[{"_id":"64187","user_id":"85414","department":[{"_id":"9"},{"_id":"952"},{"_id":"321"}],"article_number":"10812865261420809","language":[{"iso":"eng"}],"type":"journal_article","publication":"Mathematics and Mechanics of Solids","abstract":[{"lang":"eng","text":"<jats:p>Carbon fiber-reinforced plastics (CFRPs) have become increasingly significant in recent decades due to their remarkable mechanical properties and lightweight nature. This study aims to advance the understanding and simulation of CFRP behavior through the development of a hyperelastic-plastic-damage homogenization method combined with mean-field theory. The material responses of both the fiber and matrix are modeled using strain energy functions that account for damage evolution, while a complete linearization of the homogenization process is derived to ensure the consistent implementation of the Newton–Raphson iteration scheme in large deformation simulations. The innovative aspect of this work lies in the constitutive linearization for the hyperelastic-plastic-damage formulation within a mean-field homogenization framework, providing an efficient Newton algorithm for modeling the nonlinear behavior of CFRP. A failure criterion for the hyperelastic model of fibers is introduced, along with a damage saturation variable in rate form for the matrix, effectively capturing damage evolution. Through discrete formulations for the homogenization, the proposed model’s capability is demonstrated via three numerical examples and validated against experimental investigations, proving its effectiveness and reliability in simulating CFRP damage.</jats:p>"}],"status":"public","publisher":"SAGE Publications","date_updated":"2026-02-17T11:22:49Z","author":[{"first_name":"Yingjie","last_name":"Zhan","full_name":"Zhan, Yingjie","id":"93591"},{"full_name":"Caylak, Ismail","last_name":"Caylak","first_name":"Ismail"},{"first_name":"Richard","id":"106876","full_name":"Ostwald, Richard","orcid":"0000-0003-2147-8444","last_name":"Ostwald"},{"first_name":"Rolf","id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken"},{"full_name":"Barth, Enrico","last_name":"Barth","first_name":"Enrico"},{"last_name":"Uhlmann","full_name":"Uhlmann, Eckart","first_name":"Eckart"}],"date_created":"2026-02-17T11:21:00Z","title":"A fully implicit mean-field damage formulation with consistent linearization at large deformations","doi":"10.1177/10812865261420809","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["1081-2865","1741-3028"]},"year":"2026","citation":{"ama":"Zhan Y, Caylak I, Ostwald R, Mahnken R, Barth E, Uhlmann E. A fully implicit mean-field damage formulation with consistent linearization at large deformations. <i>Mathematics and Mechanics of Solids</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1177/10812865261420809\">10.1177/10812865261420809</a>","ieee":"Y. Zhan, I. Caylak, R. Ostwald, R. Mahnken, E. Barth, and E. Uhlmann, “A fully implicit mean-field damage formulation with consistent linearization at large deformations,” <i>Mathematics and Mechanics of Solids</i>, Art. no. 10812865261420808, 2026, doi: <a href=\"https://doi.org/10.1177/10812865261420809\">10.1177/10812865261420809</a>.","chicago":"Zhan, Yingjie, Ismail Caylak, Richard Ostwald, Rolf Mahnken, Enrico Barth, and Eckart Uhlmann. “A Fully Implicit Mean-Field Damage Formulation with Consistent Linearization at Large Deformations.” <i>Mathematics and Mechanics of Solids</i>, 2026. <a href=\"https://doi.org/10.1177/10812865261420809\">https://doi.org/10.1177/10812865261420809</a>.","apa":"Zhan, Y., Caylak, I., Ostwald, R., Mahnken, R., Barth, E., &#38; Uhlmann, E. (2026). A fully implicit mean-field damage formulation with consistent linearization at large deformations. <i>Mathematics and Mechanics of Solids</i>, Article 10812865261420808. <a href=\"https://doi.org/10.1177/10812865261420809\">https://doi.org/10.1177/10812865261420809</a>","short":"Y. Zhan, I. Caylak, R. Ostwald, R. Mahnken, E. Barth, E. Uhlmann, Mathematics and Mechanics of Solids (2026).","mla":"Zhan, Yingjie, et al. “A Fully Implicit Mean-Field Damage Formulation with Consistent Linearization at Large Deformations.” <i>Mathematics and Mechanics of Solids</i>, 10812865261420808, SAGE Publications, 2026, doi:<a href=\"https://doi.org/10.1177/10812865261420809\">10.1177/10812865261420809</a>.","bibtex":"@article{Zhan_Caylak_Ostwald_Mahnken_Barth_Uhlmann_2026, title={A fully implicit mean-field damage formulation with consistent linearization at large deformations}, DOI={<a href=\"https://doi.org/10.1177/10812865261420809\">10.1177/10812865261420809</a>}, number={10812865261420808}, journal={Mathematics and Mechanics of Solids}, publisher={SAGE Publications}, author={Zhan, Yingjie and Caylak, Ismail and Ostwald, Richard and Mahnken, Rolf and Barth, Enrico and Uhlmann, Eckart}, year={2026} }"}},{"doi":"10.1007/s41939-025-01026-4","title":"Damage-incorporated four-step mean-field method for simulating CFRP machining: a novel algorithmic approach","date_created":"2025-09-05T07:40:31Z","author":[{"first_name":"Yingjie","last_name":"Zhan","full_name":"Zhan, Yingjie","id":"93591"},{"id":"75","full_name":"Caylak, Ismail","last_name":"Caylak","first_name":"Ismail"},{"first_name":"Richard","orcid":"0000-0003-2147-8444","last_name":"Ostwald","id":"106876","full_name":"Ostwald, Richard"},{"full_name":"Barth, Enrico","last_name":"Barth","first_name":"Enrico"},{"first_name":"Eckart","last_name":"Uhlmann","full_name":"Uhlmann, Eckart"}],"volume":8,"date_updated":"2025-10-20T12:05:57Z","publisher":"Springer Science and Business Media LLC","citation":{"apa":"Zhan, Y., Caylak, I., Ostwald, R., Barth, E., &#38; Uhlmann, E. (2025). Damage-incorporated four-step mean-field method for simulating CFRP machining: a novel algorithmic approach. <i>Multiscale and Multidisciplinary Modeling, Experiments and Design</i>, <i>8</i>(10), Article 434. <a href=\"https://doi.org/10.1007/s41939-025-01026-4\">https://doi.org/10.1007/s41939-025-01026-4</a>","short":"Y. Zhan, I. Caylak, R. Ostwald, E. Barth, E. Uhlmann, Multiscale and Multidisciplinary Modeling, Experiments and Design 8 (2025).","mla":"Zhan, Yingjie, et al. “Damage-Incorporated Four-Step Mean-Field Method for Simulating CFRP Machining: A Novel Algorithmic Approach.” <i>Multiscale and Multidisciplinary Modeling, Experiments and Design</i>, vol. 8, no. 10, 434, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s41939-025-01026-4\">10.1007/s41939-025-01026-4</a>.","bibtex":"@article{Zhan_Caylak_Ostwald_Barth_Uhlmann_2025, title={Damage-incorporated four-step mean-field method for simulating CFRP machining: a novel algorithmic approach}, volume={8}, DOI={<a href=\"https://doi.org/10.1007/s41939-025-01026-4\">10.1007/s41939-025-01026-4</a>}, number={10434}, journal={Multiscale and Multidisciplinary Modeling, Experiments and Design}, publisher={Springer Science and Business Media LLC}, author={Zhan, Yingjie and Caylak, Ismail and Ostwald, Richard and Barth, Enrico and Uhlmann, Eckart}, year={2025} }","chicago":"Zhan, Yingjie, Ismail Caylak, Richard Ostwald, Enrico Barth, and Eckart Uhlmann. “Damage-Incorporated Four-Step Mean-Field Method for Simulating CFRP Machining: A Novel Algorithmic Approach.” <i>Multiscale and Multidisciplinary Modeling, Experiments and Design</i> 8, no. 10 (2025). <a href=\"https://doi.org/10.1007/s41939-025-01026-4\">https://doi.org/10.1007/s41939-025-01026-4</a>.","ieee":"Y. Zhan, I. Caylak, R. Ostwald, E. Barth, and E. Uhlmann, “Damage-incorporated four-step mean-field method for simulating CFRP machining: a novel algorithmic approach,” <i>Multiscale and Multidisciplinary Modeling, Experiments and Design</i>, vol. 8, no. 10, Art. no. 434, 2025, doi: <a href=\"https://doi.org/10.1007/s41939-025-01026-4\">10.1007/s41939-025-01026-4</a>.","ama":"Zhan Y, Caylak I, Ostwald R, Barth E, Uhlmann E. Damage-incorporated four-step mean-field method for simulating CFRP machining: a novel algorithmic approach. <i>Multiscale and Multidisciplinary Modeling, Experiments and Design</i>. 2025;8(10). doi:<a href=\"https://doi.org/10.1007/s41939-025-01026-4\">10.1007/s41939-025-01026-4</a>"},"intvolume":"         8","year":"2025","issue":"10","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["2520-8160","2520-8179"]},"language":[{"iso":"eng"}],"article_number":"434","user_id":"85414","department":[{"_id":"9"},{"_id":"952"},{"_id":"321"}],"_id":"61138","status":"public","type":"journal_article","publication":"Multiscale and Multidisciplinary Modeling, Experiments and Design"}]