[{"title":"Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations","doi":"10.1007/s12221-023-00122-x","publisher":"Springer Science and Business Media LLC","date_updated":"2023-03-24T08:42:33Z","date_created":"2023-02-16T12:37:11Z","author":[{"full_name":"Penner, Eduard","last_name":"Penner","first_name":"Eduard"},{"first_name":"Ismail","id":"75","full_name":"Caylak, Ismail","last_name":"Caylak"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"year":"2023","citation":{"chicago":"Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations.” <i>Fibers and Polymers</i>, 2023. <a href=\"https://doi.org/10.1007/s12221-023-00122-x\">https://doi.org/10.1007/s12221-023-00122-x</a>.","ieee":"E. Penner, I. Caylak, and R. Mahnken, “Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations,” <i>Fibers and Polymers</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s12221-023-00122-x\">10.1007/s12221-023-00122-x</a>.","ama":"Penner E, Caylak I, Mahnken R. Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations. <i>Fibers and Polymers</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s12221-023-00122-x\">10.1007/s12221-023-00122-x</a>","mla":"Penner, Eduard, et al. “Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations.” <i>Fibers and Polymers</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s12221-023-00122-x\">10.1007/s12221-023-00122-x</a>.","bibtex":"@article{Penner_Caylak_Mahnken_2023, title={Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations}, DOI={<a href=\"https://doi.org/10.1007/s12221-023-00122-x\">10.1007/s12221-023-00122-x</a>}, journal={Fibers and Polymers}, publisher={Springer Science and Business Media LLC}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2023} }","short":"E. Penner, I. Caylak, R. Mahnken, Fibers and Polymers (2023).","apa":"Penner, E., Caylak, I., &#38; Mahnken, R. (2023). Experimental Investigations of Carbon Fiber Reinforced Polymer Composites and Their Constituents to Determine Their Elastic Material Properties and Complementary Inhomogeneous Experiments with Local Strain Considerations. <i>Fibers and Polymers</i>. <a href=\"https://doi.org/10.1007/s12221-023-00122-x\">https://doi.org/10.1007/s12221-023-00122-x</a>"},"publication_status":"published","publication_identifier":{"issn":["1229-9197","1875-0052"]},"keyword":["Polymers and Plastics","General Chemical Engineering","General Chemistry"],"language":[{"iso":"eng"}],"_id":"42165","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Composite materials, such as fiber reinforced polymers, become increasingly important due to their excellent mechanical and lightweight properties. In this respect, this paper reports the characterization of a unidirectional carbon fiber reinforced polymer composite material. Particularly, the mechanical behavior of the overall composite and of the individual constituents of the composite is investigated. To this end, tensile and shear tests are performed for the composite. As a result, statistics for five transversely isotropic material parameters can be established for the composite. For the description of the mechanical properties of the constituents, tensile tests for the carbon fiber as well as for the polymer matrix are carried out. In addition, the volume fraction of fibers in the matrix is determined experimentally using an ashing technique and Archimedes’ principle. For the Young’s modulus of the fiber, the Young’s modulus and transverse contraction of the matrix, as well as the volume fraction of the constituents, statistics can be concluded. The resulting mechanical properties on both scales are useful for the application and validation of different material models and homogenization methods. Finally, in order to validate the obtained properties in the future, inhomogeneous tests were performed, once a flat plate with a hole and a flat plate with semicircular notches.</jats:p>"}],"status":"public","type":"journal_article","publication":"Fibers and Polymers"},{"department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","_id":"43095","language":[{"iso":"eng"}],"keyword":["Civil and Structural Engineering","Ceramics and Composites"],"article_number":"116911","publication":"Composite Structures","type":"journal_article","status":"public","author":[{"full_name":"Lenz, Peter","last_name":"Lenz","first_name":"Peter"},{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"}],"date_created":"2023-03-24T08:35:59Z","date_updated":"2023-03-24T08:45:42Z","publisher":"Elsevier BV","doi":"10.1016/j.compstruct.2023.116911","title":"Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation","publication_identifier":{"issn":["0263-8223"]},"publication_status":"published","citation":{"ieee":"P. Lenz and R. Mahnken, “Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation,” <i>Composite Structures</i>, Art. no. 116911, 2023, doi: <a href=\"https://doi.org/10.1016/j.compstruct.2023.116911\">10.1016/j.compstruct.2023.116911</a>.","chicago":"Lenz, Peter, and Rolf Mahnken. “Non-Local Integral-Type Damage Combined to Mean-Field Homogenization Methods for Composites and Its Parallel Implementation.” <i>Composite Structures</i>, 2023. <a href=\"https://doi.org/10.1016/j.compstruct.2023.116911\">https://doi.org/10.1016/j.compstruct.2023.116911</a>.","ama":"Lenz P, Mahnken R. Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation. <i>Composite Structures</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1016/j.compstruct.2023.116911\">10.1016/j.compstruct.2023.116911</a>","short":"P. Lenz, R. Mahnken, Composite Structures (2023).","bibtex":"@article{Lenz_Mahnken_2023, title={Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation}, DOI={<a href=\"https://doi.org/10.1016/j.compstruct.2023.116911\">10.1016/j.compstruct.2023.116911</a>}, number={116911}, journal={Composite Structures}, publisher={Elsevier BV}, author={Lenz, Peter and Mahnken, Rolf}, year={2023} }","mla":"Lenz, Peter, and Rolf Mahnken. “Non-Local Integral-Type Damage Combined to Mean-Field Homogenization Methods for Composites and Its Parallel Implementation.” <i>Composite Structures</i>, 116911, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.compstruct.2023.116911\">10.1016/j.compstruct.2023.116911</a>.","apa":"Lenz, P., &#38; Mahnken, R. (2023). Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation. <i>Composite Structures</i>, Article 116911. <a href=\"https://doi.org/10.1016/j.compstruct.2023.116911\">https://doi.org/10.1016/j.compstruct.2023.116911</a>"},"year":"2023"},{"language":[{"iso":"eng"}],"keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics"],"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"44888","status":"public","type":"journal_article","publication":"PAMM","doi":"10.1002/pamm.202200214","title":"Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains","author":[{"full_name":"Lenz, Peter","last_name":"Lenz","first_name":"Peter"},{"id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"}],"date_created":"2023-05-16T12:15:44Z","volume":22,"publisher":"Wiley","date_updated":"2023-05-16T12:17:50Z","citation":{"chicago":"Lenz, Peter, and Rolf Mahnken. “Thermo‐chemo‐mechanical Modelling of a Curing Process Combined with Mean‐field Homogenization Methods at Large Strains.” <i>PAMM</i> 22, no. 1 (2023). <a href=\"https://doi.org/10.1002/pamm.202200214\">https://doi.org/10.1002/pamm.202200214</a>.","ieee":"P. Lenz and R. Mahnken, “Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains,” <i>PAMM</i>, vol. 22, no. 1, 2023, doi: <a href=\"https://doi.org/10.1002/pamm.202200214\">10.1002/pamm.202200214</a>.","ama":"Lenz P, Mahnken R. Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains. <i>PAMM</i>. 2023;22(1). doi:<a href=\"https://doi.org/10.1002/pamm.202200214\">10.1002/pamm.202200214</a>","bibtex":"@article{Lenz_Mahnken_2023, title={Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains}, volume={22}, DOI={<a href=\"https://doi.org/10.1002/pamm.202200214\">10.1002/pamm.202200214</a>}, number={1}, journal={PAMM}, publisher={Wiley}, author={Lenz, Peter and Mahnken, Rolf}, year={2023} }","short":"P. Lenz, R. Mahnken, PAMM 22 (2023).","mla":"Lenz, Peter, and Rolf Mahnken. “Thermo‐chemo‐mechanical Modelling of a Curing Process Combined with Mean‐field Homogenization Methods at Large Strains.” <i>PAMM</i>, vol. 22, no. 1, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/pamm.202200214\">10.1002/pamm.202200214</a>.","apa":"Lenz, P., &#38; Mahnken, R. (2023). Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains. <i>PAMM</i>, <i>22</i>(1). <a href=\"https://doi.org/10.1002/pamm.202200214\">https://doi.org/10.1002/pamm.202200214</a>"},"intvolume":"        22","year":"2023","issue":"1","publication_status":"published","publication_identifier":{"issn":["1617-7061","1617-7061"]},"quality_controlled":"1"},{"title":"A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites","publisher":"Elsevier BV","date_updated":"2023-05-16T12:17:43Z","author":[{"full_name":"Cheng, Chun","last_name":"Cheng","first_name":"Chun"},{"last_name":"Song","full_name":"Song, Chunlei","first_name":"Chunlei"},{"last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf","first_name":"Rolf"},{"first_name":"Zhipeng","last_name":"Yuan","full_name":"Yuan, Zhipeng"},{"last_name":"Yu","full_name":"Yu, Liang","first_name":"Liang"},{"first_name":"Xiaozhe","full_name":"Ju, Xiaozhe","last_name":"Ju"}],"date_created":"2023-05-16T12:10:06Z","year":"2023","citation":{"ama":"Cheng C, Song C, Mahnken R, Yuan Z, Yu L, Ju X. A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites. Published online 2023.","ieee":"C. Cheng, C. Song, R. Mahnken, Z. Yuan, L. Yu, and X. Ju, “A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites.” Elsevier BV, 2023.","chicago":"Cheng, Chun, Chunlei Song, Rolf Mahnken, Zhipeng Yuan, Liang Yu, and Xiaozhe Ju. “A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites.” Elsevier BV, 2023.","apa":"Cheng, C., Song, C., Mahnken, R., Yuan, Z., Yu, L., &#38; Ju, X. (2023). <i>A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites</i>. Elsevier BV.","bibtex":"@article{Cheng_Song_Mahnken_Yuan_Yu_Ju_2023, title={A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites}, publisher={Elsevier BV}, author={Cheng, Chun and Song, Chunlei and Mahnken, Rolf and Yuan, Zhipeng and Yu, Liang and Ju, Xiaozhe}, year={2023} }","short":"C. Cheng, C. Song, R. Mahnken, Z. Yuan, L. Yu, X. Ju, (2023).","mla":"Cheng, Chun, et al. <i>A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites</i>. Elsevier BV, 2023."},"publication_status":"published","language":[{"iso":"eng"}],"_id":"44887","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","status":"public","type":"preprint"},{"title":"A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations","publisher":"Wiley","date_created":"2023-05-16T12:20:19Z","year":"2023","quality_controlled":"1","issue":"1","keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics"],"language":[{"iso":"eng"}],"publication":"PAMM","doi":"10.1002/pamm.202200080","date_updated":"2023-05-16T12:21:15Z","author":[{"orcid":"0000-0002-5034-9708","last_name":"Westermann","full_name":"Westermann, Hendrik","id":"60816","first_name":"Hendrik"},{"first_name":"Rolf","full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken"}],"volume":22,"citation":{"ama":"Westermann H, Mahnken R. A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations. <i>PAMM</i>. 2023;22(1). doi:<a href=\"https://doi.org/10.1002/pamm.202200080\">10.1002/pamm.202200080</a>","chicago":"Westermann, Hendrik, and Rolf Mahnken. “A Thermodynamic Framework for the Phase‐field Approach Considering Carbide Precipitation during Phase Transformations.” <i>PAMM</i> 22, no. 1 (2023). <a href=\"https://doi.org/10.1002/pamm.202200080\">https://doi.org/10.1002/pamm.202200080</a>.","ieee":"H. Westermann and R. Mahnken, “A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations,” <i>PAMM</i>, vol. 22, no. 1, 2023, doi: <a href=\"https://doi.org/10.1002/pamm.202200080\">10.1002/pamm.202200080</a>.","apa":"Westermann, H., &#38; Mahnken, R. (2023). A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations. <i>PAMM</i>, <i>22</i>(1). <a href=\"https://doi.org/10.1002/pamm.202200080\">https://doi.org/10.1002/pamm.202200080</a>","short":"H. Westermann, R. Mahnken, PAMM 22 (2023).","mla":"Westermann, Hendrik, and Rolf Mahnken. “A Thermodynamic Framework for the Phase‐field Approach Considering Carbide Precipitation during Phase Transformations.” <i>PAMM</i>, vol. 22, no. 1, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/pamm.202200080\">10.1002/pamm.202200080</a>.","bibtex":"@article{Westermann_Mahnken_2023, title={A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations}, volume={22}, DOI={<a href=\"https://doi.org/10.1002/pamm.202200080\">10.1002/pamm.202200080</a>}, number={1}, journal={PAMM}, publisher={Wiley}, author={Westermann, Hendrik and Mahnken, Rolf}, year={2023} }"},"intvolume":"        22","publication_status":"published","publication_identifier":{"issn":["1617-7061","1617-7061"]},"_id":"44891","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"status":"public","type":"journal_article"},{"title":"A finite strain gradient theory for viscoplasticity by means of micromorphic regularization","date_created":"2023-05-16T12:21:32Z","publisher":"Wiley","year":"2023","issue":"1","quality_controlled":"1","language":[{"iso":"eng"}],"keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics"],"publication":"PAMM","doi":"10.1002/pamm.202200074","author":[{"first_name":"Ayoub","full_name":"Hamdoun, Ayoub","last_name":"Hamdoun"},{"last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf","first_name":"Rolf"}],"volume":22,"date_updated":"2023-05-16T12:23:15Z","citation":{"apa":"Hamdoun, A., &#38; Mahnken, R. (2023). A finite strain gradient theory for viscoplasticity by means of micromorphic regularization. <i>PAMM</i>, <i>22</i>(1). <a href=\"https://doi.org/10.1002/pamm.202200074\">https://doi.org/10.1002/pamm.202200074</a>","short":"A. Hamdoun, R. Mahnken, PAMM 22 (2023).","mla":"Hamdoun, Ayoub, and Rolf Mahnken. “A Finite Strain Gradient Theory for Viscoplasticity by Means of Micromorphic Regularization.” <i>PAMM</i>, vol. 22, no. 1, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/pamm.202200074\">10.1002/pamm.202200074</a>.","bibtex":"@article{Hamdoun_Mahnken_2023, title={A finite strain gradient theory for viscoplasticity by means of micromorphic regularization}, volume={22}, DOI={<a href=\"https://doi.org/10.1002/pamm.202200074\">10.1002/pamm.202200074</a>}, number={1}, journal={PAMM}, publisher={Wiley}, author={Hamdoun, Ayoub and Mahnken, Rolf}, year={2023} }","ieee":"A. Hamdoun and R. Mahnken, “A finite strain gradient theory for viscoplasticity by means of micromorphic regularization,” <i>PAMM</i>, vol. 22, no. 1, 2023, doi: <a href=\"https://doi.org/10.1002/pamm.202200074\">10.1002/pamm.202200074</a>.","chicago":"Hamdoun, Ayoub, and Rolf Mahnken. “A Finite Strain Gradient Theory for Viscoplasticity by Means of Micromorphic Regularization.” <i>PAMM</i> 22, no. 1 (2023). <a href=\"https://doi.org/10.1002/pamm.202200074\">https://doi.org/10.1002/pamm.202200074</a>.","ama":"Hamdoun A, Mahnken R. A finite strain gradient theory for viscoplasticity by means of micromorphic regularization. <i>PAMM</i>. 2023;22(1). doi:<a href=\"https://doi.org/10.1002/pamm.202200074\">10.1002/pamm.202200074</a>"},"intvolume":"        22","publication_status":"published","publication_identifier":{"issn":["1617-7061","1617-7061"]},"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"44892","status":"public","type":"journal_article"},{"keyword":["Electrical and Electronic Engineering","Atomic and Molecular Physics","and Optics"],"language":[{"iso":"eng"}],"_id":"44890","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"status":"public","type":"journal_article","publication":"PAMM","title":"Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity","doi":"10.1002/pamm.202200053","date_updated":"2023-05-25T10:02:34Z","publisher":"Wiley","author":[{"full_name":"Tchomgue Simeu, Arnold","id":"83075","last_name":"Tchomgue Simeu","first_name":"Arnold"},{"first_name":"Rolf","last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf"}],"date_created":"2023-05-16T12:18:15Z","volume":22,"year":"2023","citation":{"ieee":"A. Tchomgue Simeu and R. Mahnken, “Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity,” <i>PAMM</i>, vol. 22, no. 1, 2023, doi: <a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>.","chicago":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Goal‐oriented Adaptivity Based on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Elasto‐plasticity.” <i>PAMM</i> 22, no. 1 (2023). <a href=\"https://doi.org/10.1002/pamm.202200053\">https://doi.org/10.1002/pamm.202200053</a>.","ama":"Tchomgue Simeu A, Mahnken R. Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity. <i>PAMM</i>. 2023;22(1). doi:<a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>","apa":"Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity. <i>PAMM</i>, <i>22</i>(1). <a href=\"https://doi.org/10.1002/pamm.202200053\">https://doi.org/10.1002/pamm.202200053</a>","short":"A. Tchomgue Simeu, R. Mahnken, PAMM 22 (2023).","bibtex":"@article{Tchomgue Simeu_Mahnken_2023, title={Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity}, volume={22}, DOI={<a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>}, number={1}, journal={PAMM}, publisher={Wiley}, author={Tchomgue Simeu, Arnold and Mahnken, Rolf}, year={2023} }","mla":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Goal‐oriented Adaptivity Based on a Model Hierarchy of Mean‐field and Full‐field Homogenization Methods in Elasto‐plasticity.” <i>PAMM</i>, vol. 22, no. 1, Wiley, 2023, doi:<a href=\"https://doi.org/10.1002/pamm.202200053\">10.1002/pamm.202200053</a>."},"intvolume":"        22","publication_status":"published","publication_identifier":{"issn":["1617-7061","1617-7061"]},"quality_controlled":"1","issue":"1"},{"author":[{"first_name":"Rolf","last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf"}],"date_created":"2023-06-23T06:47:36Z","publisher":"Springer Science and Business Media LLC","date_updated":"2023-06-23T06:48:42Z","doi":"10.1007/s00466-023-02347-2","title":"Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0178-7675","1432-0924"]},"citation":{"apa":"Mahnken, R. (2023). Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation. <i>Computational Mechanics</i>. <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">https://doi.org/10.1007/s00466-023-02347-2</a>","mla":"Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.” <i>Computational Mechanics</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>.","bibtex":"@article{Mahnken_2023, title={Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation}, DOI={<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf}, year={2023} }","short":"R. Mahnken, Computational Mechanics (2023).","ama":"Mahnken R. Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation. <i>Computational Mechanics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>","chicago":"Mahnken, Rolf. “Derivation of Third Order Runge–Kutta Methods (ELDIRK) by Embedding of Lower Order Implicit Time Integration Schemes for Local and Global Error Estimation.” <i>Computational Mechanics</i>, 2023. <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">https://doi.org/10.1007/s00466-023-02347-2</a>.","ieee":"R. Mahnken, “Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation,” <i>Computational Mechanics</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s00466-023-02347-2\">10.1007/s00466-023-02347-2</a>."},"year":"2023","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"45757","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"type":"journal_article","publication":"Computational Mechanics","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Three prominent low order implicit time integration schemes are the first order implicit Euler-method, the second order trapezoidal rule and the second order Ellsiepen method. Its advantages are stability and comparatively low computational cost, however, they require the solution of a nonlinear system of equations. This paper presents a general approach for the construction of third order Runge–Kutta methods by embedding the above mentioned implicit schemes into the class of ELDIRK-methods. These will be defined to have an <jats:italic>Explicit Last</jats:italic> stage in the general Butcher array of <jats:italic>Diagonal Implicit Runge–Kutta</jats:italic> (DIRK) methods, with the consequence, that no additional system of equations must be solved. The main results—valid also for non-linear ordinary differential equations—are as follows: Two extra function calculations are required in order to embed the implicit Euler-method and one extra function calculation is required for the trapezoidal-rule and the Ellsiepen method, in order to obtain the third order properties, respectively. Two numerical examples are concerned with a parachute with viscous damping and a two-dimensional laser beam simulation. Here, we verify the higher order convergence behaviours of the proposed new ELDIRK-methods, and its successful performances for asymptotically exact global error estimation of so-called reversed embedded RK-method are shown.\r\n</jats:p>"}]},{"_id":"46762","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","language":[{"iso":"eng"}],"publication":"XI International Conference on Adaptive Modeling and Simulation","type":"conference","status":"public","date_updated":"2023-09-01T07:54:31Z","publisher":"CIMNE","date_created":"2023-09-01T07:52:20Z","author":[{"full_name":"Tchomgue Simeu, Arnold","id":"83075","last_name":"Tchomgue Simeu","first_name":"Arnold"},{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"}],"title":"Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations","doi":"10.23967/admos.2023.054","quality_controlled":"1","publication_status":"published","year":"2023","citation":{"ieee":"A. Tchomgue Simeu and R. Mahnken, “Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations,” 2023, doi: <a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>.","chicago":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Mesh- and Model Adaptivity for Elasto-Plastic Mean-Field and Full-Field Homogenization Based on Downwind  and Upwind Approximations.” In <i>XI International Conference on Adaptive Modeling and Simulation</i>. CIMNE, 2023. <a href=\"https://doi.org/10.23967/admos.2023.054\">https://doi.org/10.23967/admos.2023.054</a>.","ama":"Tchomgue Simeu A, Mahnken R. Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations. In: <i>XI International Conference on Adaptive Modeling and Simulation</i>. CIMNE; 2023. doi:<a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>","bibtex":"@inproceedings{Tchomgue Simeu_Mahnken_2023, title={Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations}, DOI={<a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>}, booktitle={XI International Conference on Adaptive Modeling and Simulation}, publisher={CIMNE}, author={Tchomgue Simeu, Arnold and Mahnken, Rolf}, year={2023} }","mla":"Tchomgue Simeu, Arnold, and Rolf Mahnken. “Mesh- and Model Adaptivity for Elasto-Plastic Mean-Field and Full-Field Homogenization Based on Downwind  and Upwind Approximations.” <i>XI International Conference on Adaptive Modeling and Simulation</i>, CIMNE, 2023, doi:<a href=\"https://doi.org/10.23967/admos.2023.054\">10.23967/admos.2023.054</a>.","short":"A. Tchomgue Simeu, R. Mahnken, in: XI International Conference on Adaptive Modeling and Simulation, CIMNE, 2023.","apa":"Tchomgue Simeu, A., &#38; Mahnken, R. (2023). Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations. <i>XI International Conference on Adaptive Modeling and Simulation</i>. <a href=\"https://doi.org/10.23967/admos.2023.054\">https://doi.org/10.23967/admos.2023.054</a>"}},{"title":"Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization","doi":"10.1016/j.compstruct.2022.115699","date_updated":"2023-01-24T13:11:40Z","publisher":"Elsevier BV","date_created":"2022-05-10T11:18:45Z","author":[{"first_name":"Xiaozhe","full_name":"Ju, Xiaozhe","last_name":"Ju"},{"full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken","first_name":"Rolf"},{"full_name":"Xu, Yangjian","last_name":"Xu","first_name":"Yangjian"},{"full_name":"Liang, Lihua","last_name":"Liang","first_name":"Lihua"},{"first_name":"Chun","full_name":"Cheng, Chun","last_name":"Cheng"},{"full_name":"Zhou, Wangmin","last_name":"Zhou","first_name":"Wangmin"}],"year":"2022","citation":{"mla":"Ju, Xiaozhe, et al. “Multiscale Analysis of Composite Structures with Goal-Oriented Mesh Adaptivity and Reduced Order Homogenization.” <i>Composite Structures</i>, 115699, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>.","short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, W. Zhou, Composite Structures (2022).","bibtex":"@article{Ju_Mahnken_Xu_Liang_Cheng_Zhou_2022, title={Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization}, DOI={<a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>}, number={115699}, journal={Composite Structures}, publisher={Elsevier BV}, author={Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua and Cheng, Chun and Zhou, Wangmin}, year={2022} }","apa":"Ju, X., Mahnken, R., Xu, Y., Liang, L., Cheng, C., &#38; Zhou, W. (2022). Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization. <i>Composite Structures</i>, Article 115699. <a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">https://doi.org/10.1016/j.compstruct.2022.115699</a>","ama":"Ju X, Mahnken R, Xu Y, Liang L, Cheng C, Zhou W. Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization. <i>Composite Structures</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>","chicago":"Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, Lihua Liang, Chun Cheng, and Wangmin Zhou. “Multiscale Analysis of Composite Structures with Goal-Oriented Mesh Adaptivity and Reduced Order Homogenization.” <i>Composite Structures</i>, 2022. <a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">https://doi.org/10.1016/j.compstruct.2022.115699</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, and W. Zhou, “Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization,” <i>Composite Structures</i>, Art. no. 115699, 2022, doi: <a href=\"https://doi.org/10.1016/j.compstruct.2022.115699\">10.1016/j.compstruct.2022.115699</a>."},"quality_controlled":"1","publication_identifier":{"issn":["0263-8223"]},"publication_status":"published","keyword":["Civil and Structural Engineering","Ceramics and Composites"],"article_number":"115699","language":[{"iso":"eng"}],"_id":"31185","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","status":"public","publication":"Composite Structures","type":"journal_article"},{"_id":"30656","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","type":"journal_article","status":"public","date_updated":"2023-01-24T13:10:27Z","volume":92,"author":[{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"}],"doi":"10.1007/s00419-021-02069-y","publication_identifier":{"issn":["0939-1533","1432-0681"]},"publication_status":"published","intvolume":"        92","page":"713-754","citation":{"ieee":"R. Mahnken, “Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters,” <i>Archive of Applied Mechanics</i>, vol. 92, no. 3, pp. 713–754, 2022, doi: <a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>.","chicago":"Mahnken, Rolf. “Strain Mode-Dependent Weighting Functions in Hyperelasticity Accounting for Verification, Validation, and Stability of Material Parameters.” <i>Archive of Applied Mechanics</i> 92, no. 3 (2022): 713–54. <a href=\"https://doi.org/10.1007/s00419-021-02069-y\">https://doi.org/10.1007/s00419-021-02069-y</a>.","ama":"Mahnken R. Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters. <i>Archive of Applied Mechanics</i>. 2022;92(3):713-754. doi:<a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>","bibtex":"@article{Mahnken_2022, title={Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters}, volume={92}, DOI={<a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>}, number={3}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf}, year={2022}, pages={713–754} }","short":"R. Mahnken, Archive of Applied Mechanics 92 (2022) 713–754.","mla":"Mahnken, Rolf. “Strain Mode-Dependent Weighting Functions in Hyperelasticity Accounting for Verification, Validation, and Stability of Material Parameters.” <i>Archive of Applied Mechanics</i>, vol. 92, no. 3, Springer Science and Business Media LLC, 2022, pp. 713–54, doi:<a href=\"https://doi.org/10.1007/s00419-021-02069-y\">10.1007/s00419-021-02069-y</a>.","apa":"Mahnken, R. (2022). Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters. <i>Archive of Applied Mechanics</i>, <i>92</i>(3), 713–754. <a href=\"https://doi.org/10.1007/s00419-021-02069-y\">https://doi.org/10.1007/s00419-021-02069-y</a>"},"keyword":["Mechanical Engineering"],"language":[{"iso":"eng"}],"publication":"Archive of Applied Mechanics","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>Optimized material parameters obtained from parameter identification for verification wrt a certain loading scenario are amenable to two deficiencies: Firstly, they may lack a general validity for different loading scenarios. Secondly, they may be prone to instability, such that a small perturbation of experimental data may ensue a large perturbation for the material parameters. This paper presents a framework for extension of hyperelastic models for rubber-like materials accounting for both deficiencies. To this end, an additive decomposition of the strain energy function is assumed into a sum of weighted strain mode related quantities. We propose a practical guide for model development accounting for the criteria of verification, validation and stability by means of the strain mode-dependent weighting functions and techniques of model reduction. The approach is successfully applied for 13 hyperelastic models with regard to the classical experimental data on vulcanized rubber published by Treloar (Trans Faraday Soc 40:59–70, 1944), showing both excellent fitting capabilties and stable material parameters.</jats:p>"}],"publisher":"Springer Science and Business Media LLC","date_created":"2022-03-28T13:24:07Z","title":"Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters","quality_controlled":"1","issue":"3","year":"2022"},{"publication_status":"published","publication_identifier":{"issn":["0178-7675","1432-0924"]},"quality_controlled":"1","issue":"3","year":"2022","citation":{"bibtex":"@article{Ju_Mahnken_Xu_Liang_2022, title={Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}, volume={69}, DOI={<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>}, number={3}, journal={Computational Mechanics}, publisher={Springer Science and Business Media LLC}, author={Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}, year={2022}, pages={847–863} }","short":"X. Ju, R. Mahnken, Y. Xu, L. Liang, Computational Mechanics 69 (2022) 847–863.","mla":"Ju, Xiaozhe, et al. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i>, vol. 69, no. 3, Springer Science and Business Media LLC, 2022, pp. 847–63, doi:<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>.","apa":"Ju, X., Mahnken, R., Xu, Y., &#38; Liang, L. (2022). Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>, <i>69</i>(3), 847–863. <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">https://doi.org/10.1007/s00466-021-02117-y</a>","chicago":"Ju, Xiaozhe, Rolf Mahnken, Yangjian Xu, and Lihua Liang. “Goal-Oriented Error Estimation and h-Adaptive Finite Elements for Hyperelastic Micromorphic Continua.” <i>Computational Mechanics</i> 69, no. 3 (2022): 847–63. <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">https://doi.org/10.1007/s00466-021-02117-y</a>.","ieee":"X. Ju, R. Mahnken, Y. Xu, and L. Liang, “Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua,” <i>Computational Mechanics</i>, vol. 69, no. 3, pp. 847–863, 2022, doi: <a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>.","ama":"Ju X, Mahnken R, Xu Y, Liang L. Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. <i>Computational Mechanics</i>. 2022;69(3):847-863. doi:<a href=\"https://doi.org/10.1007/s00466-021-02117-y\">10.1007/s00466-021-02117-y</a>"},"intvolume":"        69","page":"847-863","publisher":"Springer Science and Business Media LLC","date_updated":"2023-01-24T13:10:56Z","date_created":"2022-03-28T13:23:17Z","author":[{"last_name":"Ju","full_name":"Ju, Xiaozhe","first_name":"Xiaozhe"},{"full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken","first_name":"Rolf"},{"full_name":"Xu, Yangjian","last_name":"Xu","first_name":"Yangjian"},{"first_name":"Lihua","full_name":"Liang, Lihua","last_name":"Liang"}],"volume":69,"title":"Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua","doi":"10.1007/s00466-021-02117-y","type":"journal_article","publication":"Computational Mechanics","status":"public","_id":"30655","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"keyword":["Applied Mathematics","Computational Mathematics","Computational Theory and Mathematics","Mechanical Engineering","Ocean Engineering","Computational Mechanics"],"language":[{"iso":"eng"}]},{"publication":"Computer Methods in Applied Mechanics and Engineering","type":"journal_article","status":"public","_id":"30657","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","keyword":["Computer Science Applications","General Physics and Astronomy","Mechanical Engineering","Mechanics of Materials","Computational Mechanics"],"article_number":"114790","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0045-7825"]},"quality_controlled":"1","publication_status":"published","year":"2022","intvolume":"       393","citation":{"apa":"Henkes, A., Wessels, H., &#38; Mahnken, R. (2022). Physics informed neural networks for continuum micromechanics. <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>393</i>, Article 114790. <a href=\"https://doi.org/10.1016/j.cma.2022.114790\">https://doi.org/10.1016/j.cma.2022.114790</a>","short":"A. Henkes, H. Wessels, R. Mahnken, Computer Methods in Applied Mechanics and Engineering 393 (2022).","bibtex":"@article{Henkes_Wessels_Mahnken_2022, title={Physics informed neural networks for continuum micromechanics}, volume={393}, DOI={<a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>}, number={114790}, journal={Computer Methods in Applied Mechanics and Engineering}, publisher={Elsevier BV}, author={Henkes, Alexander and Wessels, Henning and Mahnken, Rolf}, year={2022} }","mla":"Henkes, Alexander, et al. “Physics Informed Neural Networks for Continuum Micromechanics.” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 393, 114790, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>.","ieee":"A. Henkes, H. Wessels, and R. Mahnken, “Physics informed neural networks for continuum micromechanics,” <i>Computer Methods in Applied Mechanics and Engineering</i>, vol. 393, Art. no. 114790, 2022, doi: <a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>.","chicago":"Henkes, Alexander, Henning Wessels, and Rolf Mahnken. “Physics Informed Neural Networks for Continuum Micromechanics.” <i>Computer Methods in Applied Mechanics and Engineering</i> 393 (2022). <a href=\"https://doi.org/10.1016/j.cma.2022.114790\">https://doi.org/10.1016/j.cma.2022.114790</a>.","ama":"Henkes A, Wessels H, Mahnken R. Physics informed neural networks for continuum micromechanics. <i>Computer Methods in Applied Mechanics and Engineering</i>. 2022;393. doi:<a href=\"https://doi.org/10.1016/j.cma.2022.114790\">10.1016/j.cma.2022.114790</a>"},"publisher":"Elsevier BV","date_updated":"2023-01-24T13:09:40Z","volume":393,"author":[{"full_name":"Henkes, Alexander","last_name":"Henkes","first_name":"Alexander"},{"full_name":"Wessels, Henning","last_name":"Wessels","first_name":"Henning"},{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"}],"date_created":"2022-03-28T13:24:32Z","title":"Physics informed neural networks for continuum micromechanics","doi":"10.1016/j.cma.2022.114790"},{"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"34074","language":[{"iso":"eng"}],"keyword":["Mechanical Engineering"],"type":"journal_article","publication":"Archive of Applied Mechanics","status":"public","author":[{"id":"335","full_name":"Mahnken, Rolf","last_name":"Mahnken","first_name":"Rolf"},{"full_name":"Mirzapour, Jamil","last_name":"Mirzapour","first_name":"Jamil"}],"date_created":"2022-11-14T12:51:05Z","volume":92,"date_updated":"2023-04-27T10:07:20Z","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s00419-022-02237-8","title":"A statistically based strain energy function for polymer chains in rubber elasticity","issue":"11","publication_status":"published","publication_identifier":{"issn":["0939-1533","1432-0681"]},"quality_controlled":"1","citation":{"bibtex":"@article{Mahnken_Mirzapour_2022, title={A statistically based strain energy function for polymer chains in rubber elasticity}, volume={92}, DOI={<a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>}, number={11}, journal={Archive of Applied Mechanics}, publisher={Springer Science and Business Media LLC}, author={Mahnken, Rolf and Mirzapour, Jamil}, year={2022}, pages={3295–3323} }","short":"R. Mahnken, J. Mirzapour, Archive of Applied Mechanics 92 (2022) 3295–3323.","mla":"Mahnken, Rolf, and Jamil Mirzapour. “A Statistically Based Strain Energy Function for Polymer Chains in Rubber Elasticity.” <i>Archive of Applied Mechanics</i>, vol. 92, no. 11, Springer Science and Business Media LLC, 2022, pp. 3295–323, doi:<a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>.","apa":"Mahnken, R., &#38; Mirzapour, J. (2022). A statistically based strain energy function for polymer chains in rubber elasticity. <i>Archive of Applied Mechanics</i>, <i>92</i>(11), 3295–3323. <a href=\"https://doi.org/10.1007/s00419-022-02237-8\">https://doi.org/10.1007/s00419-022-02237-8</a>","ama":"Mahnken R, Mirzapour J. A statistically based strain energy function for polymer chains in rubber elasticity. <i>Archive of Applied Mechanics</i>. 2022;92(11):3295-3323. doi:<a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>","ieee":"R. Mahnken and J. Mirzapour, “A statistically based strain energy function for polymer chains in rubber elasticity,” <i>Archive of Applied Mechanics</i>, vol. 92, no. 11, pp. 3295–3323, 2022, doi: <a href=\"https://doi.org/10.1007/s00419-022-02237-8\">10.1007/s00419-022-02237-8</a>.","chicago":"Mahnken, Rolf, and Jamil Mirzapour. “A Statistically Based Strain Energy Function for Polymer Chains in Rubber Elasticity.” <i>Archive of Applied Mechanics</i> 92, no. 11 (2022): 3295–3323. <a href=\"https://doi.org/10.1007/s00419-022-02237-8\">https://doi.org/10.1007/s00419-022-02237-8</a>."},"page":"3295-3323","intvolume":"        92","year":"2022"},{"year":"2022","citation":{"short":"R. Clemens, E. Barth, E. Uhlmann, Y. Zhan, I. Caylak, R. Mahnken, SSRN Electronic Journal (2022).","bibtex":"@article{Clemens_Barth_Uhlmann_Zhan_Caylak_Mahnken_2022, title={Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp}, DOI={<a href=\"https://doi.org/10.2139/ssrn.4259246\">10.2139/ssrn.4259246</a>}, journal={SSRN Electronic Journal}, publisher={Elsevier BV}, author={Clemens, Robin and Barth, Enrico and Uhlmann, Eckart and Zhan, Yingjie and Caylak, Ismail and Mahnken, Rolf}, year={2022} }","mla":"Clemens, Robin, et al. “Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp.” <i>SSRN Electronic Journal</i>, Elsevier BV, 2022, doi:<a href=\"https://doi.org/10.2139/ssrn.4259246\">10.2139/ssrn.4259246</a>.","apa":"Clemens, R., Barth, E., Uhlmann, E., Zhan, Y., Caylak, I., &#38; Mahnken, R. (2022). Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp. <i>SSRN Electronic Journal</i>. <a href=\"https://doi.org/10.2139/ssrn.4259246\">https://doi.org/10.2139/ssrn.4259246</a>","chicago":"Clemens, Robin, Enrico Barth, Eckart Uhlmann, Yingjie Zhan, Ismail Caylak, and Rolf Mahnken. “Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp.” <i>SSRN Electronic Journal</i>, 2022. <a href=\"https://doi.org/10.2139/ssrn.4259246\">https://doi.org/10.2139/ssrn.4259246</a>.","ieee":"R. Clemens, E. Barth, E. Uhlmann, Y. Zhan, I. Caylak, and R. Mahnken, “Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp,” <i>SSRN Electronic Journal</i>, 2022, doi: <a href=\"https://doi.org/10.2139/ssrn.4259246\">10.2139/ssrn.4259246</a>.","ama":"Clemens R, Barth E, Uhlmann E, Zhan Y, Caylak I, Mahnken R. Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp. <i>SSRN Electronic Journal</i>. Published online 2022. doi:<a href=\"https://doi.org/10.2139/ssrn.4259246\">10.2139/ssrn.4259246</a>"},"publication_identifier":{"issn":["1556-5068"]},"quality_controlled":"1","publication_status":"published","title":"Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp","doi":"10.2139/ssrn.4259246","date_updated":"2023-04-27T10:08:09Z","publisher":"Elsevier BV","author":[{"first_name":"Robin","last_name":"Clemens","full_name":"Clemens, Robin"},{"full_name":"Barth, Enrico","last_name":"Barth","first_name":"Enrico"},{"last_name":"Uhlmann","full_name":"Uhlmann, Eckart","first_name":"Eckart"},{"full_name":"Zhan, Yingjie","last_name":"Zhan","first_name":"Yingjie"},{"first_name":"Ismail","full_name":"Caylak, Ismail","id":"75","last_name":"Caylak"},{"last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335","first_name":"Rolf"}],"date_created":"2023-02-02T12:49:43Z","status":"public","publication":"SSRN Electronic Journal","type":"journal_article","keyword":["General Earth and Planetary Sciences","General Environmental Science"],"language":[{"iso":"eng"}],"_id":"41485","department":[{"_id":"9"},{"_id":"154"}],"user_id":"335"},{"publication_identifier":{"issn":["0045-7825"]},"publication_status":"published","intvolume":"       398","citation":{"short":"X. 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