[{"title":"Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua","doi":"10.1016/j.ijsolstr.2025.113465","date_updated":"2025-06-06T14:24:50Z","publisher":"Elsevier BV","date_created":"2025-06-03T19:48:12Z","author":[{"first_name":"Hendrik","id":"60816","full_name":"Westermann, Hendrik","last_name":"Westermann","orcid":"0000-0002-5034-9708"},{"full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"}],"year":"2025","citation":{"chicago":"Westermann, Hendrik, and Rolf Mahnken. “Thermodynamically Consistent Phase-Field Modeling for Polycrystalline Multi-Phase Continua.” <i>International Journal of Solids and Structures</i>, 2025. <a href=\"https://doi.org/10.1016/j.ijsolstr.2025.113465\">https://doi.org/10.1016/j.ijsolstr.2025.113465</a>.","ieee":"H. Westermann and R. Mahnken, “Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua,” <i>International Journal of Solids and Structures</i>, Art. no. 113465, 2025, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2025.113465\">10.1016/j.ijsolstr.2025.113465</a>.","ama":"Westermann H, Mahnken R. Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua. <i>International Journal of Solids and Structures</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2025.113465\">10.1016/j.ijsolstr.2025.113465</a>","bibtex":"@article{Westermann_Mahnken_2025, title={Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2025.113465\">10.1016/j.ijsolstr.2025.113465</a>}, number={113465}, journal={International Journal of Solids and Structures}, publisher={Elsevier BV}, author={Westermann, Hendrik and Mahnken, Rolf}, year={2025} }","mla":"Westermann, Hendrik, and Rolf Mahnken. “Thermodynamically Consistent Phase-Field Modeling for Polycrystalline Multi-Phase Continua.” <i>International Journal of Solids and Structures</i>, 113465, Elsevier BV, 2025, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2025.113465\">10.1016/j.ijsolstr.2025.113465</a>.","short":"H. Westermann, R. Mahnken, International Journal of Solids and Structures (2025).","apa":"Westermann, H., &#38; Mahnken, R. (2025). Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua. <i>International Journal of Solids and Structures</i>, Article 113465. <a href=\"https://doi.org/10.1016/j.ijsolstr.2025.113465\">https://doi.org/10.1016/j.ijsolstr.2025.113465</a>"},"publication_identifier":{"issn":["0020-7683"]},"publication_status":"published","article_number":"113465","language":[{"iso":"eng"}],"_id":"60124","user_id":"60816","status":"public","publication":"International Journal of Solids and Structures","type":"journal_article"},{"doi":"10.1016/j.ijsolstr.2023.112642","date_updated":"2024-02-29T13:58:14Z","author":[{"first_name":"Peter","last_name":"Lenz","full_name":"Lenz, Peter"},{"first_name":"Rolf","full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken"}],"volume":290,"citation":{"apa":"Lenz, P., &#38; Mahnken, R. (2024). Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains. <i>International Journal of Solids and Structures</i>, <i>290</i>, Article 112642. <a href=\"https://doi.org/10.1016/j.ijsolstr.2023.112642\">https://doi.org/10.1016/j.ijsolstr.2023.112642</a>","bibtex":"@article{Lenz_Mahnken_2024, title={Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains}, volume={290}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2023.112642\">10.1016/j.ijsolstr.2023.112642</a>}, number={112642}, journal={International Journal of Solids and Structures}, publisher={Elsevier BV}, author={Lenz, Peter and Mahnken, Rolf}, year={2024} }","short":"P. Lenz, R. Mahnken, International Journal of Solids and Structures 290 (2024).","mla":"Lenz, Peter, and Rolf Mahnken. “Multiscale Simulation of Polymer Curing of Composites Combined Mean-Field Homogenisation Methods at Large Strains.” <i>International Journal of Solids and Structures</i>, vol. 290, 112642, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2023.112642\">10.1016/j.ijsolstr.2023.112642</a>.","ama":"Lenz P, Mahnken R. Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains. <i>International Journal of Solids and Structures</i>. 2024;290. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2023.112642\">10.1016/j.ijsolstr.2023.112642</a>","ieee":"P. Lenz and R. Mahnken, “Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains,” <i>International Journal of Solids and Structures</i>, vol. 290, Art. no. 112642, 2024, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2023.112642\">10.1016/j.ijsolstr.2023.112642</a>.","chicago":"Lenz, Peter, and Rolf Mahnken. “Multiscale Simulation of Polymer Curing of Composites Combined Mean-Field Homogenisation Methods at Large Strains.” <i>International Journal of Solids and Structures</i> 290 (2024). <a href=\"https://doi.org/10.1016/j.ijsolstr.2023.112642\">https://doi.org/10.1016/j.ijsolstr.2023.112642</a>."},"intvolume":"       290","publication_status":"published","publication_identifier":{"issn":["0020-7683"]},"article_number":"112642","_id":"52218","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"status":"public","type":"journal_article","title":"Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains","publisher":"Elsevier BV","date_created":"2024-02-29T13:57:56Z","year":"2024","quality_controlled":"1","keyword":["Applied Mathematics","Mechanical Engineering","Mechanics of Materials","Condensed Matter Physics","General Materials Science","Modeling and Simulation"],"language":[{"iso":"eng"}],"publication":"International Journal of Solids and Structures"},{"_id":"27774","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"article_number":"111266","language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Solids and Structures","status":"public","date_updated":"2023-01-24T13:00:59Z","date_created":"2021-11-23T23:14:09Z","author":[{"first_name":"Peter","last_name":"Lenz","id":"49691","full_name":"Lenz, Peter"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"title":"A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains","doi":"10.1016/j.ijsolstr.2021.111266","publication_status":"published","publication_identifier":{"issn":["0020-7683"]},"quality_controlled":"1","year":"2021","citation":{"apa":"Lenz, P., &#38; Mahnken, R. (2021). A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains. <i>International Journal of Solids and Structures</i>, Article 111266. <a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111266\">https://doi.org/10.1016/j.ijsolstr.2021.111266</a>","short":"P. Lenz, R. Mahnken, International Journal of Solids and Structures (2021).","mla":"Lenz, Peter, and Rolf Mahnken. “A General Framework for Mean-Field Homogenization of Multi-Layered Linear Elastic Composites Subjected to Thermal and Curing Induced Strains.” <i>International Journal of Solids and Structures</i>, 111266, 2021, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111266\">10.1016/j.ijsolstr.2021.111266</a>.","bibtex":"@article{Lenz_Mahnken_2021, title={A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111266\">10.1016/j.ijsolstr.2021.111266</a>}, number={111266}, journal={International Journal of Solids and Structures}, author={Lenz, Peter and Mahnken, Rolf}, year={2021} }","chicago":"Lenz, Peter, and Rolf Mahnken. “A General Framework for Mean-Field Homogenization of Multi-Layered Linear Elastic Composites Subjected to Thermal and Curing Induced Strains.” <i>International Journal of Solids and Structures</i>, 2021. <a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111266\">https://doi.org/10.1016/j.ijsolstr.2021.111266</a>.","ieee":"P. Lenz and R. Mahnken, “A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains,” <i>International Journal of Solids and Structures</i>, Art. no. 111266, 2021, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111266\">10.1016/j.ijsolstr.2021.111266</a>.","ama":"Lenz P, Mahnken R. A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains. <i>International Journal of Solids and Structures</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111266\">10.1016/j.ijsolstr.2021.111266</a>"}},{"doi":"10.1016/j.ijsolstr.2021.111103","title":"A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity","date_created":"2021-12-22T12:39:10Z","author":[{"full_name":"Ju, X.","last_name":"Ju","first_name":"X."},{"first_name":"Rolf","id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken"},{"first_name":"Y.","last_name":"Xu","full_name":"Xu, Y."},{"full_name":"Liang, L.","last_name":"Liang","first_name":"L."},{"last_name":"Zhou","full_name":"Zhou, W.","first_name":"W."}],"date_updated":"2023-01-24T12:56:29Z","citation":{"apa":"Ju, X., Mahnken, R., Xu, Y., Liang, L., &#38; Zhou, W. (2021). A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity. <i>International Journal of Solids and Structures</i>, Article 111103. <a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111103\">https://doi.org/10.1016/j.ijsolstr.2021.111103</a>","mla":"Ju, X., et al. “A Nonuniform Transformation Field Analysis for Composites with Strength Difference Effects in Elastoplasticity.” <i>International Journal of Solids and Structures</i>, 111103, 2021, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111103\">10.1016/j.ijsolstr.2021.111103</a>.","bibtex":"@article{Ju_Mahnken_Xu_Liang_Zhou_2021, title={A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111103\">10.1016/j.ijsolstr.2021.111103</a>}, number={111103}, journal={International Journal of Solids and Structures}, author={Ju, X. and Mahnken, Rolf and Xu, Y. and Liang, L. and Zhou, W.}, year={2021} }","short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, W. Zhou, International Journal of Solids and Structures (2021).","ama":"Ju X, Mahnken R, Xu Y, Liang L, Zhou W. A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity. <i>International Journal of Solids and Structures</i>. Published online 2021. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111103\">10.1016/j.ijsolstr.2021.111103</a>","chicago":"Ju, X., Rolf Mahnken, Y. Xu, L. Liang, and W. Zhou. “A Nonuniform Transformation Field Analysis for Composites with Strength Difference Effects in Elastoplasticity.” <i>International Journal of Solids and Structures</i>, 2021. <a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111103\">https://doi.org/10.1016/j.ijsolstr.2021.111103</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, L. Liang, and W. Zhou, “A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity,” <i>International Journal of Solids and Structures</i>, Art. no. 111103, 2021, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2021.111103\">10.1016/j.ijsolstr.2021.111103</a>."},"year":"2021","publication_status":"published","publication_identifier":{"issn":["0020-7683"]},"quality_controlled":"1","language":[{"iso":"eng"}],"article_number":"111103","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"29088","status":"public","type":"journal_article","publication":"International Journal of Solids and Structures"},{"title":"„A coupled phase field/diffusion model for upper and lower bainitic transformation”","author":[{"first_name":"M.","last_name":"Düsing","full_name":"Düsing, M."},{"last_name":"Mahnken","full_name":"Mahnken, R.","first_name":"R."}],"date_created":"2019-05-21T13:03:05Z","volume":135,"date_updated":"2019-05-21T13:12:27Z","publisher":"Elsevier","citation":{"mla":"Düsing, M., and R. Mahnken. “„A Coupled Phase Field/Diffusion Model for Upper and Lower Bainitic Transformation”.” <i>International Journal of Solids and Structures</i>, vol. 135, Elsevier, 2018, pp. 172–83.","bibtex":"@article{Düsing_Mahnken_2018, title={„A coupled phase field/diffusion model for upper and lower bainitic transformation”}, volume={135}, journal={International Journal of Solids and Structures}, publisher={Elsevier}, author={Düsing, M. and Mahnken, R.}, year={2018}, pages={172–183} }","short":"M. Düsing, R. Mahnken, International Journal of Solids and Structures 135 (2018) 172–183.","apa":"Düsing, M., &#38; Mahnken, R. (2018). „A coupled phase field/diffusion model for upper and lower bainitic transformation”. <i>International Journal of Solids and Structures</i>, <i>135</i>, 172–183.","ieee":"M. Düsing and R. Mahnken, “„A coupled phase field/diffusion model for upper and lower bainitic transformation”,” <i>International Journal of Solids and Structures</i>, vol. 135, pp. 172–183, 2018.","chicago":"Düsing, M., and R. Mahnken. “„A Coupled Phase Field/Diffusion Model for Upper and Lower Bainitic Transformation”.” <i>International Journal of Solids and Structures</i> 135 (2018): 172–83.","ama":"Düsing M, Mahnken R. „A coupled phase field/diffusion model for upper and lower bainitic transformation”. <i>International Journal of Solids and Structures</i>. 2018;135:172-183."},"intvolume":"       135","page":"172-183","year":"2018","publication_status":"published","publication_identifier":{"issn":["0020-7683"]},"language":[{"iso":"eng"}],"keyword":["Coupled phase field/diffusion model","Bainite","Multiphase field method","Cahn–Hilliard diffusion","Diffusion across the interface","Lower bainitic transformation","Upper bainitic transformation","Thermodynamic framework","Microforce balance"],"user_id":"78813","department":[{"_id":"154"}],"_id":"9899","status":"public","abstract":[{"text":"Bainite is a steel microstructure consisting of three phases, bainitic ferrite, austenite and carbides. It forms in two different morphologies, upper and lower bainite, where different diffusion mechanisms are dominant. The aim of this work is to simulate both transformations within a unified model. To this end, we extend an own previously published model for lower bainite with diffusion across the phase interface. As a central idea we introduce weighted Helmholtz energy functions and a weighted mobility tensor, respectively. The individual Helmholtz energy functions and mobility terms are related to the different diffusion mechanisms which are responsible for the formation of both morphologies. Two representative examples illustrate the capability of the coupled phase field/diffusion model and show the expected behaviour.","lang":"eng"}],"type":"journal_article","publication":"International Journal of Solids and Structures"},{"volume":162,"date_created":"2019-10-14T12:43:13Z","author":[{"full_name":"Düsing, Martin","last_name":"Düsing","first_name":"Martin"},{"first_name":"Rolf","full_name":"Mahnken, Rolf","last_name":"Mahnken"}],"date_updated":"2022-01-06T06:51:45Z","doi":"10.1016/j.ijsolstr.2018.11.027","title":"A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation","publication_identifier":{"issn":["0020-7683"]},"publication_status":"published","intvolume":"       162","page":"45-59","citation":{"ieee":"M. Düsing and R. Mahnken, “A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation,” <i>International Journal of Solids and Structures</i>, vol. 162, pp. 45–59, 2018.","chicago":"Düsing, Martin, and Rolf Mahnken. “A Coupled Phase Field/Diffusional/Mechanical Framework for Simulation of Upper and Lower Bainitic Transformation.” <i>International Journal of Solids and Structures</i> 162 (2018): 45–59. <a href=\"https://doi.org/10.1016/j.ijsolstr.2018.11.027\">https://doi.org/10.1016/j.ijsolstr.2018.11.027</a>.","ama":"Düsing M, Mahnken R. A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation. <i>International Journal of Solids and Structures</i>. 2018;162:45-59. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2018.11.027\">10.1016/j.ijsolstr.2018.11.027</a>","bibtex":"@article{Düsing_Mahnken_2018, title={A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation}, volume={162}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2018.11.027\">10.1016/j.ijsolstr.2018.11.027</a>}, journal={International Journal of Solids and Structures}, author={Düsing, Martin and Mahnken, Rolf}, year={2018}, pages={45–59} }","mla":"Düsing, Martin, and Rolf Mahnken. “A Coupled Phase Field/Diffusional/Mechanical Framework for Simulation of Upper and Lower Bainitic Transformation.” <i>International Journal of Solids and Structures</i>, vol. 162, 2018, pp. 45–59, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2018.11.027\">10.1016/j.ijsolstr.2018.11.027</a>.","short":"M. Düsing, R. Mahnken, International Journal of Solids and Structures 162 (2018) 45–59.","apa":"Düsing, M., &#38; Mahnken, R. (2018). A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation. <i>International Journal of Solids and Structures</i>, <i>162</i>, 45–59. <a href=\"https://doi.org/10.1016/j.ijsolstr.2018.11.027\">https://doi.org/10.1016/j.ijsolstr.2018.11.027</a>"},"year":"2018","department":[{"_id":"154"}],"user_id":"78813","_id":"13814","language":[{"iso":"eng"}],"publication":"International Journal of Solids and Structures","type":"journal_article","status":"public"},{"_id":"24428","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"International Journal of Solids and Structures","status":"public","date_updated":"2023-01-24T14:11:28Z","date_created":"2021-09-14T13:36:20Z","author":[{"last_name":"Cheng","full_name":"Cheng, C.","first_name":"C."},{"first_name":"Rolf","full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken"}],"title":"A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations","doi":"10.1016/j.ijsolstr.2018.10.007","publication_status":"published","publication_identifier":{"issn":["0020-7683"]},"quality_controlled":"1","year":"2018","citation":{"apa":"Cheng, C., &#38; Mahnken, R. (2018). A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations. <i>International Journal of Solids and Structures</i>, 1–17. <a href=\"https://doi.org/10.1016/j.ijsolstr.2018.10.007\">https://doi.org/10.1016/j.ijsolstr.2018.10.007</a>","mla":"Cheng, C., and Rolf Mahnken. “A Multi-Mechanism Model for Cutting Simulation: A Ginzburg-Landau Type Phase Gradient and Numerical Implementations.” <i>International Journal of Solids and Structures</i>, 2018, pp. 1–17, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2018.10.007\">10.1016/j.ijsolstr.2018.10.007</a>.","short":"C. Cheng, R. Mahnken, International Journal of Solids and Structures (2018) 1–17.","bibtex":"@article{Cheng_Mahnken_2018, title={A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2018.10.007\">10.1016/j.ijsolstr.2018.10.007</a>}, journal={International Journal of Solids and Structures}, author={Cheng, C. and Mahnken, Rolf}, year={2018}, pages={1–17} }","chicago":"Cheng, C., and Rolf Mahnken. “A Multi-Mechanism Model for Cutting Simulation: A Ginzburg-Landau Type Phase Gradient and Numerical Implementations.” <i>International Journal of Solids and Structures</i>, 2018, 1–17. <a href=\"https://doi.org/10.1016/j.ijsolstr.2018.10.007\">https://doi.org/10.1016/j.ijsolstr.2018.10.007</a>.","ieee":"C. Cheng and R. Mahnken, “A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations,” <i>International Journal of Solids and Structures</i>, pp. 1–17, 2018, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2018.10.007\">10.1016/j.ijsolstr.2018.10.007</a>.","ama":"Cheng C, Mahnken R. A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations. <i>International Journal of Solids and Structures</i>. Published online 2018:1-17. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2018.10.007\">10.1016/j.ijsolstr.2018.10.007</a>"},"page":"1-17"},{"date_updated":"2019-05-27T10:51:04Z","date_created":"2019-05-27T10:04:12Z","author":[{"last_name":"Düsing","full_name":"Düsing, Martin","first_name":"Martin"},{"full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"}],"title":"\"A coupled phase field/diffusion model for upper and lower bainitic transformation\"","doi":"10.1016/j.ijsolstr.2017.11.018","publication_identifier":{"issn":["0020-7683"]},"publication_status":"published","year":"2017","page":"172-183","citation":{"bibtex":"@article{Düsing_Mahnken_2017, title={“A coupled phase field/diffusion model for upper and lower bainitic transformation”}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2017.11.018\">10.1016/j.ijsolstr.2017.11.018</a>}, journal={International Journal of Solids and Structures}, author={Düsing, Martin and Mahnken, Rolf}, year={2017}, pages={172–183} }","mla":"Düsing, Martin, and Rolf Mahnken. “‘A Coupled Phase Field/Diffusion Model for Upper and Lower Bainitic Transformation.’” <i>International Journal of Solids and Structures</i>, 2017, pp. 172–83, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2017.11.018\">10.1016/j.ijsolstr.2017.11.018</a>.","short":"M. Düsing, R. Mahnken, International Journal of Solids and Structures (2017) 172–183.","apa":"Düsing, M., &#38; Mahnken, R. (2017). “A coupled phase field/diffusion model for upper and lower bainitic transformation.” <i>International Journal of Solids and Structures</i>, 172–183. <a href=\"https://doi.org/10.1016/j.ijsolstr.2017.11.018\">https://doi.org/10.1016/j.ijsolstr.2017.11.018</a>","chicago":"Düsing, Martin, and Rolf Mahnken. “‘A Coupled Phase Field/Diffusion Model for Upper and Lower Bainitic Transformation.’” <i>International Journal of Solids and Structures</i>, 2017, 172–83. <a href=\"https://doi.org/10.1016/j.ijsolstr.2017.11.018\">https://doi.org/10.1016/j.ijsolstr.2017.11.018</a>.","ieee":"M. Düsing and R. Mahnken, “‘A coupled phase field/diffusion model for upper and lower bainitic transformation,’” <i>International Journal of Solids and Structures</i>, pp. 172–183, 2017.","ama":"Düsing M, Mahnken R. “A coupled phase field/diffusion model for upper and lower bainitic transformation.” <i>International Journal of Solids and Structures</i>. 2017:172-183. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2017.11.018\">10.1016/j.ijsolstr.2017.11.018</a>"},"_id":"9988","department":[{"_id":"154"}],"user_id":"78813","language":[{"iso":"eng"}],"publication":"International Journal of Solids and Structures","type":"journal_article","status":"public"},{"status":"public","type":"journal_article","publication":"International Journal of Solids and Structures","language":[{"iso":"eng"}],"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"24642","citation":{"apa":"Cheng, C., &#38; Mahnken, R. (2016). Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization. <i>International Journal of Solids and Structures</i>, 127–141. <a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">https://doi.org/10.1016/j.ijsolstr.2016.10.010</a>","mla":"Cheng, C., and Rolf Mahnken. “Extension of a Multi-Mechanism Model: Hardness-Based Flow and Transformation Induced Plasticity for Austenitization.” <i>International Journal of Solids and Structures</i>, 2016, pp. 127–41, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">10.1016/j.ijsolstr.2016.10.010</a>.","short":"C. Cheng, R. 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Thermodynamic consistent modeling of polymer curing coupled to visco–elasticity at large strains. <i>International Journal of Solids and Structures</i>, 2003–2021. <a href=\"https://doi.org/10.1016/j.ijsolstr.2013.01.033\">https://doi.org/10.1016/j.ijsolstr.2013.01.033</a>","short":"R. 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Shaban, R. Mahnken, L. Wilke, H. Potente, and H. Ridder, “Simulation of rate dependent plasticity for polymers with asymmetric effects,” <i>International Journal of Solids and Structures</i>, pp. 6148–6162, 2007, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2007.02.017\">10.1016/j.ijsolstr.2007.02.017</a>.","chicago":"Shaban, A., Rolf Mahnken, L. Wilke, H. Potente, and H. Ridder. “Simulation of Rate Dependent Plasticity for Polymers with Asymmetric Effects.” <i>International Journal of Solids and Structures</i>, 2007, 6148–62. <a href=\"https://doi.org/10.1016/j.ijsolstr.2007.02.017\">https://doi.org/10.1016/j.ijsolstr.2007.02.017</a>.","ama":"Shaban A, Mahnken R, Wilke L, Potente H, Ridder H. Simulation of rate dependent plasticity for polymers with asymmetric effects. <i>International Journal of Solids and Structures</i>. 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Ridder, International Journal of Solids and Structures (2007) 6148–6162.","mla":"Shaban, A., et al. “Simulation of Rate Dependent Plasticity for Polymers with Asymmetric Effects.” <i>International Journal of Solids and Structures</i>, 2007, pp. 6148–62, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2007.02.017\">10.1016/j.ijsolstr.2007.02.017</a>.","bibtex":"@article{Shaban_Mahnken_Wilke_Potente_Ridder_2007, title={Simulation of rate dependent plasticity for polymers with asymmetric effects}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2007.02.017\">10.1016/j.ijsolstr.2007.02.017</a>}, journal={International Journal of Solids and Structures}, author={Shaban, A. and Mahnken, Rolf and Wilke, L. and Potente, H. and Ridder, H.}, year={2007}, pages={6148–6162} }"}},{"doi":"10.1016/s0020-7683(03)00388-3","title":"Creep simulation of asymmetric effects by use of stress mode dependent weighting functions","date_created":"2021-12-14T11:58:15Z","author":[{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"}],"date_updated":"2023-01-25T14:34:22Z","page":"6189-6209","citation":{"ama":"Mahnken R. Creep simulation of asymmetric effects by use of stress mode dependent weighting functions. <i>International Journal of Solids and Structures</i>. Published online 2003:6189-6209. doi:<a href=\"https://doi.org/10.1016/s0020-7683(03)00388-3\">10.1016/s0020-7683(03)00388-3</a>","chicago":"Mahnken, Rolf. “Creep Simulation of Asymmetric Effects by Use of Stress Mode Dependent Weighting Functions.” <i>International Journal of Solids and Structures</i>, 2003, 6189–6209. <a href=\"https://doi.org/10.1016/s0020-7683(03)00388-3\">https://doi.org/10.1016/s0020-7683(03)00388-3</a>.","ieee":"R. Mahnken, “Creep simulation of asymmetric effects by use of stress mode dependent weighting functions,” <i>International Journal of Solids and Structures</i>, pp. 6189–6209, 2003, doi: <a href=\"https://doi.org/10.1016/s0020-7683(03)00388-3\">10.1016/s0020-7683(03)00388-3</a>.","apa":"Mahnken, R. (2003). Creep simulation of asymmetric effects by use of stress mode dependent weighting functions. <i>International Journal of Solids and Structures</i>, 6189–6209. <a href=\"https://doi.org/10.1016/s0020-7683(03)00388-3\">https://doi.org/10.1016/s0020-7683(03)00388-3</a>","bibtex":"@article{Mahnken_2003, title={Creep simulation of asymmetric effects by use of stress mode dependent weighting functions}, DOI={<a href=\"https://doi.org/10.1016/s0020-7683(03)00388-3\">10.1016/s0020-7683(03)00388-3</a>}, journal={International Journal of Solids and Structures}, author={Mahnken, Rolf}, year={2003}, pages={6189–6209} }","mla":"Mahnken, Rolf. “Creep Simulation of Asymmetric Effects by Use of Stress Mode Dependent Weighting Functions.” <i>International Journal of Solids and Structures</i>, 2003, pp. 6189–209, doi:<a href=\"https://doi.org/10.1016/s0020-7683(03)00388-3\">10.1016/s0020-7683(03)00388-3</a>.","short":"R. Mahnken, International Journal of Solids and Structures (2003) 6189–6209."},"year":"2003","publication_identifier":{"issn":["0020-7683"]},"quality_controlled":"1","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"9"},{"_id":"154"}],"user_id":"335","_id":"28783","status":"public","publication":"International Journal of Solids and Structures","type":"journal_article"}]