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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>","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>","short":"C. Cheng, Z. Wang, Z. Jin, X. Ju, S. Schweizer, T. Tröster, R. Mahnken, Composites Part B: Engineering 224 (2021).","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>."},"quality_controlled":"1","publication_identifier":{"issn":["1359-8368"]},"author":[{"full_name":"Cheng, C.","last_name":"Cheng","first_name":"C."},{"full_name":"Wang, Z.","first_name":"Z.","last_name":"Wang"},{"first_name":"Z.","last_name":"Jin","full_name":"Jin, Z."},{"full_name":"Ju, X.","last_name":"Ju","first_name":"X."},{"full_name":"Schweizer, Swetlana","first_name":"Swetlana","last_name":"Schweizer","id":"8938"},{"full_name":"Tröster, Thomas","first_name":"Thomas","last_name":"Tröster","id":"553"},{"full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf","id":"335"}],"title":"Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure","year":"2021","intvolume":"       224","publication_status":"published","date_updated":"2025-06-06T08:08:32Z","language":[{"iso":"eng"}],"article_number":"109209","doi":"10.1016/j.compositesb.2021.109209","publication":"Composites Part B: Engineering","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."}],"date_created":"2021-08-18T06:20:21Z","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"},{"_id":"149"}],"type":"journal_article","keyword":["Non-linear mean-field homogenization Average asymmetric plasticity of matrix Fibre–matrix interface debonding Micro-mechanical FE-simulation Progressive failure"]},{"doi":"10.1007/978-3-662-62833-1_3","user_id":"15952","_id":"29086","language":[{"iso":"eng"}],"date_updated":"2025-06-06T08:09:10Z","publication_status":"published","title":"Hybridprofile für Trag- und Crashstrukturen","status":"public","year":"2021","author":[{"full_name":"Drossel, Welf-G","last_name":"Drossel","first_name":"Welf-G"},{"last_name":"Bobbert","first_name":"Mathias","full_name":"Bobbert, Mathias","id":"7850"},{"full_name":"Böhme, Marcus","last_name":"Böhme","first_name":"Marcus"},{"full_name":"Dammann, Christian","first_name":"Christian","last_name":"Dammann"},{"last_name":"Dittes","first_name":"Axel","full_name":"Dittes, Axel"},{"last_name":"Gießmann","first_name":"Mina","full_name":"Gießmann, Mina"},{"full_name":"Hühne, Christian","last_name":"Hühne","first_name":"Christian"},{"full_name":"Ihlemann, Jörn","first_name":"Jörn","last_name":"Ihlemann"},{"full_name":"Kießling, Robert","first_name":"Robert","last_name":"Kießling"},{"last_name":"Lampke","first_name":"Thomas","full_name":"Lampke, Thomas"},{"last_name":"Lenz","first_name":"Peter","full_name":"Lenz, Peter","id":"49691"},{"id":"335","last_name":"Mahnken","first_name":"Rolf","full_name":"Mahnken, Rolf"},{"id":"32056","orcid":"0000-0002-2763-1246","last_name":"Meschut","first_name":"Gerson","full_name":"Meschut, Gerson"},{"full_name":"Müller, Roland","first_name":"Roland","last_name":"Müller"},{"full_name":"Nier, Matthias","first_name":"Matthias","last_name":"Nier"},{"last_name":"Prussak","first_name":"Robert","full_name":"Prussak, Robert"},{"full_name":"Riemer, Matthias","first_name":"Matthias","last_name":"Riemer"},{"full_name":"Sander, Sascha","first_name":"Sascha","last_name":"Sander","id":"23175"},{"id":"43720","first_name":"Mirko","last_name":"Schaper","full_name":"Schaper, Mirko"},{"full_name":"Scharf, Ingolf","last_name":"Scharf","first_name":"Ingolf"},{"full_name":"Scholze, Mario","last_name":"Scholze","first_name":"Mario"},{"full_name":"Schwöbel, Stephan-Daniel","last_name":"Schwöbel","first_name":"Stephan-Daniel"},{"first_name":"Semen","last_name":"Sharafiev","full_name":"Sharafiev, Semen"},{"last_name":"Sinapius","first_name":"Michael","full_name":"Sinapius, Michael"},{"last_name":"Stefaniak","first_name":"Daniel","full_name":"Stefaniak, Daniel"},{"first_name":"Thomas","last_name":"Tröster","full_name":"Tröster, Thomas","id":"553"},{"last_name":"Wagner","first_name":"Martin F. -X.","full_name":"Wagner, Martin F. -X."},{"first_name":"Zheng","last_name":"Wang","full_name":"Wang, Zheng"},{"last_name":"Zinn","first_name":"Carolin","full_name":"Zinn, Carolin"}],"publication_identifier":{"isbn":["9783662628324","9783662628331"]},"type":"book_chapter","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"},{"_id":"149"}],"place":"Berlin, Heidelberg","date_created":"2021-12-22T12:29:50Z","quality_controlled":"1","publication":"Intrinsische Hybridverbunde für Leichtbautragstrukturen","citation":{"ieee":"W.-G. Drossel <i>et al.</i>, “Hybridprofile für Trag- und Crashstrukturen,” in <i>Intrinsische Hybridverbunde für Leichtbautragstrukturen</i>, Berlin, Heidelberg, 2021.","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>","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>.","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>.","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} }","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>"}},{"type":"journal_article","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"date_created":"2021-09-14T11:18:05Z","quality_controlled":"1","publication":"Computer Methods in Applied Mechanics and Engineering","citation":{"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>","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>.","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>.","short":"I. Caylak, E. Penner, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2020).","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>."},"user_id":"335","doi":"10.1016/j.cma.2020.113439","article_number":"113439","_id":"24374","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-01-24T14:03:55Z","year":"2020","title":"Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters","status":"public","author":[{"first_name":"Ismail","last_name":"Caylak","full_name":"Caylak, Ismail","id":"75"},{"last_name":"Penner","first_name":"Eduard","full_name":"Penner, Eduard","id":"27973"},{"full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf","id":"335"}],"publication_identifier":{"issn":["0045-7825"]}},{"date_created":"2020-09-08T10:24:25Z","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"type":"journal_article","citation":{"short":"E. Penner, I. Caylak, A. Dridger, R. Mahnken, Mathematics and Mechanics of Complex Systems (2019) 99–129.","chicago":"Penner, Eduard, Ismail Caylak, Alex Dridger, and Rolf Mahnken. “A Polynomial Chaos Expanded Hybrid Fuzzy-Stochastic Model for Transversely Fiber Reinforced Plastics.” <i>Mathematics and Mechanics of Complex Systems</i>, 2019, 99–129. <a href=\"https://doi.org/10.2140/memocs.2019.7.99\">https://doi.org/10.2140/memocs.2019.7.99</a>.","apa":"Penner, E., Caylak, I., Dridger, A., &#38; Mahnken, R. (2019). A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics. <i>Mathematics and Mechanics of Complex Systems</i>, 99–129. <a href=\"https://doi.org/10.2140/memocs.2019.7.99\">https://doi.org/10.2140/memocs.2019.7.99</a>","ieee":"E. Penner, I. Caylak, A. Dridger, and R. Mahnken, “A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics,” <i>Mathematics and Mechanics of Complex Systems</i>, pp. 99–129, 2019, doi: <a href=\"https://doi.org/10.2140/memocs.2019.7.99\">10.2140/memocs.2019.7.99</a>.","ama":"Penner E, Caylak I, Dridger A, Mahnken R. A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics. <i>Mathematics and Mechanics of Complex Systems</i>. Published online 2019:99-129. doi:<a href=\"https://doi.org/10.2140/memocs.2019.7.99\">10.2140/memocs.2019.7.99</a>","bibtex":"@article{Penner_Caylak_Dridger_Mahnken_2019, title={A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics}, DOI={<a href=\"https://doi.org/10.2140/memocs.2019.7.99\">10.2140/memocs.2019.7.99</a>}, journal={Mathematics and Mechanics of Complex Systems}, author={Penner, Eduard and Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}, year={2019}, pages={99–129} }","mla":"Penner, Eduard, et al. “A Polynomial Chaos Expanded Hybrid Fuzzy-Stochastic Model for Transversely Fiber Reinforced Plastics.” <i>Mathematics and Mechanics of Complex Systems</i>, 2019, pp. 99–129, doi:<a href=\"https://doi.org/10.2140/memocs.2019.7.99\">10.2140/memocs.2019.7.99</a>."},"publication":"Mathematics and Mechanics of Complex Systems","quality_controlled":"1","language":[{"iso":"eng"}],"_id":"19122","page":"99-129","doi":"10.2140/memocs.2019.7.99","user_id":"335","author":[{"last_name":"Penner","first_name":"Eduard","full_name":"Penner, Eduard","id":"27973"},{"id":"75","last_name":"Caylak","first_name":"Ismail","full_name":"Caylak, Ismail"},{"first_name":"Alex","last_name":"Dridger","full_name":"Dridger, Alex"},{"id":"335","full_name":"Mahnken, Rolf","first_name":"Rolf","last_name":"Mahnken"}],"publication_identifier":{"issn":["2325-3444","2326-7186"]},"title":"A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics","year":"2019","status":"public","date_updated":"2023-01-24T14:07:05Z","publication_status":"published"},{"doi":"10.1002/pamm.201900356","user_id":"335","language":[{"iso":"eng"}],"_id":"19120","date_updated":"2023-01-24T14:05:01Z","publication_status":"published","author":[{"id":"75","last_name":"Caylak","first_name":"Ismail","full_name":"Caylak, Ismail"},{"full_name":"Penner, Eduard","first_name":"Eduard","last_name":"Penner","id":"27973"},{"id":"335","last_name":"Mahnken","first_name":"Rolf","full_name":"Mahnken, Rolf"}],"publication_identifier":{"issn":["1617-7061","1617-7061"]},"year":"2019","title":"A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics","status":"public","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"type":"journal_article","date_created":"2020-09-08T10:23:48Z","citation":{"bibtex":"@article{Caylak_Penner_Mahnken_2019, title={A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics}, DOI={<a href=\"https://doi.org/10.1002/pamm.201900356\">10.1002/pamm.201900356</a>}, journal={PAMM}, author={Caylak, Ismail and Penner, Eduard and Mahnken, Rolf}, year={2019} }","ama":"Caylak I, Penner E, Mahnken R. A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics. <i>PAMM</i>. Published online 2019. doi:<a href=\"https://doi.org/10.1002/pamm.201900356\">10.1002/pamm.201900356</a>","mla":"Caylak, Ismail, et al. “A Fuzzy Uncertainty Model for Analytical and Numerical Homogenization of Transversely Fiber Reinforced Plastics.” <i>PAMM</i>, 2019, doi:<a href=\"https://doi.org/10.1002/pamm.201900356\">10.1002/pamm.201900356</a>.","chicago":"Caylak, Ismail, Eduard Penner, and Rolf Mahnken. “A Fuzzy Uncertainty Model for Analytical and Numerical Homogenization of Transversely Fiber Reinforced Plastics.” <i>PAMM</i>, 2019. <a href=\"https://doi.org/10.1002/pamm.201900356\">https://doi.org/10.1002/pamm.201900356</a>.","short":"I. Caylak, E. Penner, R. Mahnken, PAMM (2019).","ieee":"I. Caylak, E. Penner, and R. Mahnken, “A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics,” <i>PAMM</i>, 2019, doi: <a href=\"https://doi.org/10.1002/pamm.201900356\">10.1002/pamm.201900356</a>.","apa":"Caylak, I., Penner, E., &#38; Mahnken, R. (2019). A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics. <i>PAMM</i>. <a href=\"https://doi.org/10.1002/pamm.201900356\">https://doi.org/10.1002/pamm.201900356</a>"},"publication":"PAMM"},{"user_id":"335","doi":"10.1002/pamm.201900177","_id":"24429","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-01-24T14:06:23Z","status":"public","year":"2019","title":"Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells","author":[{"full_name":"Ju, Xiaozhe","first_name":"Xiaozhe","last_name":"Ju"},{"id":"335","last_name":"Mahnken","first_name":"Rolf","full_name":"Mahnken, Rolf"}],"publication_identifier":{"issn":["1617-7061","1617-7061"]},"type":"journal_article","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"date_created":"2021-09-14T13:40:01Z","quality_controlled":"1","publication":"PAMM","citation":{"apa":"Ju, X., &#38; Mahnken, R. (2019). Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells. <i>PAMM</i>. <a href=\"https://doi.org/10.1002/pamm.201900177\">https://doi.org/10.1002/pamm.201900177</a>","ieee":"X. Ju and R. Mahnken, “Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells,” <i>PAMM</i>, 2019, doi: <a href=\"https://doi.org/10.1002/pamm.201900177\">10.1002/pamm.201900177</a>.","chicago":"Ju, Xiaozhe, and Rolf Mahnken. “Model Adaptivity on Mean‐field and Full‐field Homogenization Methods Considering Hierarchical Unit Cells.” <i>PAMM</i>, 2019. <a href=\"https://doi.org/10.1002/pamm.201900177\">https://doi.org/10.1002/pamm.201900177</a>.","short":"X. Ju, R. Mahnken, PAMM (2019).","mla":"Ju, Xiaozhe, and Rolf Mahnken. “Model Adaptivity on Mean‐field and Full‐field Homogenization Methods Considering Hierarchical Unit Cells.” <i>PAMM</i>, 2019, doi:<a href=\"https://doi.org/10.1002/pamm.201900177\">10.1002/pamm.201900177</a>.","ama":"Ju X, Mahnken R. Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells. <i>PAMM</i>. Published online 2019. doi:<a href=\"https://doi.org/10.1002/pamm.201900177\">10.1002/pamm.201900177</a>","bibtex":"@article{Ju_Mahnken_2019, title={Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells}, DOI={<a href=\"https://doi.org/10.1002/pamm.201900177\">10.1002/pamm.201900177</a>}, journal={PAMM}, author={Ju, Xiaozhe and Mahnken, Rolf}, year={2019} }"}},{"date_created":"2020-09-15T18:05:56Z","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"type":"journal_article","citation":{"ama":"Lenz P, Mahnken R. Damage simulation of fiber reinforced composites using mean‐field homogenization methods. <i>PAMM</i>. Published online 2019. doi:<a href=\"https://doi.org/10.1002/pamm.201900370\">10.1002/pamm.201900370</a>","bibtex":"@article{Lenz_Mahnken_2019, title={Damage simulation of fiber reinforced composites using mean‐field homogenization methods}, DOI={<a href=\"https://doi.org/10.1002/pamm.201900370\">10.1002/pamm.201900370</a>}, journal={PAMM}, author={Lenz, Peter and Mahnken, Rolf}, year={2019} }","mla":"Lenz, Peter, and Rolf Mahnken. “Damage Simulation of Fiber Reinforced Composites Using Mean‐field Homogenization Methods.” <i>PAMM</i>, 2019, doi:<a href=\"https://doi.org/10.1002/pamm.201900370\">10.1002/pamm.201900370</a>.","short":"P. Lenz, R. 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Dammann, “A least squares approach for effective shear properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -layered sphere model,” <i>Archive of Applied Mechanics</i>, pp. 2081–2099, 2018, doi: <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">10.1007/s00419-018-1431-5</a>.","apa":"Mahnken, R., Lenz, P., &#38; Dammann, C. (2018). A least squares approach for effective shear properties in an                                                                   $${{\\varvec{n}}}$$                                                                            n                                                                    -layered sphere model. <i>Archive of Applied Mechanics</i>, 2081–2099. <a href=\"https://doi.org/10.1007/s00419-018-1431-5\">https://doi.org/10.1007/s00419-018-1431-5</a>","short":"R. Mahnken, P. Lenz, C. 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