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We present a numerical study of the fused deposition modeling 3D printing process of fiber-reinforced polymers by means of Smoothed Particle Hydrodynamics (SPH). For this purpose, a classical microstructure-based fiber suspension model coupled with a constitutive model for the suspending polymer is implemented within an SPH framework. The chosen model is reviewed, together with the details and specificities of its implementation in SPH. The results for several representative cases are then presented, mainly in terms of contours of fiber orientation tensor components and orientation distributions across the deposited layer thickness. The impact of the fiber concentration and its aspect ratio in a semi-concentrated regime and the effect of the ratio between extrusion and substrate velocities are investigated. Some insights into the link between the flow field and fiber orientation evolution within the printing head and as the material exits the nozzle are given. The main findings lie in the prediction of a skin/core structure in the deposited layer in which the skin regions exhibit a higher fiber alignment with respect to the core region. This effect is found to be enhanced by an increase in fiber concentration and to be sensitive to the substrate-to-extrusion velocity ratio. It is indeed enhanced in cases where the substrate velocity is low compared to the extrusion velocity and accompanied by a larger swelling of the deposit at the nozzle exit.

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SUMMARYAnisotropic diffusion phenomenon in fluids is simulated using smoothed particle hydrodynamics (SPH). A new SPH approximation for diffusion operator, named anisotropic SPH approximation for anisotropic diffusion (ASPHAD), is derived. Basic idea of the derivation is that anisotropic diffusion operator is first approximated by an integral in a coordinate system in which it is isotropic. The coordinate transformation is a combination of a coordinate rotation and a scaling in accordance with diffusion tensor. Then, inverse coordinate transformation and particle discretization are applied to the integral to achieve ASPHAD. Noting that weight function used in the integral approximation has anisotropic smoothing length, which becomes isotropic under the inverse transformation. ASPHAD is general and unique for both isotropic and anisotropic diffusions with either constant or variable diffusing coefficients. ASPHAD was numerically examined in some cases of isotropic and anisotropic diffusions of a contaminant in fluid, and the simulation results are very consistent with corresponding analytical solutions.

In the present article, the cell model (or self-consistent scheme) is used to derive constitutive equations for rod suspensions in non-Newtonian viscous matrices such as power-law, Ellis and Carreau fluids. It is found that the shear-thinning character of the matrix influences considerably the rod contribution to the stress tensor, but has no impact on the rod orientation dynamics: the same microstructure evolution as the one encountered in Newtonian fluids is obtained. The rod suspension behaves differently than the unfilled matrix in the sense that, depending on rod orientation, the onset of shear thinning in the composite occurs at lower or higher shear rates. Our analysis also provides a semi-analytical model for rod suspensions in an Ellis fluid, which appears to be suitable for predicting a Newtonian plateau at low shear rates and a shear-thinning behaviour at high shear rates. In addition, the model predictions are in good agreement with the shear viscosity measurements of glass-fibre-filled polystyrene melts (Chan et al., J. Rheol., vol. 22 (5), 1978, pp. 507–524), demonstrating its ability to describe the rheological behaviour of such polymer composites. Finally, the proposed approach is extended to a Carreau fluid although its solution requires the numerical solution of a set of partial differential equations.