The Mathematics of Smoothed Particle Hydrodynamics (SPH) Consistency

Since its inception Smoothed Particle Hydrodynamics (SPH) has been widely employed as a numerical tool in different areas of science, engineering, and more recently in the animation of fluids for computer graphics applications. Although SPH is still in the process of experiencing continual theoretical and technical developments, the method has been improved over the years to overcome some shortcomings and deficiencies. Its widespread success is due to its simplicity, ease of implementation, and robustness in modeling complex systems. However, despite recent progress in consolidating its theoretical foundations, a long-standing key aspect of SPH is related to the loss of particle consistency, which affects its accuracy and convergence properties. In this paper, an overview of the mathematical aspects of the SPH consistency is presented with a focus on the most recent developments.

Towards the Determination of Machining Allowances and Surface Roughness of 3D-Printed Parts Subjected to Abrasive Flow Machining

Abrasive flow machining (AFM) is considered as one of the best-suited techniques for surface finishing of laser powder bed fused (LPBF) parts. In order to determine the AFM-related allowances to be applied during the design of LPBF parts, a numerical tool allowing to predict the material removal and the surface roughness of these parts as a function of the AFM conditions is developed. This numerical tool is based on the use of a simplified viscoelastic non-Newtonian medium flow model and calibrated using specially designed artifacts containing four planar surfaces with different surface roughnesses to account for the build orientation dependence of the surface finish of LPBF parts. The model calibration allows the determination of the abrasive medium-polished part slip coefficient, the fluid relaxation time and the abrading (Preston) coefficient, as well as of the surface roughness evolution as a function of the material removal. For model validation, LPBF parts printed from the same material as the calibration artifacts, but having a relatively complex tubular geometry, were polished using the same abrasive medium. The average discrepancy between the calculated and experimental material removal and surface roughness values did not exceed 25%, which is deemed acceptable for real-case applications. A practical application of the numerical tool developed was demonstrated using the predicted AFM allowances for the generation of a compensated computer-aided design (CAD) model of the part to be printed.

Microscale modelling of dielectrophoresis assembly processes

This work presents a microscale approach for simulating the dielectrophoresis assembly of polarizable particles under an external electric field. The model is shown to capture interesting dynamical and topological features, such as the formation of chains of particles and their incipient aggregation into hierarchical structures. A quantitative characterization in terms of the number and size of these structures is also discussed. This computational model could represent a viable numerical tool to study the mechanical properties of particle-based hierarchical materials and suggest new strategies for enhancing their design and manufacture. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

Hunting BFKL in semi-hard reactions at the LHC

The agreement between calculations inspired by the resummation of energy logarithms, known as BFKL approach, and experimental data in the semi-hard sector of QCD has become manifest after a wealthy series of phenomenological analyses. However, the contingency that the same data could be concurrently portrayed at the hand of fixed-order, DGLAP-based calculations, has been pointed out recently, but not yet punctually addressed. Taking advantage of the richness of configurations gained by combining the acceptances of CMS and CASTOR detectors, we give results in the full next-to-leading logarithmic approximation of cross sections, azimuthal correlations and azimuthal distributions for three distinct semi-hard processes, each of them featuring a peculiar final-state exclusiveness. Then, making use of disjoint intervals for the transverse momenta of the emitted objects, i.e. $$\kappa $$ κ -windows, we clearly highlight how high-energy resummed and fixed-order driven predictions for semi-hard sensitive observables can be decisively discriminated in the kinematic ranges typical of current and forthcoming analyses at the LHC. The scale-optimization issue is also introduced and explored, while the uncertainty coming from the use of different PDF and FF set is deservedly handled. Finally, a brief overview of , a numerical tool recently developed, suited for the computation of inclusive semi-hard reactions is provided.

Automotive dry clutch fully coupled transient tribodynamics

Determining the root causes of Noise, Vibration and Harshness (NVH) phenomena in modern automotive drivetrains is a task of critical importance. This research investigates the stability of dry clutch systems vibrational behaviour during engagement. A fully coupled dry clutch numerical model including the influence of friction is presented and validated using vehicle measurements. The clutch component frictional properties are measured using parts that exhibit aggressive NVH behaviour using representative tribometric experiments. The validated numerical tool highlights the occurrence of instabilities which are caused by modal couplings, particularly between the input shaft bending and clutch disc radial motions. Such a validated transient dynamics model of a dry clutch system has not hitherto been presented in the open literature.

Infill Design Reinforcement of 3D Printed Parts Using Refinement Technique Adapted to Continuous Extrusion

In this paper, we introduce an advanced numerical tool aimed to optimise the infill design of 3D printed parts by reducing printing time. In 3D printing, the term infill refers to the internal structure of a part. To create the infill design, slicing software is used, which generally creates the infill uniformly throughout the part. When such a part is subjected to external loading, all the infill regions will not experience the same amount of stress. Therefore, using uniform infill throughout the part is not the most optimised solution in terms of material usage. We do propose to evolve the infill design with respect to the mechanical stresses generated by the external loads. To achieve this, an advanced numerical tool has been developed, based on refinement techniques, to control the infill design. This tool is coupled with Finite Element Simulation (FE Simulation) software, which helps to identify the zones where the material is required as an infill to reinforce a part, whereas the refinement technique makes it possible to place the material as an infill in such a way that the airtime during the printing of the part is zero. Zero airtime printing is defined as the ability to deposit each layer of a part, without stopping the material extrusion during the displacement of the nozzle. Therefore, the proposed numerical tool guides us to generate the infill design of a part, in such a way that it will consume zero airtime while manufacturing. Simultaneously, it will increase the stiffness of the part. The proposed approach is here applied to a rectangular structure subjected to four-point bending, made up of PLA material (Poly-Lactic Acid).