{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T05:02:49Z","timestamp":1780549369498,"version":"3.54.1"},"reference-count":60,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T00:00:00Z","timestamp":1779753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>This study presents an experimental and numerical investigation of warpage in injection-moulded ABS plates, with emphasis on the influence of modelling assumptions and residual stress development on warpage prediction. Two sets of processing conditions with different mould-temperature balances were investigated experimentally, and warpage was measured using a coordinate measuring machine (CMM). Filling and packing were simulated using Moldex3D, while warpage was predicted using two integrated Moldex3D solvers and a coupled Moldex3D\u2013Abaqus thermomechanical approach. Although identical thermal input data were used, the three approaches produced noticeably different warpage predictions. The Moldex3D enhanced solver consistently over-predicted warpage magnitude, while the Moldex3D nonlinear solver captured the nonlinear effects but showed unrealistic localised deformation. The thermomechanical approach predicted the warpage shape more accurately for both parameter sets and showed the closest overall agreement with the experimental results.<\/jats:p>","DOI":"10.3390\/polym18111310","type":"journal-article","created":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T13:28:21Z","timestamp":1779802101000},"page":"1310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Warpage of Injection-Moulded Thin Plates: Numerical Evaluation of Simulation Strategies and Experimental Validation"],"prefix":"10.3390","volume":"18","author":[{"given":"Toma\u017e","family":"Kastelic","sequence":"first","affiliation":[{"name":"Cafuta d.o.o., Kalce 5j, SI-1370 Logatec, Slovenia"},{"name":"Faculty of Mechanical Engineering, University of Ljubljana, A\u0161ker\u010deva 6, SI-1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1987-2787","authenticated-orcid":false,"given":"Nikolaj","family":"Mole","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Ljubljana, A\u0161ker\u010deva 6, SI-1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ga\u0161per","family":"Cafuta","sequence":"additional","affiliation":[{"name":"Cafuta d.o.o., Kalce 5j, SI-1370 Logatec, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2875-7075","authenticated-orcid":false,"given":"Bojan","family":"Starman","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Ljubljana, A\u0161ker\u010deva 6, SI-1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1922-930X","authenticated-orcid":false,"given":"Miroslav","family":"Halilovi\u010d","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Ljubljana, A\u0161ker\u010deva 6, SI-1000 Ljubljana, Slovenia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gaspar-Cunha, A., Melo, J.B., Marques, T., and Pontes, A. (2025). A Review on Injection Molding: Conformal Cooling Channels, Modelling, Surrogate Models and Multi-Objective Optimization. Polymers, 17.","DOI":"10.20944\/preprints202503.1555.v1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3065","DOI":"10.1007\/s00170-022-08888-9","article-title":"Numerical simulation of the mold filling process and its experimental validation","volume":"120","author":"Baum","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.jmapro.2019.10.014","article-title":"High precision validation of micro injection molding process simulations","volume":"48","author":"Tosello","year":"2019","journal-title":"J. Manuf. Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1177\/0892705720930746","article-title":"Improvement of warpage prediction through integrative simulation approach for thermoplastic material","volume":"35","author":"Divekar","year":"2022","journal-title":"J. Thermoplast. Compos. Mater."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Phansalkar, S., Kim, C., and Han, B. (2021). Why Is It Still Difficult to Make Accurate Prediction of the Warpage after Advanced Molding Processes?. Proceedings of the 2021 IEEE 71st Electronic Components and Technology Conference (ECTC), San Diego, CA, USA, 2021, IEEE.","DOI":"10.1109\/ECTC32696.2021.00239"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhou, H. (2013). Computer Modeling for Injection Molding: Simulation, Optimization, and Control, Wiley.","DOI":"10.1002\/9781118444887"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shoemaker, J. (2006). Moldflow Design Guide: A Resource for Plastics Engineers, Hanser. [1st ed.].","DOI":"10.3139\/9783446418547.fm"},{"key":"ref_8","first-page":"28","article-title":"Warpage of injection moulded parts as the result of mould temperature difference","volume":"44","author":"Jaruga","year":"2010","journal-title":"Arch. Mater. Sci. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, M.L., Chang, R.Y., and Hsu, C.H. (2018). Molding Simulation: Theory and Practice, Hanser Publishers\/Munich Hanser Publications. [1st ed.].","DOI":"10.3139\/9781569906200.fm"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1002\/pen.10579","article-title":"Prediction of process-induced warpage in injection molded thermoplastics","volume":"36","author":"Akay","year":"1996","journal-title":"Polym. Eng. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zheng, R., Tanner, R.I., and Fan, X.J. (2011). Injection Molding: Integration of Theory and Modeling Methods, Springer.","DOI":"10.1007\/978-3-642-21263-5"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1886","DOI":"10.1002\/pen.10585","article-title":"Residual thermal stresses in injection molded products","volume":"36","author":"Zoetelief","year":"1996","journal-title":"Polym. Eng. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1002\/pen.11015","article-title":"Residual thermal stresses in injection moldings of thermoplastics: A theoretical and experimental study","volume":"42","author":"Kamal","year":"2002","journal-title":"Polym. Eng. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"304","DOI":"10.14314\/polimery.2008.304","article-title":"Numerical simulation and experimental validation of residual stress induced constrained shrinkage of injection molded parts","volume":"53","author":"Azdast","year":"2008","journal-title":"Polimery"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1002\/polb.20724","article-title":"Residual stresses and birefringence in injection molding of amorphous polymers: Simulation and comparison with experiment","volume":"44","author":"Isayev","year":"2006","journal-title":"J. Polym. Sci. Part B Polym. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1016\/j.eurpolymj.2005.04.019","article-title":"Study on residual stresses of thin-walled injection molding","volume":"41","author":"Wang","year":"2005","journal-title":"Eur. Polym. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/S0924-0136(00)00472-6","article-title":"Analysis of thermal residual stress in plastic injection molding","volume":"101","author":"Chen","year":"2000","journal-title":"J. Mater. Process. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2220","DOI":"10.1002\/pen.25225","article-title":"Prediction of Residual Stresses in Injection-Molded Plates Using the Residual Temperature Field Concept","volume":"59","year":"2019","journal-title":"Polym. Eng. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0079-6700(94)00037-3","article-title":"The computation of properties of injection-moulded products","volume":"20","author":"Douven","year":"1995","journal-title":"Prog. Polym. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"82","DOI":"10.3139\/217.940082","article-title":"Residual Stresses in Quenched and Injection Moulded Products","volume":"9","author":"Jansen","year":"1994","journal-title":"Int. Polym. Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0377-0257(98)00148-7","article-title":"Thermoviscoelastic simulation of thermally and pressure-induced stresses in injection moulding for the prediction of shrinkage and warpage for fibre-reinforced thermoplastics","volume":"84","author":"Zheng","year":"1999","journal-title":"J. Non-Newton. Fluid Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3139\/217.1698","article-title":"Residual Stress and Warpage Models for Complex Injection Molded Parts","volume":"17","author":"Young","year":"2002","journal-title":"Int. Polym. Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1016\/S0263-8223(00)00045-3","article-title":"Prediction of shrinkage and warpage in consideration of residual stress in integrated simulation of injection molding","volume":"47","author":"Choi","year":"1999","journal-title":"Compos. Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4399","DOI":"10.1007\/s10853-014-8170-y","article-title":"Residual stresses in injection molded products","volume":"49","year":"2014","journal-title":"J. Mater. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/pen.760220405","article-title":"An analysis of thermal warpage in injection molded flat parts due to unbalanced cooling","volume":"22","author":"Jacques","year":"1982","journal-title":"Polym. Eng. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1002\/pen.760311408","article-title":"Integrated simulation to predict warpage of injection molded parts","volume":"31","author":"Matsuoka","year":"1991","journal-title":"Polym. Eng. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1007\/BF00354424","article-title":"Thermal stresses and strains in injection moulding: Experiments and computations","volume":"30","author":"Denizart","year":"1995","journal-title":"J. Mater. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1002\/pen.760250504","article-title":"Volumetric effects in the injection molding of polymers","volume":"25","author":"Isayev","year":"1985","journal-title":"Polym. Eng. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1002\/pen.10598","article-title":"Effect of pressure history on shrinkage and residual stresses\u2014injection molding with constrained shrinkage","volume":"36","author":"Jansen","year":"1996","journal-title":"Polym. Eng. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1002\/pen.10468","article-title":"Modeling and simulation of thermally induced stress and warpage in injection molded thermoplastics","volume":"36","author":"Liu","year":"1996","journal-title":"Polym. Eng. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"60","DOI":"10.3139\/217.920060","article-title":"Thermoviscoelastic Calculation of Residual Stresses and Residual Shapes of Injection Molded Parts","volume":"7","author":"Kabanemi","year":"1992","journal-title":"Int. Polym. Process."},{"key":"ref_32","unstructured":"Fan, Z., Yu, H., Zuo, Z., and Speight, R. (2017, January 8\u201310). Anisotropic thermo-viscous-elastic residual stress model for warpage simulation of injection molded part. Proceedings of the SPE ANTEC 2017, Anaheim, CA, USA."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Turk, J., and Sven\u0161ek, D. (2023). Thermoelasticity of Injection-Molded Parts. Polymers, 15.","DOI":"10.3390\/polym15132841"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Alms, J., Kahve, C., Laschet, G., \u00c7elik, H., Mentges, N., and Hopmann, C. (2024). Validation of a Multi-Scale Simulation for Precise Warpage Prediction of Injection Molded Semi-Crystalline Parts, St. Gallen, Switzerland, AIP Publishing LLC.","DOI":"10.1063\/5.0204979"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2517","DOI":"10.1007\/s00170-016-8390-1","article-title":"The application of modified viscoplastic constitutive relationship on the warpage prediction of injection-molded part","volume":"86","author":"Sun","year":"2016","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s10965-016-0980-y","article-title":"The application of modified PVT data on the warpage prediction of injection molded part","volume":"23","author":"Sun","year":"2016","journal-title":"J. Polym. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.32802\/asmscj.2021.697","article-title":"Increase in Warpage Prediction Accuracy for Glass Filled Polyamide Material (PA66) through Integrative Simulation Approach","volume":"15","author":"Gaval","year":"2021","journal-title":"ASM Sci. J."},{"key":"ref_38","first-page":"1","article-title":"Experimental and Numerical Study Determining the Warpage Phenomenon of Thin-Wall Injection Molding","volume":"2020","author":"Huang","year":"2020","journal-title":"Adv. Polym. Technol."},{"key":"ref_39","unstructured":"Fan, Z., and Speight, R. (2017, January 20\u201325). Modeling and material data issues of injection molding simulation. Proceedings of the 21st International Conference on Composite Materials, Xi\u2019an, China."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Lin, W.C., Fan, F.Y., Huang, C.F., Shen, Y.K., and Wang, H. (2022). Analysis of the Warpage Phenomenon of Micro-Sized Parts with Precision Injection Molding by Experiment, Numerical Simulation, and Grey Theory. Polymers, 14.","DOI":"10.3390\/polym14091845"},{"key":"ref_41","unstructured":"Gapi\u0144ski, B., Szostak, M., and Ivanov, V. (2019). Injection Moulding Simulation and Validation of Thin Wall Components for Precision Applications. Advances in Manufacturing II, Springer International Publishing. Lecture Notes in Mechanical Engineering."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.polymertesting.2019.02.028","article-title":"Investigation on the internal mechanism of the deviation between numerical simulation and experiments in injection molding product development","volume":"75","author":"Huang","year":"2019","journal-title":"Polym. Test."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Wang, J., Liu, T., Zheng, K., Liu, H., Cui, H., and Li, H. (2024). Local thermal warpage deformation of polypropylene injection molded flat part and neural network prediction model. Front. Mater., 11.","DOI":"10.3389\/fmats.2024.1421546"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Liao, Y.L., and Tsai, H.H. (2022). A Comparison of Numerical and Actual Measurements of Large-Scale Rib-Structured Pallet Flatness Using Recycled Polypropylene in Injection Molding. Polymers, 14.","DOI":"10.3390\/polym14081631"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1957","DOI":"10.1007\/s00170-022-10337-6","article-title":"Correction of mould cavity geometry for warpage compensation","volume":"123","author":"Kastelic","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_46","unstructured":"Farotti, E. (2020). Effects of Process Parameters on Injection Molding of Thermoplastics: In-Cavity Properties and Mechanical Characterization. [Ph.D. Thesis, Universit\u00e0 Politecnica delle Marche Scuola di Dottorato di Ricerca in Scienze dell\u2019Ingegneria]."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.polymertesting.2019.03.024","article-title":"A new characterizing method for warpage measurement of injection-molded thermoplastics","volume":"76","author":"Sun","year":"2019","journal-title":"Polym. Test."},{"key":"ref_48","unstructured":"CoreTech System Co., Ltd. (2024). Moldex3D Help and User Documentation, CoreTech System Co., Ltd."},{"key":"ref_49","unstructured":"Bergman, T.L., and Lavine, A.S. (2017). Fundamentals of Heat and Mass Transfer, John Wiley & Sons. [8th ed.]."},{"key":"ref_50","unstructured":"Goodship, V., Arburg Limited, and Rapra Technology Limited (2004). Practical Guide to Injection Moulding, Rapra Technology."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Costa, F.S. (2014). The Influence of Mold Deflection on the Prediction of Packing Pressure Decay and Part Shrinkage, Nuremberg, Germany, American Institute of Physics.","DOI":"10.1063\/1.4873845"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.jmapro.2020.10.028","article-title":"Learning quality characteristics for plastic injection molding processes using a combination of simulated and measured data","volume":"60","author":"Finkeldey","year":"2020","journal-title":"J. Manuf. Process."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Schmidt, N., Kvaktun, D., and Schiffers, R. (2024). Discrepancies in Injection Molding Simulation and Reality: An Analysis, St. Gallen, Switzerland, AIP Publishing LLC.","DOI":"10.1063\/5.0204975"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1007\/s00170-022-09992-6","article-title":"Strategies for adjusting process parameters in CAE simulation to meet real injection molding condition of screw positions and cavity pressure curves","volume":"122","author":"Wang","year":"2022","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1002\/pen.760320708","article-title":"The measurement of thermal stress distributions along the flow path in injection-molded flat plates","volume":"32","author":"Hastenberg","year":"1992","journal-title":"Polym. Eng. Sci."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2022","DOI":"10.1002\/pen.10898","article-title":"Relevance of mold-induced thermal boundary conditions and cavity deformation in the simulation of injection molding","volume":"41","author":"Pantani","year":"2001","journal-title":"Polym. Eng. Sci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1007\/BF00366642","article-title":"Calculation of residual stresses in injection molded products","volume":"30","author":"Baaijens","year":"1991","journal-title":"Rheol. Acta"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Costa, F.S., and Yuan, Z. (2015). Mold Deflection Effects on the Prediction of Packing Pressure Decay and Shrinkage of Semi-Crystalline Polymers, Cleveland, Ohio, USA, AIP Publishing LLC.","DOI":"10.1063\/1.4918416"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1080\/23080477.2014.11665603","article-title":"The Elastic Mold Deformation During the Filling and Packing Stage of the Injection Molding Process","volume":"2","author":"Kleindel","year":"2014","journal-title":"Smart Sci."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1692","DOI":"10.1002\/pen.11301","article-title":"Nature of contact between polymer and mold in injection molding. Part II: Influence of mold deflection on pressure history and shrinkage","volume":"40","author":"Delaunay","year":"2000","journal-title":"Polym. Eng. Sci."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/11\/1310\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T04:16:07Z","timestamp":1780546567000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/11\/1310"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,26]]},"references-count":60,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["polym18111310"],"URL":"https:\/\/doi.org\/10.3390\/polym18111310","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,26]]}}}