Injection molding is a multiphase process that requires accurate simulation of the filling phase. This is a key element in predicting the complete injection molding cycle. The filling phase presents a complex set of challenges, including migrating melt fronts, multi-phase flow, non-Newtonian fluid dynamics, and intertwined heat transfer. Evolving from 1D to 2D, 2.5D, and 3D techniques, filling simulation research has adapted to capture the intricacies of injection-molded parts. However, the need for accuracy in the characterization of the rheological properties of polymers during filling is still of paramount importance. In order to systematically categorize the numerical methods used to simulate the filling phase of injection molding, this review paper provides a comprehensive summary. Particular emphasis is given to the complex interaction of multiple geometric parameters that significantly influence the dynamic evolution of the filling process. In addition, a spectrum of rheological models is thoroughly and exhaustively explored in the manuscript. These models serve as basic mathematical constructs to help describe the complex viscous behavior of polymers during the filling phase. These models cover a spectrum of complexity and include widely recognized formulations such as the Power-Law, second-order, Herschel–Bulkley, Carreau, Bird–Carreau, and Cross models. The paper presents their implementation to include the temperature-dependent influence on viscosity. In this context, the extensions of these models are explained in detail. These extensions are designed to take into account the dynamic viscosity changes caused by the different thermal conditions during the filling process. An important contribution of this study is the systematic classification of these models. This categorization encompasses both academic research and practical integration into commercial software frameworks. In addition to the theoretical importance of these models, their practical value in overcoming challenges in the field of injection molding is emphasized. By systematically outlining these models within a structured framework, this classification promotes a comprehensive understanding of their intrinsic characteristics and relevance in different scenarios.

This contribution provides a detailed comparison of the impact of various rheological models on the filling phase of injection molding simulations in order to enhance the accuracy of flow predictions and improve material processing. The challenge of accurately modeling polymer melt flow behavior under different temperature and shear rate conditions is crucial for optimizing injection molding processes. Therefore, the study examines commonly used rheological models, including Power-Law, Second-Order, Herschel-Bulkley, Carreau and Cross models. Using experimental data for validation, the accuracy of each model in predicting the flow front and viscosity distribution for a quadratic molded part with a PA66 polymer is evaluated. The Carreau-WLF Winter model showed the highest accuracy, with the lowest RMSE values, closely followed by the Carreau model. The Second-Order model exhibited significant deviations in the edge region from experimental results, indicating its limitations. Results indicate that models incorporating both shear rate and temperature dependencies, such as Carreau-WLF Winter, provide superior predictions compared to those including only shear rate dependence. These findings suggest that selecting appropriate rheological models can significantly enhance the predictive capability of injection molding simulations, leading to better process optimization and higher quality in manufactured parts. The study emphasizes the significance of comprehensive rheological analysis and identifies potential avenues for future research and industrial applications in polymer processing.

The present study deals with the simulation of the filling process in injection molding using Ansys CFX and its experimental validation. For this purpose, the filling process of an exemplary mold is investigated numerically as well as experimentally at different time steps. For the numerical investigation, a suitable model is elaborated in Ansys CFX, which enables such a comparison. In particular, the representation of a suitable viscosity model for polymers is not common in Ansys CFX. Therefore, the Carreau-WLF viscosity model is adapted for the considered polymer Schulamind 66 SK 1000 and integrated into Ansys CFX. The contribution focuses on the comparison of the numerically calculated flow front contour and the respective filling levels of the melt from experiments. Furthermore, a detailed numerical analysis of temperature and viscosity profiles is included in order to illustrate the effect of shear-induced temperature changes and the interplay between the temperature field and the viscosity of the injected polymer. In conclusion, the numerical model nicely fits the experimental results despite some slight deviations in the early filling stages.

This contribution investigates the application of surrogate modeling, specifically Kriging and Response Surface Methodology (RSM), in optimizing injection molding simulation processes. Injection molding simulations are computationally intensive due to the multi-physical interactions involved, making surrogate models an attractive alternative to reduce computational effort. The authors employ Kriging and RSM models to simulate the injection molding of three different geometrical configurations, assessing their performance in predicting parameters for process quality/efficiency like deformation, shrinkage, and cycle time. The study makes use of MATLABs fmincon optimization algorithm with the models, emphasizing cycle time minimization while maintaining deformation and shrinkage within acceptable limits. In addition to the prediction accuracy, this contribution demonstrates that both surrogate models reduce the computational cost per evaluation by several orders of magnitude compared to full injection molding simulations and provide fast, iterative optimization. Findings indicate that Kriging outperforms RSM, especially in complex geometries, by providing more accurate predictions with lower error rates. The validation against digital twin simulations supports the effectiveness of Kriging, making it preferable for applications requiring high precision in process optimization.

Injection molding can undoubtedly be regarded as one of the most widely used manufacturing processes for polymers (Guevara-Morales & Figueroa-Lopez, 2014). Furthermore, injection molding has found its way into various branches of industry (Fernandez et al., 2018) since it has several essential advantages over other processing techniques in terms of good surface finish, the ability to process complex parts without the need for secondary operations, and low cost for mass production. In order to find optimal process settings, it is necessary to gain a deeper insight into the filling process and the underlying physical phenomena, as well as a thorough understanding of the complex material behavior. In this context, the numerical simulation of the injection molding process is increasingly important. Therefore, the current contribution is dedicated to present a thorough comparative numerical study for the mold filling of an exemplary thin-walled mold geometry, including a realistic non-Newtonian viscosity model for the polymer melt. For the numerical simulation, the authors employ the commercial CFD software packages Cadmould 3D-F and ANSYS CFX. While ANSYS CFX is a well-established CFD software for numerical modelling of multiphysical phenomena, Cadmould 3D-F is a highly specialized and computationally efficient alternative suitable for certain geometric configurations in the context of injection molding. The present study is new in the sense that it demonstrates the equivalence of the considered software packages for the simulation of the injection molding process in thin-walled moldgeometries.

This contribution presents a simulation-based approach for optimizing injection molding processes using digital twins. It combines surrogate modeling via response surface methodology (RSM) with the evolutionary algorithm NSGA-II to efficiently capture complex relationships between process parameters and objectives. A key element is the adaptive enhancement of the training dataset within the decision-relevant region of interest (ADEROI) by a modified greedy max–min algorithm. This strategy closes data gaps, improves model accuracy in the potentially optimal region, and directs additional simulations to informative areas. Leave-one-out (LOO) and hold-out (HO) cross-validations show strong root mean square error (RMSE) and $R^2$ values for deformation, shrinkage, cycle time, and mass. NSGA-II converges after 403 generations and results in 191 Pareto-optimal solutions, which are consolidated into preference-consistent operating points. These points make trade-offs between analyzed objectives’ deformation, shrinkage, and cycle time explicit for process pre-design. Preferred solutions are identified through weighted sums of normalized objectives and inversely mapped process parameters. Their agreement with the physics-based digital twin at the hundredths level supports the plausibility of the selected operating points within the investigated simulation-based workflow. A retrospective benchmark against a scaled single-stage LHS baseline shows that ADEROI achieves ROI-equivalent point density with fewer simulation runs for the investigated case, reducing the estimated runtime by $39.1\%$ and resulting in a $1.64\times$ speed-up. The quantitative validation is limited to one thin-walled PP keyholder component; further geometries, mold layouts, and polymer materials are required to empirically assess generalizability.