This paper evaluates the behavior of a single rigid ellipsoidal particle suspended in homogeneous viscous flow with a power-law generalized Newtonian fluid rheology using a custom-built finite element analysis (FEA) simulation. The combined effects of the shear-thinning fluid rheology, the particle aspect ratio, the initial particle orientation, and the shear-extensional rate factor in various homogeneous flow regimes on the particles dynamics and surface pressure evolution are investigated. The shear-thinning fluid behavior was found to modify the particle's trajectory and alter the particle's kinematic response. Moreover, the pressure distribution over the particle's surface is significantly reduced by the shear-thinning fluid rheology. The FEA model is validated by comparing results of the Newtonian case with results obtained from the well-known Jeffery's analytical model. Furthermore, Jeffery's model is extended to define the particle's trajectory in a special class of homogeneous Newtonian flows with combined extension and shear rate components typically found in axisymmetric nozzle flow contractions. The findings provide an improved understanding of key transport phenomenon related to physical processes involving fluid–structure interaction such as that which occurs within the flow field developed during material extrusion–deposition additive manufacturing of fiber-reinforced polymeric composites. These results provide insight into important microstructural formations within the print beads.

This study presents a finite element analysis (FEA)-based numerical homogenization method for evaluating the effective thermo-mechanical properties of a large-area additively manufactured particulate-filled composite using realistic periodic representative volume elements (RVEs) generated from reconstructed X-ray µ-CT image scans of a 3D-printed bead. The numerical results of the predicted effective properties, including the elastic stiffness, coefficient of thermal expansion (CTE) and thermal conductivity, were benchmarked with the Mori–Tanaka–Benveniste analytical estimates, which were found to be comparable. Initial sensitivity analysis using a single region of interest (ROI) extracted from the bead’s volume was performed to determine a suitable RVE size. The impact of inherent micro-porosities on the resulting composite material’s behavior was also quantified in the current investigation and was shown to reduce the composite’s effective properties. Using a suitable RVE size, the effect of anisotropy due to spatial variation in the microstructure across the bead specimen on the computed composite’s effective properties was also assessed. The results show that the regions closer to the exposed surface of the print bead with highly aligned and densely packed fiber particulates have superior properties as compared to inner regions with a more randomly oriented and less densely packed fibrous microstructure.

Fiber orientation is an important descriptor of the microstructure for short fiber polymer composite materials where accurate and efficient prediction of the orientation state is crucial when evaluating the bulk thermo-mechanical response of the material. Macroscopic fiber orientation models employ the moment-tensor form in representing the fiber orientation state, and they all require a closure approximation for the higher-order orientation tensors. In addition, various models have more recently been developed to account for rotary diffusion due to fiber-fiber and fiber-matrix interactions which can now more accurately simulate the experimentally observed slow fiber kinematics in polymer composite processing. It is common to use explicit numerical initial value problem-ordinary differential equation (IVP-ODE) solvers such as the 4th- and 5th-order Dormand Prince Runge–Kutta (RK45) method to predict the transient and steady-state fiber orientation response. Here, we propose a computationally efficient method based on the Newton-Raphson (NR) iterative technique for determining steady state orientation tensor values by evaluating exact derivatives of the moment-tensor evolution equation with respect to the independent components of the orientation tensor. We consider various existing macroscopic-fiber orientation models and several closure approximations to ensure the robustness and reliability of the method. The performance and stability of the approach for obtaining physical solutions in various homogeneous flow fields is demonstrated through several examples. Validation of our orientation tensor exact derivatives is performed by benchmarking with results of finite difference techniques. Overall, our results show that the proposed NR method accurately predicts the steady state orientation for all tensor models, closure approximations and flow types considered in this paper and was relatively faster compared to the RK45 method. The NR convergence and stability behavior was seen to be sensitive to the initial orientation tensor guess value, the fiber orientation tensor model type and complexity, the flow type and extension to shear rate ratio.

The dilemma of most upcoming researchers in the field of fiber reinforced polymer (FRP) composite processing is not the lack or accessibility to relevant background literature but rather their comprehensive nature, or their applicability to the specific needs of the researcher. Most existing literature either target just a specific modeling aspect or present high-level overview of the overall FRP process which lacks necessary underlying physics, coupling across hierarchical physics scales and computational techniques needed to improve on existing process simulation tools without necessarily reinventing the wheel. The current review article presents detailed understanding of the overall FRP composite process, the relevant transport phenomena and underlying physics across various scales and current trends in computational solution techniques used to predict FRP composite melt-flow phenomena in order to develop well equipped process-structure-property (PSP) maps for improved process monitoring and optimized print properties and performance. The overall position of potential research opportunities from survey of existing simulation efforts includes (i) the refinement of existing and development of new quantitative and qualitative multiscale models for predicting transport phenomena, (ii) development of new closed-form tensor evolution equations and constitutive relations with new information of the bulk fiber and melt-flow field states, and (iii) proper model benchmarking with experimental observation from in-situ process monitoring, and development of machine learning tools for the creation of a robust PSP map.