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Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure. <i>Composites Part B: Engineering</i>. 2021;224. doi:<a href=\"https://doi.org/10.1016/j.compositesb.2021.109209\">10.1016/j.compositesb.2021.109209</a>","chicago":"Cheng, C., Z. Wang, Z. Jin, X. Ju, Swetlana Schweizer, Thomas Tröster, and Rolf Mahnken. “Non-Linear Mean-Field Modelling of UD Composite Laminates Accounting for Average Asymmetric Plasticity of the Matrix, Debonding and Progressive Failure.” <i>Composites Part B: Engineering</i> 224 (2021). <a href=\"https://doi.org/10.1016/j.compositesb.2021.109209\">https://doi.org/10.1016/j.compositesb.2021.109209</a>.","ieee":"C. Cheng <i>et al.</i>, “Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure,” <i>Composites Part B: Engineering</i>, vol. 224, Art. no. 109209, 2021, doi: <a href=\"https://doi.org/10.1016/j.compositesb.2021.109209\">10.1016/j.compositesb.2021.109209</a>.","apa":"Cheng, C., Wang, Z., Jin, Z., Ju, X., Schweizer, S., Tröster, T., &#38; Mahnken, R. (2021). Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure. <i>Composites Part B: Engineering</i>, <i>224</i>, Article 109209. <a href=\"https://doi.org/10.1016/j.compositesb.2021.109209\">https://doi.org/10.1016/j.compositesb.2021.109209</a>","bibtex":"@article{Cheng_Wang_Jin_Ju_Schweizer_Tröster_Mahnken_2021, title={Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure}, volume={224}, DOI={<a href=\"https://doi.org/10.1016/j.compositesb.2021.109209\">10.1016/j.compositesb.2021.109209</a>}, number={109209}, journal={Composites Part B: Engineering}, author={Cheng, C. and Wang, Z. and Jin, Z. and Ju, X. and Schweizer, Swetlana and Tröster, Thomas and Mahnken, Rolf}, year={2021} }","mla":"Cheng, C., et al. “Non-Linear Mean-Field Modelling of UD Composite Laminates Accounting for Average Asymmetric Plasticity of the Matrix, Debonding and Progressive Failure.” <i>Composites Part B: Engineering</i>, vol. 224, 109209, 2021, doi:<a href=\"https://doi.org/10.1016/j.compositesb.2021.109209\">10.1016/j.compositesb.2021.109209</a>.","short":"C. Cheng, Z. Wang, Z. Jin, X. Ju, S. Schweizer, T. Tröster, R. Mahnken, Composites Part B: Engineering 224 (2021)."},"year":"2021","volume":224,"author":[{"full_name":"Cheng, C.","last_name":"Cheng","first_name":"C."},{"last_name":"Wang","full_name":"Wang, Z.","first_name":"Z."},{"last_name":"Jin","full_name":"Jin, Z.","first_name":"Z."},{"last_name":"Ju","full_name":"Ju, X.","first_name":"X."},{"first_name":"Swetlana","last_name":"Schweizer","id":"8938","full_name":"Schweizer, Swetlana"},{"first_name":"Thomas","id":"553","full_name":"Tröster, Thomas","last_name":"Tröster"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"date_created":"2021-08-18T06:20:21Z","date_updated":"2025-06-06T08:08:32Z","doi":"10.1016/j.compositesb.2021.109209","title":"Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure","publication":"Composites Part B: Engineering","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"As an effective and accurate method for modelling composite materials, mean-field homogenization is still not well studied in modelling non-linear and damage behaviours of UD composites. Investigated micro FE-simulations show that the matrix of UD composites exhibits different average plastic behaviour, named as average asymmetric matrix plasticity (AAMP), when the composite behaves different under shear, longitudinal and transverse loadings. In this study, a non-linear mean-field debonding model (NMFDM) combining a mean-field model and a fibre–matrix interface debonding model, is developed to simulate UD composites under consideration of AAMP, fibre–matrix interface damage and progressive failure. AAMP is considered by using so-called stress mode factor, which is expressed in terms of basic invariants of the matrix deviatoric stress tensor and is used as an indicator for detection of differences in the loading mode. The material behaviour of UD composites with imperfect interface is assumed identical as for perfect interface and stiffness reduced fibres. Progressive failure criteria are established with consideration of fibre breakage and matrix crack for different fibre orientations. As a representative example for the NMFDM, a C30/E201 UD composite is studied. To verify the model, experiments are conducted on polymers, carbon fibres and UD CFRPs. Finally, the model is applied to simulate a perforated CFRP laminate, which shows excellent prediction ability on deformation, debonding and progressive failure."}],"department":[{"_id":"9"},{"_id":"154"},{"_id":"321"},{"_id":"149"}],"user_id":"15952","_id":"23431","language":[{"iso":"eng"}],"keyword":["Non-linear mean-field homogenization Average asymmetric plasticity of matrix Fibre–matrix interface debonding Micro-mechanical FE-simulation Progressive failure"],"article_number":"109209"},{"publication":"Intrinsische Hybridverbunde für Leichtbautragstrukturen","type":"book_chapter","status":"public","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"},{"_id":"149"}],"user_id":"15952","_id":"29086","language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9783662628324","9783662628331"]},"quality_controlled":"1","publication_status":"published","citation":{"chicago":"Drossel, Welf-G, Mathias Bobbert, Marcus Böhme, Christian Dammann, Axel Dittes, Mina Gießmann, Christian Hühne, et al. “Hybridprofile Für Trag- Und Crashstrukturen.” In <i>Intrinsische Hybridverbunde Für Leichtbautragstrukturen</i>. Berlin, Heidelberg, 2021. <a href=\"https://doi.org/10.1007/978-3-662-62833-1_3\">https://doi.org/10.1007/978-3-662-62833-1_3</a>.","ieee":"W.-G. Drossel <i>et al.</i>, “Hybridprofile für Trag- und Crashstrukturen,” in <i>Intrinsische Hybridverbunde für Leichtbautragstrukturen</i>, Berlin, Heidelberg, 2021.","ama":"Drossel W-G, Bobbert M, Böhme M, et al. Hybridprofile für Trag- und Crashstrukturen. In: <i>Intrinsische Hybridverbunde Für Leichtbautragstrukturen</i>. ; 2021. doi:<a href=\"https://doi.org/10.1007/978-3-662-62833-1_3\">10.1007/978-3-662-62833-1_3</a>","apa":"Drossel, W.-G., Bobbert, M., Böhme, M., Dammann, C., Dittes, A., Gießmann, M., Hühne, C., Ihlemann, J., Kießling, R., Lampke, T., Lenz, P., Mahnken, R., Meschut, G., Müller, R., Nier, M., Prussak, R., Riemer, M., Sander, S., Schaper, M., … Zinn, C. (2021). Hybridprofile für Trag- und Crashstrukturen. In <i>Intrinsische Hybridverbunde für Leichtbautragstrukturen</i>. <a href=\"https://doi.org/10.1007/978-3-662-62833-1_3\">https://doi.org/10.1007/978-3-662-62833-1_3</a>","bibtex":"@inbook{Drossel_Bobbert_Böhme_Dammann_Dittes_Gießmann_Hühne_Ihlemann_Kießling_Lampke_et al._2021, place={Berlin, Heidelberg}, title={Hybridprofile für Trag- und Crashstrukturen}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-62833-1_3\">10.1007/978-3-662-62833-1_3</a>}, booktitle={Intrinsische Hybridverbunde für Leichtbautragstrukturen}, author={Drossel, Welf-G and Bobbert, Mathias and Böhme, Marcus and Dammann, Christian and Dittes, Axel and Gießmann, Mina and Hühne, Christian and Ihlemann, Jörn and Kießling, Robert and Lampke, Thomas and et al.}, year={2021} }","short":"W.-G. Drossel, M. Bobbert, M. Böhme, C. Dammann, A. Dittes, M. Gießmann, C. Hühne, J. Ihlemann, R. Kießling, T. Lampke, P. Lenz, R. Mahnken, G. Meschut, R. Müller, M. Nier, R. Prussak, M. Riemer, S. Sander, M. Schaper, I. Scharf, M. Scholze, S.-D. Schwöbel, S. Sharafiev, M. Sinapius, D. Stefaniak, T. Tröster, M.F.-X. Wagner, Z. Wang, C. Zinn, in: Intrinsische Hybridverbunde Für Leichtbautragstrukturen, Berlin, Heidelberg, 2021.","mla":"Drossel, Welf-G., et al. “Hybridprofile Für Trag- Und Crashstrukturen.” <i>Intrinsische Hybridverbunde Für Leichtbautragstrukturen</i>, 2021, doi:<a href=\"https://doi.org/10.1007/978-3-662-62833-1_3\">10.1007/978-3-662-62833-1_3</a>."},"year":"2021","place":"Berlin, Heidelberg","author":[{"first_name":"Welf-G","full_name":"Drossel, Welf-G","last_name":"Drossel"},{"last_name":"Bobbert","full_name":"Bobbert, Mathias","id":"7850","first_name":"Mathias"},{"first_name":"Marcus","full_name":"Böhme, Marcus","last_name":"Böhme"},{"last_name":"Dammann","full_name":"Dammann, Christian","first_name":"Christian"},{"first_name":"Axel","last_name":"Dittes","full_name":"Dittes, Axel"},{"first_name":"Mina","full_name":"Gießmann, Mina","last_name":"Gießmann"},{"full_name":"Hühne, Christian","last_name":"Hühne","first_name":"Christian"},{"last_name":"Ihlemann","full_name":"Ihlemann, Jörn","first_name":"Jörn"},{"first_name":"Robert","full_name":"Kießling, Robert","last_name":"Kießling"},{"first_name":"Thomas","full_name":"Lampke, Thomas","last_name":"Lampke"},{"first_name":"Peter","id":"49691","full_name":"Lenz, Peter","last_name":"Lenz"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"},{"first_name":"Gerson","id":"32056","full_name":"Meschut, Gerson","last_name":"Meschut","orcid":"0000-0002-2763-1246"},{"first_name":"Roland","full_name":"Müller, Roland","last_name":"Müller"},{"last_name":"Nier","full_name":"Nier, Matthias","first_name":"Matthias"},{"last_name":"Prussak","full_name":"Prussak, Robert","first_name":"Robert"},{"first_name":"Matthias","last_name":"Riemer","full_name":"Riemer, Matthias"},{"id":"23175","full_name":"Sander, Sascha","last_name":"Sander","first_name":"Sascha"},{"last_name":"Schaper","id":"43720","full_name":"Schaper, Mirko","first_name":"Mirko"},{"first_name":"Ingolf","full_name":"Scharf, Ingolf","last_name":"Scharf"},{"first_name":"Mario","full_name":"Scholze, Mario","last_name":"Scholze"},{"first_name":"Stephan-Daniel","last_name":"Schwöbel","full_name":"Schwöbel, Stephan-Daniel"},{"first_name":"Semen","last_name":"Sharafiev","full_name":"Sharafiev, Semen"},{"first_name":"Michael","last_name":"Sinapius","full_name":"Sinapius, Michael"},{"full_name":"Stefaniak, Daniel","last_name":"Stefaniak","first_name":"Daniel"},{"last_name":"Tröster","full_name":"Tröster, Thomas","id":"553","first_name":"Thomas"},{"first_name":"Martin F. -X.","last_name":"Wagner","full_name":"Wagner, Martin F. -X."},{"full_name":"Wang, Zheng","last_name":"Wang","first_name":"Zheng"},{"full_name":"Zinn, Carolin","last_name":"Zinn","first_name":"Carolin"}],"date_created":"2021-12-22T12:29:50Z","date_updated":"2025-06-06T08:09:10Z","doi":"10.1007/978-3-662-62833-1_3","title":"Hybridprofile für Trag- und Crashstrukturen"},{"status":"public","publication":"Computer Methods in Applied Mechanics and Engineering","type":"journal_article","article_number":"113439","language":[{"iso":"eng"}],"_id":"24374","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","year":"2020","citation":{"short":"I. Caylak, E. Penner, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2020).","bibtex":"@article{Caylak_Penner_Mahnken_2020, title={Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters}, DOI={<a href=\"https://doi.org/10.1016/j.cma.2020.113439\">10.1016/j.cma.2020.113439</a>}, number={113439}, journal={Computer Methods in Applied Mechanics and Engineering}, author={Caylak, Ismail and Penner, Eduard and Mahnken, Rolf}, year={2020} }","mla":"Caylak, Ismail, et al. “Mean-Field and Full-Field Homogenization with Polymorphic Uncertain Geometry and Material Parameters.” <i>Computer Methods in Applied Mechanics and Engineering</i>, 113439, 2020, doi:<a href=\"https://doi.org/10.1016/j.cma.2020.113439\">10.1016/j.cma.2020.113439</a>.","apa":"Caylak, I., Penner, E., &#38; Mahnken, R. (2020). Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters. <i>Computer Methods in Applied Mechanics and Engineering</i>, Article 113439. <a href=\"https://doi.org/10.1016/j.cma.2020.113439\">https://doi.org/10.1016/j.cma.2020.113439</a>","ieee":"I. Caylak, E. Penner, and R. Mahnken, “Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters,” <i>Computer Methods in Applied Mechanics and Engineering</i>, Art. no. 113439, 2020, doi: <a href=\"https://doi.org/10.1016/j.cma.2020.113439\">10.1016/j.cma.2020.113439</a>.","chicago":"Caylak, Ismail, Eduard Penner, and Rolf Mahnken. “Mean-Field and Full-Field Homogenization with Polymorphic Uncertain Geometry and Material Parameters.” <i>Computer Methods in Applied Mechanics and Engineering</i>, 2020. <a href=\"https://doi.org/10.1016/j.cma.2020.113439\">https://doi.org/10.1016/j.cma.2020.113439</a>.","ama":"Caylak I, Penner E, Mahnken R. Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters. <i>Computer Methods in Applied Mechanics and Engineering</i>. Published online 2020. doi:<a href=\"https://doi.org/10.1016/j.cma.2020.113439\">10.1016/j.cma.2020.113439</a>"},"quality_controlled":"1","publication_identifier":{"issn":["0045-7825"]},"publication_status":"published","title":"Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters","doi":"10.1016/j.cma.2020.113439","date_updated":"2023-01-24T14:03:55Z","author":[{"last_name":"Caylak","id":"75","full_name":"Caylak, Ismail","first_name":"Ismail"},{"last_name":"Penner","id":"27973","full_name":"Penner, Eduard","first_name":"Eduard"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"date_created":"2021-09-14T11:18:05Z"},{"language":[{"iso":"eng"}],"department":[{"_id":"154"}],"user_id":"78813","_id":"13431","status":"public","publication":"Safety and Reliability","type":"journal_article","doi":"10.1080/09617353.2018.1552477","title":"\"A possibilistic finite element method for sparse data\"","date_created":"2019-09-20T12:44:28Z","author":[{"last_name":"Dridger","full_name":"Dridger, A.","first_name":"A."},{"last_name":"Caylak","full_name":"Caylak, I.","first_name":"I."},{"full_name":"Mahnken, R.","last_name":"Mahnken","first_name":"R."},{"last_name":"Penner","full_name":"Penner, E.","first_name":"E."}],"date_updated":"2022-01-06T06:51:36Z","page":"58-82","citation":{"bibtex":"@article{Dridger_Caylak_Mahnken_Penner_2019, title={“A possibilistic finite element method for sparse data”}, DOI={<a href=\"https://doi.org/10.1080/09617353.2018.1552477\">10.1080/09617353.2018.1552477</a>}, journal={Safety and Reliability}, author={Dridger, A. and Caylak, I. and Mahnken, R. and Penner, E.}, year={2019}, pages={58–82} }","mla":"Dridger, A., et al. “‘A Possibilistic Finite Element Method for Sparse Data.’” <i>Safety and Reliability</i>, 2019, pp. 58–82, doi:<a href=\"https://doi.org/10.1080/09617353.2018.1552477\">10.1080/09617353.2018.1552477</a>.","short":"A. Dridger, I. Caylak, R. Mahnken, E. Penner, Safety and Reliability (2019) 58–82.","apa":"Dridger, A., Caylak, I., Mahnken, R., &#38; Penner, E. (2019). “A possibilistic finite element method for sparse data.” <i>Safety and Reliability</i>, 58–82. <a href=\"https://doi.org/10.1080/09617353.2018.1552477\">https://doi.org/10.1080/09617353.2018.1552477</a>","ama":"Dridger A, Caylak I, Mahnken R, Penner E. “A possibilistic finite element method for sparse data.” <i>Safety and Reliability</i>. 2019:58-82. doi:<a href=\"https://doi.org/10.1080/09617353.2018.1552477\">10.1080/09617353.2018.1552477</a>","chicago":"Dridger, A., I. Caylak, R. Mahnken, and E. Penner. “‘A Possibilistic Finite Element Method for Sparse Data.’” <i>Safety and Reliability</i>, 2019, 58–82. <a href=\"https://doi.org/10.1080/09617353.2018.1552477\">https://doi.org/10.1080/09617353.2018.1552477</a>.","ieee":"A. Dridger, I. Caylak, R. Mahnken, and E. Penner, “‘A possibilistic finite element method for sparse data,’” <i>Safety and Reliability</i>, pp. 58–82, 2019."},"year":"2019","publication_identifier":{"issn":["0961-7353","2469-4126"]},"publication_status":"published"},{"_id":"13432","department":[{"_id":"154"}],"user_id":"78813","language":[{"iso":"eng"}],"publication":"Computer Methods in Applied Mechanics and Engineering","type":"journal_article","status":"public","date_updated":"2022-01-06T06:51:36Z","date_created":"2019-09-20T12:53:03Z","author":[{"first_name":"Xiaozhe","last_name":"Ju","full_name":"Ju, Xiaozhe"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf"}],"title":"\"Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity\"","doi":"10.1016/j.cma.2019.01.031","publication_identifier":{"issn":["0045-7825"]},"publication_status":"published","year":"2019","page":"297-329","citation":{"bibtex":"@article{Ju_Mahnken_2019, title={“Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity”}, DOI={<a href=\"https://doi.org/10.1016/j.cma.2019.01.031\">10.1016/j.cma.2019.01.031</a>}, journal={Computer Methods in Applied Mechanics and Engineering}, author={Ju, Xiaozhe and Mahnken, Rolf}, year={2019}, pages={297–329} }","short":"X. Ju, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2019) 297–329.","mla":"Ju, Xiaozhe, and Rolf Mahnken. “‘Goal-Oriented h-Type Adaptive Finite Elements for Micromorphic Elastoplasticity.’” <i>Computer Methods in Applied Mechanics and Engineering</i>, 2019, pp. 297–329, doi:<a href=\"https://doi.org/10.1016/j.cma.2019.01.031\">10.1016/j.cma.2019.01.031</a>.","apa":"Ju, X., &#38; Mahnken, R. (2019). “Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity.” <i>Computer Methods in Applied Mechanics and Engineering</i>, 297–329. <a href=\"https://doi.org/10.1016/j.cma.2019.01.031\">https://doi.org/10.1016/j.cma.2019.01.031</a>","ieee":"X. Ju and R. Mahnken, “‘Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity,’” <i>Computer Methods in Applied Mechanics and Engineering</i>, pp. 297–329, 2019.","chicago":"Ju, Xiaozhe, and Rolf Mahnken. “‘Goal-Oriented h-Type Adaptive Finite Elements for Micromorphic Elastoplasticity.’” <i>Computer Methods in Applied Mechanics and Engineering</i>, 2019, 297–329. <a href=\"https://doi.org/10.1016/j.cma.2019.01.031\">https://doi.org/10.1016/j.cma.2019.01.031</a>.","ama":"Ju X, Mahnken R. “Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity.” <i>Computer Methods in Applied Mechanics and Engineering</i>. 2019:297-329. doi:<a href=\"https://doi.org/10.1016/j.cma.2019.01.031\">10.1016/j.cma.2019.01.031</a>"}},{"department":[{"_id":"154"}],"user_id":"78813","_id":"13434","language":[{"iso":"eng"}],"article_number":"e201900005","publication":"GAMM-Mitteilungen","type":"journal_article","status":"public","date_created":"2019-09-20T13:21:03Z","author":[{"full_name":"Mäck, Markus","last_name":"Mäck","first_name":"Markus"},{"first_name":"Ismail","full_name":"Caylak, Ismail","last_name":"Caylak"},{"first_name":"Philipp","full_name":"Edler, Philipp","last_name":"Edler"},{"first_name":"Steffen","full_name":"Freitag, Steffen","last_name":"Freitag"},{"first_name":"Michael","last_name":"Hanss","full_name":"Hanss, Michael"},{"last_name":"Mahnken","full_name":"Mahnken, Rolf","first_name":"Rolf"},{"first_name":"Günther","last_name":"Meschke","full_name":"Meschke, Günther"},{"last_name":"Penner","full_name":"Penner, Eduard","first_name":"Eduard"}],"date_updated":"2022-01-06T06:51:36Z","doi":"10.1002/gamm.201900005","title":"\"Optimization with constraints considering polymorphic uncertainties\"","publication_identifier":{"issn":["0936-7195"]},"publication_status":"published","citation":{"apa":"Mäck, M., Caylak, I., Edler, P., Freitag, S., Hanss, M., Mahnken, R., … Penner, E. (2019). “Optimization with constraints considering polymorphic uncertainties.” <i>GAMM-Mitteilungen</i>. <a href=\"https://doi.org/10.1002/gamm.201900005\">https://doi.org/10.1002/gamm.201900005</a>","mla":"Mäck, Markus, et al. “‘Optimization with Constraints Considering Polymorphic Uncertainties.’” <i>GAMM-Mitteilungen</i>, e201900005, 2019, doi:<a href=\"https://doi.org/10.1002/gamm.201900005\">10.1002/gamm.201900005</a>.","bibtex":"@article{Mäck_Caylak_Edler_Freitag_Hanss_Mahnken_Meschke_Penner_2019, title={“Optimization with constraints considering polymorphic uncertainties”}, DOI={<a href=\"https://doi.org/10.1002/gamm.201900005\">10.1002/gamm.201900005</a>}, number={e201900005}, journal={GAMM-Mitteilungen}, author={Mäck, Markus and Caylak, Ismail and Edler, Philipp and Freitag, Steffen and Hanss, Michael and Mahnken, Rolf and Meschke, Günther and Penner, Eduard}, year={2019} }","short":"M. Mäck, I. Caylak, P. Edler, S. Freitag, M. Hanss, R. Mahnken, G. Meschke, E. Penner, GAMM-Mitteilungen (2019).","ama":"Mäck M, Caylak I, Edler P, et al. “Optimization with constraints considering polymorphic uncertainties.” <i>GAMM-Mitteilungen</i>. 2019. doi:<a href=\"https://doi.org/10.1002/gamm.201900005\">10.1002/gamm.201900005</a>","chicago":"Mäck, Markus, Ismail Caylak, Philipp Edler, Steffen Freitag, Michael Hanss, Rolf Mahnken, Günther Meschke, and Eduard Penner. “‘Optimization with Constraints Considering Polymorphic Uncertainties.’” <i>GAMM-Mitteilungen</i>, 2019. <a href=\"https://doi.org/10.1002/gamm.201900005\">https://doi.org/10.1002/gamm.201900005</a>.","ieee":"M. Mäck <i>et al.</i>, “‘Optimization with constraints considering polymorphic uncertainties,’” <i>GAMM-Mitteilungen</i>, 2019."},"year":"2019"},{"publication":"International Journal for Numerical Methods in Engineering","type":"journal_article","status":"public","_id":"13805","department":[{"_id":"154"}],"user_id":"78813","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0029-5981","1097-0207"]},"publication_status":"published","year":"2019","citation":{"apa":"Mahnken, R., &#38; Ju, X. (2019). Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity. <i>International Journal for Numerical Methods in Engineering</i>. <a href=\"https://doi.org/10.1002/nme.6209\">https://doi.org/10.1002/nme.6209</a>","short":"R. Mahnken, X. Ju, International Journal for Numerical Methods in Engineering (2019).","bibtex":"@article{Mahnken_Ju_2019, title={Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity}, DOI={<a href=\"https://doi.org/10.1002/nme.6209\">10.1002/nme.6209</a>}, journal={International Journal for Numerical Methods in Engineering}, author={Mahnken, Rolf and Ju, Xiaozhe}, year={2019} }","mla":"Mahnken, Rolf, and Xiaozhe Ju. “Goal‐oriented Adaptivity Based on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Linear Elasticity.” <i>International Journal for Numerical Methods in Engineering</i>, 2019, doi:<a href=\"https://doi.org/10.1002/nme.6209\">10.1002/nme.6209</a>.","ama":"Mahnken R, Ju X. Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity. <i>International Journal for Numerical Methods in Engineering</i>. 2019. doi:<a href=\"https://doi.org/10.1002/nme.6209\">10.1002/nme.6209</a>","chicago":"Mahnken, Rolf, and Xiaozhe Ju. “Goal‐oriented Adaptivity Based on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Linear Elasticity.” <i>International Journal for Numerical Methods in Engineering</i>, 2019. <a href=\"https://doi.org/10.1002/nme.6209\">https://doi.org/10.1002/nme.6209</a>.","ieee":"R. Mahnken and X. 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