vibration.

Accurate quantification of material properties is crucial for optimizing composite structure design. However, the inherent heterogeneity in composite microstructures often leads to uncertainty in material properties, prompting conservative design approaches that result in suboptimal structures. This study introduces a method to quantify uncertainty in composite material properties based on microstructural morphology. Statistical metrics are defined to characterize the fiber architecture, evaluated using micro-scans of composite samples. Transverse tensile stiffness and strength are estimated via a statistical finite element analysis, where multiple Representative Volume Elements (RVE) are created from micro-imaging data to model microstructural variations. A convergence study establishes the minimum RVE size for reliable uncertainty quantification. Process modelling is introduced to simulate curing effects, including residual stress development, which affects transverse tensile strength. The correlation between fiber metrics and estimated material properties is examined, revealing a positive relationship for transverse tensile strength. The results indicate that fiber metrics analysis can serve as a computationally efficient technique for virtual material characterization and uncertainty quantification, potentially reducing composite design and analysis development time.

Permeability quantifies the flow conductivity of fabric reinforcements and is key to predicting mold filling times and resin flow in liquid composite molding (LCM). Flow depends on the micron-level channels within the tows and the millimeter-level channels between them. This study presents a general multi-scale permeability prediction framework for fabrics considering realistic inter- and intra-tow geometry. A misaligned fiber representative volume element model was constructed by a random perturbation method at the micro-scale with orientation parameters identified from microscopic images of the cross-section. At the meso-scale, a tow cross-section wrapping algorithm and an interference elimination algorithm were proposed to construct continuous as-woven tows from the virtual fiber compression simulation. The governing fluid dynamics equations were solved to obtain the flow field within the multi-scale gaps and compute the permeability. The simplified model's permeability predictions differed from experimental results by 12.7% to 16%. This work provides valuable insights for further research and development in LCM.Highlights Fabric permeability framework considers realistic tow geometry for prediction. Microscale misaligned fiber SVE model predicts tow permeability. Adaptive winding & interference algorithms aid tow description transition. A simplified model predicts permeability reasonably without 3D measurements. A multiscale numerical prediction strategy of fabric in-plane permeability. image

This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the "learner" identifies a limited set of candidates within the input design space whose predicted outputs closely align with desired outcomes. Subsequently, in the second stage, a separate surrogate model, functioning as an "evaluator," is employed to assess the reduced candidate space generated in the first stage. This evaluation process eliminates inaccurate and uncertain solutions, guided by a user-defined coverage level. The framework's distinctive contribution is the integration of conformal inference, providing a versatile and efficient approach that can be widely applicable. To demonstrate the effectiveness of the proposed framework compared to conventional single-stage inverse problems, we conduct several benchmark tests and investigate an engineering application focused on the micromechanical modeling of fiber-reinforced composites. The results affirm the superiority of our proposed framework, as it consistently produces more reliable solutions. Therefore, the introduced framework offers a unique perspective on fostering interactions between machine learning-based surrogate models in real-world applications.

This paper investigates the use of probabilistic neural networks (PNNs) to model aleatoric uncertainty, which refers to the inherent variability in the input-output relationships of a system, often characterized by unequal variance or heteroscedasticity. Unlike traditional neural networks that produce deterministic outputs, PNNs generate probability distributions for the target variable, allowing the determination of both predicted means and variances in regression scenarios. Contributions of this paper include the development of a probabilistic distance metric to optimize PNN architecture, and the deployment of PNNs in controlled data sets as well as a practical material science case involving fiber-reinforced composites. The findings confirm that PNNs effectively model aleatoric uncertainty, proving to be more appropriate than the commonly employed Gaussian process regression for this purpose. Specifically, in a real-world scientific machine learning context, PNNs yield remarkably accurate output mean estimates with R-squared scores approaching 0.97, and their predicted variances exhibit a high correlation coefficient of nearly 0.77, closely matching observed data variances. Hence, this research contributes to the ongoing exploration of leveraging the sophisticated representational capacity of neural networks to delineate complex input-output relationships in scientific problems.

Ultra-violet (UV) radiation has been used to produce functionally graded materials by locally modulating crosslink density. Functionally graded adhesives are an important subset of functionally graded materials, but photocuring is of limited use when creating structural adhesive joints, most of which involve opaque adherends. As a result of these and other difficulties generating such materials in practice, the advantages of functionally graded adhesives have been reported theoretically, but experimental investigations remain rare. For this reason, our group has focused on dual cure systems sensitive to post-curing via high energy radiation as a means of locally modulating properties. Here, a series of thermally cured epoxy resins are shown to exhibit different levels of sensitivity toward gamma ( gamma ) irradiation as a function of the concentration of a bisphenol-derived unsaturated chain extender incorporated into an epoxy-anhydride network that contains unsaturations as well. It was observed that addition of the chain extender slowed curing and impacted the thermal properties of the cured epoxy networks but greatly favored radiation-induced crosslinking over degradation given the observed shifts in properties. A theory proposed by Shibayama relating T g to crosslink density is applied to better understand the structure and crosslinking behavior of thermally cured epoxies before and after radiation post-curing and provides a useful means to predict radiation-induced changes in performance. The development of such heat / gamma radiation dual curable formulations, the understanding of their behavior upon irradiation and the ability to predict key properties via a simple analytical model provides a new perspective for the successful generation of functionally graded materials through methods described in our prior work.

Crystallization kinetics were used to develop a spherulite growth model, which can determine local crystalline distributions through an optimization algorithm. Kinetics were used to simulate spherulite homogeneous nucleation, growth, and heterogeneous nucleation in a domain discretized into voxels. From this, an overall crystallinity was found, and an algorithm was used to find crystallinities of individual spherulites based on volume. Then, local crystallinities within the spherulites were found based on distance relative to the nucleus. Results show validation of this model to differential scanning calorimetry data for polyether ether ketone at different cooldown rates, and to experimental microscopic images of spherulite morphologies. Application of this model to various cooldown rates and the effect on crystalline distributions are also shown. This model serves as a tool for predicting the resulting semi-crystalline microstructures of polymers for different manufacturing methods. These can then be directly converted into a multiscale thermomechanical model.

Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to variability and flaws during manufacturing, making failure predictions difficult. These flaws may occur at the microscale where mechanical properties vary locally due toized regions of fiber clusters and matrix pockets create regions of varying mechanical properties. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using a reduced order micromechanical model and NASA's Multiscale Analysis Tool (NASMAT). Mesoscale models were created with equivalent element sizes to microstructures and properties sampled from microscale simulation results. Results showed how microscale size affects certain mechanical properties. Also shown is how well mesoscale models agree to experiments when using stochastic element properties and varying element size.

This paper presents an overview of research conducted to track the variation in fiber reinforced composites at the microscale induced from manufacturing, and determine the effect composite properties. For this effort, the microscale was first quantified using statistical descriptors. These descriptors are needed in order to determine statistical equivalency of artificially generated microstructures. The artificially generated microstructures have been made using a combination of randomly distributed fibers and simulations. Numerical parameters of the simulation can be manipulated to produce different features found in common microstructures such as fiber clusters and matrix-rich regions. Finally, reduced order structural models were used to quantify the variation in the response due to variations at the microstructure. Meso-scale simulations utilize integration point variation in material properties to simulate the overall variation in the response. Machine learning can be used to replace models at the microscale level and capture variation without having to link multi-scale models.

Meso-scale modeling can be an effective way to predict textile-reinforced composite performance when the geometry of the textile is known. Digital element fiber models can be used to obtain the geometry of the textile reinforcement, but these are frequently too compact because the fibers are parallel within a tow and do not provide as much resistance to compaction as tows with fiber entanglement found in textiles. A novel entanglement simulation procedure was created to obtain more realistic textile geometry. By combining artificial fiber entanglement with manufacturing process simulation, a method was developed to create fiber bundle models using entanglement to control the compaction behavior. To introduce fiber entanglement into a tow, select fibers are swapped with each other in the tow at a cross-section. This allows entanglement to be introduced after the basic textile structure is already made, and prevents individual fibers from leaving the tow and getting entangled into neighboring tows. This fiber entanglement process was controlled by three parameters, which dictate how many, how often, and how far away from each other fibers are swapped. A parametric study was conducted which showed that the entanglement within a fiber bundle could be used to control the compaction pressure versus fiber volume fraction response of the bundle. The method was then applied to a woven textile model where it was found that increasing the amount of entanglement within the tows increased the pressure required to compact the textile to the desired thickness. This method for artificial fiber entanglement and manufacturing process simulation shows the potential to be able to predict the entanglement required to create fiber bundles using a desired mold compression pressure to achieve a desired compaction behavior.

Adhesively bonded joints are widely used in various industries, highlighting the importance of understanding their behavior. While fracture toughness tests provide valuable insights, they are complex and time-consuming. As a result, engineers often rely on tensile test data alone, considering its simplicity and practicality. However, the prevalence of defects in tensile specimens can lead to an underestimation of adhesive elongation at break. Tensile specimens distribute loads over a larger area, making them more susceptible to premature failure caused by localized flaws compared to bond line loads. To address this limitation and improve accuracy, this study proposes a novel approach. Tensile tests are conducted to determine the distribution of elongation at break, and inverse modeling using User Material (UMAT) in ABAQUS is employed to acquire the defect distribution in the specimens for different mesh sizes. Single Lap Joint (SLJ) tension tests are performed to compare force-displacement results from experimental data with simulation. The results highlight the significance of considering proper flaw distribution in the adhesive layer. By incorporating the defect distribution obtained from inverse modeling, the prediction of failure displacement can be enhanced compared to using adhesive with uniform properties based solely on average tensile data.

Statistically equivalent, artificial microstructures with similar fiber morphologies to as-manufactured scans are commonly used in micromechanical modeling. Features such as fiber clusters and matrix pockets are impor-tant as they may influence macroscale failure. In this study, a method of generating statistically equivalent artificial microstructures to experimental scans using local fiber volume fraction, fiber clusters, and matrix pockets was examined. 3000 artificial microstructures were created with a generator by randomly sampling input parameters which changed the fiber morphology. Fiber cluster and matrix pocket areas, densities, and orientations were used to characterize microstructures by sorting neighboring fiber triads. Experimental scans were used validate inputs from the artificial microstructure generator. Results showed the microstructures generated produced descriptors within range of the experimental scans. Microstructures were generated to match different descriptors of scanned specimens. First only local volume fraction was matched, and results compared to scans, then all descriptors were matched and compared.

Generating realistic tow geometries is important for making effective models for textile composite materials. The geometry of the tows is controlled by the compaction response of the textile during manufacturing. Attaining a realistic compaction response from a textile model has been difficult due to the representation of fibers as unentangled. These tows containing idealized, parallel fibers without fiber entanglement or meandering compact with less resistance than tows with the entanglement found in manufactured textile composites. In this study, a method of introducing entanglement to the tows within a textile was created which selectively swapped fiber positions at different cross sections along the length of the tow. This method introduces entanglement and meandering into a textile while ensuring the fibers do not cross into the bounds of the surrounding tows. The entanglement was controlled by varying the frequency (probability of swapping) and distance (swapping radius standard deviation) of fiber path pairs being swapped within each tow at cross sections separated by the swapping plane spacing along the length of the tow. When applied to a plain weave textile, it was found that the greater the entanglement, the greater the compaction pressure vs composite thickness of the plain weave textile. While examining the ability for entanglement to control the compaction response of the textile, it was found that the compaction pressure-composite thickness response of a manufactured specimen was able to be replicated.