--- _id: '42165' abstract: - lang: eng text: AbstractComposite 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. author: - first_name: Eduard full_name: Penner, Eduard last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: 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. Fibers and Polymers. Published online 2023. doi:10.1007/s12221-023-00122-x apa: Penner, E., Caylak, I., & 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. Fibers and Polymers. https://doi.org/10.1007/s12221-023-00122-x 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={10.1007/s12221-023-00122-x}, journal={Fibers and Polymers}, publisher={Springer Science and Business Media LLC}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2023} }' 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.” Fibers and Polymers, 2023. https://doi.org/10.1007/s12221-023-00122-x. 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,” Fibers and Polymers, 2023, doi: 10.1007/s12221-023-00122-x.' 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.” Fibers and Polymers, Springer Science and Business Media LLC, 2023, doi:10.1007/s12221-023-00122-x. short: E. Penner, I. Caylak, R. Mahnken, Fibers and Polymers (2023). date_created: 2023-02-16T12:37:11Z date_updated: 2023-03-24T08:42:33Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1007/s12221-023-00122-x keyword: - Polymers and Plastics - General Chemical Engineering - General Chemistry language: - iso: eng publication: Fibers and Polymers publication_identifier: issn: - 1229-9197 - 1875-0052 publication_status: published publisher: Springer Science and Business Media LLC status: public 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 type: journal_article user_id: '335' year: '2023' ... --- _id: '41485' author: - first_name: Robin full_name: Clemens, Robin last_name: Clemens - first_name: Enrico full_name: Barth, Enrico last_name: Barth - first_name: Eckart full_name: Uhlmann, Eckart last_name: Uhlmann - first_name: Yingjie full_name: Zhan, Yingjie last_name: Zhan - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: 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. SSRN Electronic Journal. Published online 2022. doi:10.2139/ssrn.4259246 apa: Clemens, R., Barth, E., Uhlmann, E., Zhan, Y., Caylak, I., & Mahnken, R. (2022). Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4259246 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={10.2139/ssrn.4259246}, 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} }' 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.” SSRN Electronic Journal, 2022. https://doi.org/10.2139/ssrn.4259246. 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,” SSRN Electronic Journal, 2022, doi: 10.2139/ssrn.4259246.' 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.” SSRN Electronic Journal, Elsevier BV, 2022, doi:10.2139/ssrn.4259246. short: R. Clemens, E. Barth, E. Uhlmann, Y. Zhan, I. Caylak, R. Mahnken, SSRN Electronic Journal (2022). date_created: 2023-02-02T12:49:43Z date_updated: 2023-04-27T10:08:09Z department: - _id: '9' - _id: '154' doi: 10.2139/ssrn.4259246 keyword: - General Earth and Planetary Sciences - General Environmental Science language: - iso: eng publication: SSRN Electronic Journal publication_identifier: issn: - 1556-5068 publication_status: published publisher: Elsevier BV quality_controlled: '1' status: public title: Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp type: journal_article user_id: '335' year: '2022' ... --- _id: '34075' author: - first_name: Eduard full_name: Penner, Eduard last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Penner E, Caylak I, Mahnken R. A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics. Mathematics and Mechanics of Complex Systems. 2022;10(1):21-50. doi:10.2140/memocs.2022.10.21 apa: Penner, E., Caylak, I., & Mahnken, R. (2022). A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics. Mathematics and Mechanics of Complex Systems, 10(1), 21–50. https://doi.org/10.2140/memocs.2022.10.21 bibtex: '@article{Penner_Caylak_Mahnken_2022, title={A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics}, volume={10}, DOI={10.2140/memocs.2022.10.21}, number={1}, journal={Mathematics and Mechanics of Complex Systems}, publisher={Mathematical Sciences Publishers}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2022}, pages={21–50} }' chicago: 'Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “A Polymorphic Uncertainty Model for the Curing Process of Transversely Fiber-Reinforced Plastics.” Mathematics and Mechanics of Complex Systems 10, no. 1 (2022): 21–50. https://doi.org/10.2140/memocs.2022.10.21.' ieee: 'E. Penner, I. Caylak, and R. Mahnken, “A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics,” Mathematics and Mechanics of Complex Systems, vol. 10, no. 1, pp. 21–50, 2022, doi: 10.2140/memocs.2022.10.21.' mla: Penner, Eduard, et al. “A Polymorphic Uncertainty Model for the Curing Process of Transversely Fiber-Reinforced Plastics.” Mathematics and Mechanics of Complex Systems, vol. 10, no. 1, Mathematical Sciences Publishers, 2022, pp. 21–50, doi:10.2140/memocs.2022.10.21. short: E. Penner, I. Caylak, R. Mahnken, Mathematics and Mechanics of Complex Systems 10 (2022) 21–50. date_created: 2022-11-14T12:55:22Z date_updated: 2023-04-27T10:04:44Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.2140/memocs.2022.10.21 intvolume: ' 10' issue: '1' keyword: - Computational Mathematics - Numerical Analysis - Civil and Structural Engineering language: - iso: eng page: 21-50 publication: Mathematics and Mechanics of Complex Systems publication_identifier: issn: - 2325-3444 - 2326-7186 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' status: public title: A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics type: journal_article user_id: '335' volume: 10 year: '2022' ... --- _id: '24392' author: - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Penner E, Caylak I, Mahnken R. An uncertainty model for the curing process of transversely fiber reinforced plastics. PAMM. Published online 2021. doi:10.1002/pamm.202000178 apa: Penner, E., Caylak, I., & Mahnken, R. (2021). An uncertainty model for the curing process of transversely fiber reinforced plastics. PAMM. https://doi.org/10.1002/pamm.202000178 bibtex: '@article{Penner_Caylak_Mahnken_2021, title={An uncertainty model for the curing process of transversely fiber reinforced plastics}, DOI={10.1002/pamm.202000178}, journal={PAMM}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2021} }' chicago: Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “An Uncertainty Model for the Curing Process of Transversely Fiber Reinforced Plastics.” PAMM, 2021. https://doi.org/10.1002/pamm.202000178. ieee: 'E. Penner, I. Caylak, and R. Mahnken, “An uncertainty model for the curing process of transversely fiber reinforced plastics,” PAMM, 2021, doi: 10.1002/pamm.202000178.' mla: Penner, Eduard, et al. “An Uncertainty Model for the Curing Process of Transversely Fiber Reinforced Plastics.” PAMM, 2021, doi:10.1002/pamm.202000178. short: E. Penner, I. Caylak, R. Mahnken, PAMM (2021). date_created: 2021-09-14T12:08:38Z date_updated: 2023-01-24T12:43:54Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1002/pamm.202000178 language: - iso: eng publication: PAMM publication_identifier: issn: - 1617-7061 - 1617-7061 publication_status: published status: public title: An uncertainty model for the curing process of transversely fiber reinforced plastics type: journal_article user_id: '335' year: '2021' ... --- _id: '24397' author: - first_name: Alexander full_name: Henkes, Alexander last_name: Henkes - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Henkes A, Caylak I, Mahnken R. A deep learning driven uncertain full‐field homogenization method. PAMM. Published online 2021. doi:10.1002/pamm.202000180 apa: Henkes, A., Caylak, I., & Mahnken, R. (2021). A deep learning driven uncertain full‐field homogenization method. PAMM. https://doi.org/10.1002/pamm.202000180 bibtex: '@article{Henkes_Caylak_Mahnken_2021, title={A deep learning driven uncertain full‐field homogenization method}, DOI={10.1002/pamm.202000180}, journal={PAMM}, author={Henkes, Alexander and Caylak, Ismail and Mahnken, Rolf}, year={2021} }' chicago: Henkes, Alexander, Ismail Caylak, and Rolf Mahnken. “A Deep Learning Driven Uncertain Full‐field Homogenization Method.” PAMM, 2021. https://doi.org/10.1002/pamm.202000180. ieee: 'A. Henkes, I. Caylak, and R. Mahnken, “A deep learning driven uncertain full‐field homogenization method,” PAMM, 2021, doi: 10.1002/pamm.202000180.' mla: Henkes, Alexander, et al. “A Deep Learning Driven Uncertain Full‐field Homogenization Method.” PAMM, 2021, doi:10.1002/pamm.202000180. short: A. Henkes, I. Caylak, R. Mahnken, PAMM (2021). date_created: 2021-09-14T12:26:45Z date_updated: 2023-01-24T12:45:09Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1002/pamm.202000180 language: - iso: eng publication: PAMM publication_identifier: issn: - 1617-7061 - 1617-7061 publication_status: published status: public title: A deep learning driven uncertain full‐field homogenization method type: journal_article user_id: '335' year: '2021' ... --- _id: '21681' author: - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken - first_name: Alex full_name: Dridger, Alex last_name: Dridger citation: ama: Penner E, Caylak I, Mahnken R, Dridger A. Fuzzy and stochastic approach applied to rubber like materials. Safety and Reliability. Published online 2021:1-19. doi:10.1080/09617353.2020.1858678 apa: Penner, E., Caylak, I., Mahnken, R., & Dridger, A. (2021). Fuzzy and stochastic approach applied to rubber like materials. Safety and Reliability, 1–19. https://doi.org/10.1080/09617353.2020.1858678 bibtex: '@article{Penner_Caylak_Mahnken_Dridger_2021, title={Fuzzy and stochastic approach applied to rubber like materials}, DOI={10.1080/09617353.2020.1858678}, journal={Safety and Reliability}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf and Dridger, Alex}, year={2021}, pages={1–19} }' chicago: Penner, Eduard, Ismail Caylak, Rolf Mahnken, and Alex Dridger. “Fuzzy and Stochastic Approach Applied to Rubber like Materials.” Safety and Reliability, 2021, 1–19. https://doi.org/10.1080/09617353.2020.1858678. ieee: 'E. Penner, I. Caylak, R. Mahnken, and A. Dridger, “Fuzzy and stochastic approach applied to rubber like materials,” Safety and Reliability, pp. 1–19, 2021, doi: 10.1080/09617353.2020.1858678.' mla: Penner, Eduard, et al. “Fuzzy and Stochastic Approach Applied to Rubber like Materials.” Safety and Reliability, 2021, pp. 1–19, doi:10.1080/09617353.2020.1858678. short: E. Penner, I. Caylak, R. Mahnken, A. Dridger, Safety and Reliability (2021) 1–19. date_created: 2021-04-21T06:35:08Z date_updated: 2023-01-24T13:06:18Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1080/09617353.2020.1858678 language: - iso: eng page: 1-19 publication: Safety and Reliability publication_identifier: issn: - 0961-7353 - 2469-4126 publication_status: published quality_controlled: '1' status: public title: Fuzzy and stochastic approach applied to rubber like materials type: journal_article user_id: '335' year: '2021' ... --- _id: '24376' article_number: '114070' author: - first_name: Alexander full_name: Henkes, Alexander last_name: Henkes - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Henkes A, Caylak I, Mahnken R. A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures. Computer Methods in Applied Mechanics and Engineering. Published online 2021. doi:10.1016/j.cma.2021.114070 apa: Henkes, A., Caylak, I., & Mahnken, R. (2021). A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures. Computer Methods in Applied Mechanics and Engineering, Article 114070. https://doi.org/10.1016/j.cma.2021.114070 bibtex: '@article{Henkes_Caylak_Mahnken_2021, title={A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures}, DOI={10.1016/j.cma.2021.114070}, number={114070}, journal={Computer Methods in Applied Mechanics and Engineering}, author={Henkes, Alexander and Caylak, Ismail and Mahnken, Rolf}, year={2021} }' chicago: Henkes, Alexander, Ismail Caylak, and Rolf Mahnken. “A Deep Learning Driven Pseudospectral PCE Based FFT Homogenization Algorithm for Complex Microstructures.” Computer Methods in Applied Mechanics and Engineering, 2021. https://doi.org/10.1016/j.cma.2021.114070. ieee: 'A. Henkes, I. Caylak, and R. Mahnken, “A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures,” Computer Methods in Applied Mechanics and Engineering, Art. no. 114070, 2021, doi: 10.1016/j.cma.2021.114070.' mla: Henkes, Alexander, et al. “A Deep Learning Driven Pseudospectral PCE Based FFT Homogenization Algorithm for Complex Microstructures.” Computer Methods in Applied Mechanics and Engineering, 114070, 2021, doi:10.1016/j.cma.2021.114070. short: A. Henkes, I. Caylak, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2021). date_created: 2021-09-14T11:21:22Z date_updated: 2023-01-24T13:02:58Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1016/j.cma.2021.114070 language: - iso: eng publication: Computer Methods in Applied Mechanics and Engineering publication_identifier: issn: - 0045-7825 publication_status: published quality_controlled: '1' status: public title: A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures type: journal_article user_id: '335' year: '2021' ... --- _id: '24374' article_number: '113439' author: - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Caylak I, Penner E, Mahnken R. Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters. Computer Methods in Applied Mechanics and Engineering. Published online 2020. doi:10.1016/j.cma.2020.113439 apa: Caylak, I., Penner, E., & Mahnken, R. (2020). Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters. Computer Methods in Applied Mechanics and Engineering, Article 113439. https://doi.org/10.1016/j.cma.2020.113439 bibtex: '@article{Caylak_Penner_Mahnken_2020, title={Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters}, DOI={10.1016/j.cma.2020.113439}, number={113439}, journal={Computer Methods in Applied Mechanics and Engineering}, author={Caylak, Ismail and Penner, Eduard and Mahnken, Rolf}, year={2020} }' chicago: Caylak, Ismail, Eduard Penner, and Rolf Mahnken. “Mean-Field and Full-Field Homogenization with Polymorphic Uncertain Geometry and Material Parameters.” Computer Methods in Applied Mechanics and Engineering, 2020. https://doi.org/10.1016/j.cma.2020.113439. ieee: 'I. Caylak, E. Penner, and R. Mahnken, “Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters,” Computer Methods in Applied Mechanics and Engineering, Art. no. 113439, 2020, doi: 10.1016/j.cma.2020.113439.' mla: Caylak, Ismail, et al. “Mean-Field and Full-Field Homogenization with Polymorphic Uncertain Geometry and Material Parameters.” Computer Methods in Applied Mechanics and Engineering, 113439, 2020, doi:10.1016/j.cma.2020.113439. short: I. Caylak, E. Penner, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2020). date_created: 2021-09-14T11:18:05Z date_updated: 2023-01-24T14:03:55Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1016/j.cma.2020.113439 language: - iso: eng publication: Computer Methods in Applied Mechanics and Engineering publication_identifier: issn: - 0045-7825 publication_status: published quality_controlled: '1' status: public title: Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters type: journal_article user_id: '335' year: '2020' ... --- _id: '19297' author: - first_name: A. full_name: Dridger, A. last_name: Dridger - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: R. full_name: Mahnken, R. last_name: Mahnken - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner citation: ama: Dridger A, Caylak I, Mahnken R, Penner E. A possibilistic finite element method for sparse data. Safety and Reliability. 2019:58-82. doi:10.1080/09617353.2018.1552477 apa: Dridger, A., Caylak, I., Mahnken, R., & Penner, E. (2019). A possibilistic finite element method for sparse data. Safety and Reliability, 58–82. https://doi.org/10.1080/09617353.2018.1552477 bibtex: '@article{Dridger_Caylak_Mahnken_Penner_2019, title={A possibilistic finite element method for sparse data}, DOI={10.1080/09617353.2018.1552477}, journal={Safety and Reliability}, author={Dridger, A. and Caylak, Ismail and Mahnken, R. and Penner, Eduard}, year={2019}, pages={58–82} }' chicago: Dridger, A., Ismail Caylak, R. Mahnken, and Eduard Penner. “A Possibilistic Finite Element Method for Sparse Data.” Safety and Reliability, 2019, 58–82. https://doi.org/10.1080/09617353.2018.1552477. ieee: A. Dridger, I. Caylak, R. Mahnken, and E. Penner, “A possibilistic finite element method for sparse data,” Safety and Reliability, pp. 58–82, 2019. mla: Dridger, A., et al. “A Possibilistic Finite Element Method for Sparse Data.” Safety and Reliability, 2019, pp. 58–82, doi:10.1080/09617353.2018.1552477. short: A. Dridger, I. Caylak, R. Mahnken, E. Penner, Safety and Reliability (2019) 58–82. date_created: 2020-09-11T09:44:02Z date_updated: 2022-01-06T06:54:01Z doi: 10.1080/09617353.2018.1552477 language: - iso: eng page: 58-82 publication: Safety and Reliability publication_identifier: issn: - 0961-7353 - 2469-4126 publication_status: published status: public title: A possibilistic finite element method for sparse data type: journal_article user_id: '75' year: '2019' ... --- _id: '19300' article_number: e201900005 author: - first_name: Markus full_name: Mäck, Markus last_name: Mäck - first_name: Ismail full_name: Caylak, Ismail id: '75' 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 full_name: Hanss, Michael last_name: Hanss - first_name: Rolf full_name: Mahnken, Rolf last_name: Mahnken - first_name: Günther full_name: Meschke, Günther last_name: Meschke - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner citation: ama: Mäck M, Caylak I, Edler P, et al. Optimization with constraints considering polymorphic uncertainties. GAMM-Mitteilungen. Published online 2019. doi:10.1002/gamm.201900005 apa: Mäck, M., Caylak, I., Edler, P., Freitag, S., Hanss, M., Mahnken, R., Meschke, G., & Penner, E. (2019). Optimization with constraints considering polymorphic uncertainties. GAMM-Mitteilungen, Article e201900005. https://doi.org/10.1002/gamm.201900005 bibtex: '@article{Mäck_Caylak_Edler_Freitag_Hanss_Mahnken_Meschke_Penner_2019, title={Optimization with constraints considering polymorphic uncertainties}, DOI={10.1002/gamm.201900005}, 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} }' chicago: Mäck, Markus, Ismail Caylak, Philipp Edler, Steffen Freitag, Michael Hanss, Rolf Mahnken, Günther Meschke, and Eduard Penner. “Optimization with Constraints Considering Polymorphic Uncertainties.” GAMM-Mitteilungen, 2019. https://doi.org/10.1002/gamm.201900005. ieee: 'M. Mäck et al., “Optimization with constraints considering polymorphic uncertainties,” GAMM-Mitteilungen, Art. no. e201900005, 2019, doi: 10.1002/gamm.201900005.' mla: Mäck, Markus, et al. “Optimization with Constraints Considering Polymorphic Uncertainties.” GAMM-Mitteilungen, e201900005, 2019, doi:10.1002/gamm.201900005. short: M. Mäck, I. Caylak, P. Edler, S. Freitag, M. Hanss, R. Mahnken, G. Meschke, E. Penner, GAMM-Mitteilungen (2019). date_created: 2020-09-11T09:48:23Z date_updated: 2022-07-27T07:04:05Z doi: 10.1002/gamm.201900005 language: - iso: eng publication: GAMM-Mitteilungen publication_identifier: issn: - 0936-7195 publication_status: published status: public title: Optimization with constraints considering polymorphic uncertainties type: journal_article user_id: '27973' year: '2019' ... --- _id: '19122' author: - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Alex full_name: Dridger, Alex last_name: Dridger - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Penner E, Caylak I, Dridger A, Mahnken R. A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics. Mathematics and Mechanics of Complex Systems. Published online 2019:99-129. doi:10.2140/memocs.2019.7.99 apa: Penner, E., Caylak, I., Dridger, A., & Mahnken, R. (2019). A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics. Mathematics and Mechanics of Complex Systems, 99–129. https://doi.org/10.2140/memocs.2019.7.99 bibtex: '@article{Penner_Caylak_Dridger_Mahnken_2019, title={A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics}, DOI={10.2140/memocs.2019.7.99}, journal={Mathematics and Mechanics of Complex Systems}, author={Penner, Eduard and Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}, year={2019}, pages={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.” Mathematics and Mechanics of Complex Systems, 2019, 99–129. https://doi.org/10.2140/memocs.2019.7.99. ieee: 'E. Penner, I. Caylak, A. Dridger, and R. Mahnken, “A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics,” Mathematics and Mechanics of Complex Systems, pp. 99–129, 2019, doi: 10.2140/memocs.2019.7.99.' mla: Penner, Eduard, et al. “A Polynomial Chaos Expanded Hybrid Fuzzy-Stochastic Model for Transversely Fiber Reinforced Plastics.” Mathematics and Mechanics of Complex Systems, 2019, pp. 99–129, doi:10.2140/memocs.2019.7.99. short: E. Penner, I. Caylak, A. Dridger, R. Mahnken, Mathematics and Mechanics of Complex Systems (2019) 99–129. date_created: 2020-09-08T10:24:25Z date_updated: 2023-01-24T14:07:05Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.2140/memocs.2019.7.99 language: - iso: eng page: 99-129 publication: Mathematics and Mechanics of Complex Systems publication_identifier: issn: - 2325-3444 - 2326-7186 publication_status: published quality_controlled: '1' status: public title: A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics type: journal_article user_id: '335' year: '2019' ... --- _id: '19120' author: - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Caylak I, Penner E, Mahnken R. A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics. PAMM. Published online 2019. doi:10.1002/pamm.201900356 apa: Caylak, I., Penner, E., & Mahnken, R. (2019). A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics. PAMM. https://doi.org/10.1002/pamm.201900356 bibtex: '@article{Caylak_Penner_Mahnken_2019, title={A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics}, DOI={10.1002/pamm.201900356}, journal={PAMM}, author={Caylak, Ismail and Penner, Eduard and Mahnken, Rolf}, year={2019} }' chicago: Caylak, Ismail, Eduard Penner, and Rolf Mahnken. “A Fuzzy Uncertainty Model for Analytical and Numerical Homogenization of Transversely Fiber Reinforced Plastics.” PAMM, 2019. https://doi.org/10.1002/pamm.201900356. ieee: 'I. Caylak, E. Penner, and R. Mahnken, “A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics,” PAMM, 2019, doi: 10.1002/pamm.201900356.' mla: Caylak, Ismail, et al. “A Fuzzy Uncertainty Model for Analytical and Numerical Homogenization of Transversely Fiber Reinforced Plastics.” PAMM, 2019, doi:10.1002/pamm.201900356. short: I. Caylak, E. Penner, R. Mahnken, PAMM (2019). date_created: 2020-09-08T10:23:48Z date_updated: 2023-01-24T14:05:01Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1002/pamm.201900356 language: - iso: eng publication: PAMM publication_identifier: issn: - 1617-7061 - 1617-7061 publication_status: published status: public title: A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics type: journal_article user_id: '335' year: '2019' ... --- _id: '19306' author: - first_name: Alex full_name: Dridger, Alex last_name: Dridger - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf last_name: Mahnken - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner citation: ama: 'Dridger A, Caylak I, Mahnken R, Penner E. On the connection between possibility theory and probability box theory in structural mechanics. In: 13th World Congress in Computational Mechanics . ; 2018.' apa: Dridger, A., Caylak, I., Mahnken, R., & Penner, E. (2018). On the connection between possibility theory and probability box theory in structural mechanics. 13th World Congress in Computational Mechanics . 13th World Congress in Computational Mechanics , New York. bibtex: '@inproceedings{Dridger_Caylak_Mahnken_Penner_2018, title={On the connection between possibility theory and probability box theory in structural mechanics}, booktitle={13th World Congress in Computational Mechanics }, author={Dridger, Alex and Caylak, Ismail and Mahnken, Rolf and Penner, Eduard}, year={2018} }' chicago: Dridger, Alex, Ismail Caylak, Rolf Mahnken, and Eduard Penner. “On the Connection between Possibility Theory and Probability Box Theory in Structural Mechanics.” In 13th World Congress in Computational Mechanics , 2018. ieee: A. Dridger, I. Caylak, R. Mahnken, and E. Penner, “On the connection between possibility theory and probability box theory in structural mechanics,” presented at the 13th World Congress in Computational Mechanics , New York, 2018. mla: Dridger, Alex, et al. “On the Connection between Possibility Theory and Probability Box Theory in Structural Mechanics.” 13th World Congress in Computational Mechanics , 2018. short: 'A. Dridger, I. Caylak, R. Mahnken, E. Penner, in: 13th World Congress in Computational Mechanics , 2018.' conference: end_date: 2018-07-27 location: New York name: '13th World Congress in Computational Mechanics ' start_date: 2018-07-22 date_created: 2020-09-11T10:04:36Z date_updated: 2022-07-27T07:07:27Z language: - iso: eng publication: '13th World Congress in Computational Mechanics ' status: public title: On the connection between possibility theory and probability box theory in structural mechanics type: conference user_id: '27973' year: '2018' ... --- _id: '19308' author: - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Alex full_name: Dridger, Alex last_name: Dridger - first_name: Rolf full_name: Mahnken, Rolf last_name: Mahnken citation: ama: Caylak I, Penner E, Dridger A, Mahnken R. Stochastic hyperelastic modeling considering dependency of material parameters. Computational Mechanics. Published online 2018:1273-1285. doi:10.1007/s00466-018-1563-z apa: Caylak, I., Penner, E., Dridger, A., & Mahnken, R. (2018). Stochastic hyperelastic modeling considering dependency of material parameters. Computational Mechanics, 1273–1285. https://doi.org/10.1007/s00466-018-1563-z bibtex: '@article{Caylak_Penner_Dridger_Mahnken_2018, title={Stochastic hyperelastic modeling considering dependency of material parameters}, DOI={10.1007/s00466-018-1563-z}, journal={Computational Mechanics}, author={Caylak, Ismail and Penner, Eduard and Dridger, Alex and Mahnken, Rolf}, year={2018}, pages={1273–1285} }' chicago: Caylak, Ismail, Eduard Penner, Alex Dridger, and Rolf Mahnken. “Stochastic Hyperelastic Modeling Considering Dependency of Material Parameters.” Computational Mechanics, 2018, 1273–85. https://doi.org/10.1007/s00466-018-1563-z. ieee: 'I. Caylak, E. Penner, A. Dridger, and R. Mahnken, “Stochastic hyperelastic modeling considering dependency of material parameters,” Computational Mechanics, pp. 1273–1285, 2018, doi: 10.1007/s00466-018-1563-z.' mla: Caylak, Ismail, et al. “Stochastic Hyperelastic Modeling Considering Dependency of Material Parameters.” Computational Mechanics, 2018, pp. 1273–85, doi:10.1007/s00466-018-1563-z. short: I. Caylak, E. Penner, A. Dridger, R. Mahnken, Computational Mechanics (2018) 1273–1285. date_created: 2020-09-11T10:05:32Z date_updated: 2022-07-27T07:05:15Z doi: 10.1007/s00466-018-1563-z language: - iso: eng page: 1273-1285 publication: Computational Mechanics publication_identifier: issn: - 0178-7675 - 1432-0924 publication_status: published status: public title: Stochastic hyperelastic modeling considering dependency of material parameters type: journal_article user_id: '75' year: '2018' ... --- _id: '19303' author: - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Alex full_name: Dridger, Alex last_name: Dridger - first_name: Rolf full_name: Mahnken, Rolf last_name: Mahnken citation: ama: Caylak I, Penner E, Dridger A, Mahnken R. A fuzzy‐stochastic model for transversely fiber reinforced plastics. PAMM. Published online 2018. doi:10.1002/pamm.201800121 apa: Caylak, I., Penner, E., Dridger, A., & Mahnken, R. (2018). A fuzzy‐stochastic model for transversely fiber reinforced plastics. PAMM. https://doi.org/10.1002/pamm.201800121 bibtex: '@article{Caylak_Penner_Dridger_Mahnken_2018, title={A fuzzy‐stochastic model for transversely fiber reinforced plastics}, DOI={10.1002/pamm.201800121}, journal={PAMM}, author={Caylak, Ismail and Penner, Eduard and Dridger, Alex and Mahnken, Rolf}, year={2018} }' chicago: Caylak, Ismail, Eduard Penner, Alex Dridger, and Rolf Mahnken. “A Fuzzy‐stochastic Model for Transversely Fiber Reinforced Plastics.” PAMM, 2018. https://doi.org/10.1002/pamm.201800121. ieee: 'I. Caylak, E. Penner, A. Dridger, and R. Mahnken, “A fuzzy‐stochastic model for transversely fiber reinforced plastics,” PAMM, 2018, doi: 10.1002/pamm.201800121.' mla: Caylak, Ismail, et al. “A Fuzzy‐stochastic Model for Transversely Fiber Reinforced Plastics.” PAMM, 2018, doi:10.1002/pamm.201800121. short: I. Caylak, E. Penner, A. Dridger, R. Mahnken, PAMM (2018). date_created: 2020-09-11T09:49:21Z date_updated: 2022-07-27T07:06:49Z doi: 10.1002/pamm.201800121 language: - iso: eng publication: PAMM publication_identifier: issn: - 1617-7061 - 1617-7061 publication_status: published status: public title: A fuzzy‐stochastic model for transversely fiber reinforced plastics type: journal_article user_id: '75' year: '2018' ... --- _id: '19124' author: - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Alex full_name: Dridger, Alex last_name: Dridger - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Penner E, Caylak I, Dridger A, Mahnken R. Possibilistic and stochastic analysis using for rubber‐like materials. PAMM. Published online 2018. doi:10.1002/pamm.201800153 apa: Penner, E., Caylak, I., Dridger, A., & Mahnken, R. (2018). Possibilistic and stochastic analysis using for rubber‐like materials. PAMM. https://doi.org/10.1002/pamm.201800153 bibtex: '@article{Penner_Caylak_Dridger_Mahnken_2018, title={Possibilistic and stochastic analysis using for rubber‐like materials}, DOI={10.1002/pamm.201800153}, journal={PAMM}, author={Penner, Eduard and Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}, year={2018} }' chicago: Penner, Eduard, Ismail Caylak, Alex Dridger, and Rolf Mahnken. “Possibilistic and Stochastic Analysis Using for Rubber‐like Materials.” PAMM, 2018. https://doi.org/10.1002/pamm.201800153. ieee: 'E. Penner, I. Caylak, A. Dridger, and R. Mahnken, “Possibilistic and stochastic analysis using for rubber‐like materials,” PAMM, 2018, doi: 10.1002/pamm.201800153.' mla: Penner, Eduard, et al. “Possibilistic and Stochastic Analysis Using for Rubber‐like Materials.” PAMM, 2018, doi:10.1002/pamm.201800153. short: E. Penner, I. Caylak, A. Dridger, R. Mahnken, PAMM (2018). date_created: 2020-09-08T10:25:18Z date_updated: 2023-01-24T14:12:07Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1002/pamm.201800153 language: - iso: eng publication: PAMM publication_identifier: issn: - 1617-7061 - 1617-7061 publication_status: published status: public title: Possibilistic and stochastic analysis using for rubber‐like materials type: journal_article user_id: '335' year: '2018' ... --- _id: '19307' author: - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Penner E, Caylak I, Mahnken R. A multivariate stochastic material model with correlated material parameters. PAMM. Published online 2018:67-68. doi:10.1002/pamm.201710020 apa: Penner, E., Caylak, I., & Mahnken, R. (2018). A multivariate stochastic material model with correlated material parameters. PAMM, 67–68. https://doi.org/10.1002/pamm.201710020 bibtex: '@article{Penner_Caylak_Mahnken_2018, title={A multivariate stochastic material model with correlated material parameters}, DOI={10.1002/pamm.201710020}, journal={PAMM}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2018}, pages={67–68} }' chicago: Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “A Multivariate Stochastic Material Model with Correlated Material Parameters.” PAMM, 2018, 67–68. https://doi.org/10.1002/pamm.201710020. ieee: 'E. Penner, I. Caylak, and R. Mahnken, “A multivariate stochastic material model with correlated material parameters,” PAMM, pp. 67–68, 2018, doi: 10.1002/pamm.201710020.' mla: Penner, Eduard, et al. “A Multivariate Stochastic Material Model with Correlated Material Parameters.” PAMM, 2018, pp. 67–68, doi:10.1002/pamm.201710020. short: E. Penner, I. Caylak, R. Mahnken, PAMM (2018) 67–68. date_created: 2020-09-11T10:05:06Z date_updated: 2023-01-24T14:12:42Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1002/pamm.201710020 language: - iso: eng page: 67-68 publication: PAMM publication_identifier: issn: - 1617-7061 publication_status: published status: public title: A multivariate stochastic material model with correlated material parameters type: journal_article user_id: '335' year: '2018' ... --- _id: '19309' author: - first_name: Eduard full_name: Penner, Eduard id: '27973' last_name: Penner - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: 'Penner E, Caylak I, Mahnken R. MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS. In: Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017). ; 2017. doi:10.7712/120217.5391.16785' apa: Penner, E., Caylak, I., & Mahnken, R. (2017). MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS. Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017). https://doi.org/10.7712/120217.5391.16785 bibtex: '@inproceedings{Penner_Caylak_Mahnken_2017, title={MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS}, DOI={10.7712/120217.5391.16785}, booktitle={Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017)}, author={Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}, year={2017} }' chicago: Penner, Eduard, Ismail Caylak, and Rolf Mahnken. “MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS.” In Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017), 2017. https://doi.org/10.7712/120217.5391.16785. ieee: 'E. Penner, I. Caylak, and R. Mahnken, “MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS,” 2017, doi: 10.7712/120217.5391.16785.' mla: Penner, Eduard, et al. “MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS.” Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017), 2017, doi:10.7712/120217.5391.16785. short: 'E. Penner, I. Caylak, R. Mahnken, in: Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017), 2017.' date_created: 2020-09-11T10:15:16Z date_updated: 2023-01-24T14:15:30Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.7712/120217.5391.16785 language: - iso: eng publication: Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017) publication_identifier: isbn: - '9786188284449' publication_status: published quality_controlled: '1' status: public title: MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS type: conference user_id: '335' year: '2017' ... --- _id: '24644' abstract: - lang: eng text: This paper presents a numerical method for solution of a stochastic partial differential equation (SPDE) for a linear elastic body with stochastic coefficients (random variables and/or random fields). To this end the stochastic finite element method (SFEM) is employed, which uses W IENER’S polynomial chaos expansion in order to decompose the coefficients into deterministic and stochastic parts. As a special case, we consider isotropic material behavior with two fluctuating parameters. Computational approaches involving GALERKIN projection are applied to reduce the SPDE into a system of deterministic PDEs. Furthermore, we consider normally distributed random variables, which are assumed to be stochastically independent, and which establish the number of stochastic dimensions. Subsequently, the resulting finite element equation is solved iteratively. Finally, in a representative example for a plate with a ring hole we study the influence of different variances for material parameters on the variances for the finite element results. author: - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Alex full_name: Dridger, Alex last_name: Dridger citation: ama: Mahnken R, Caylak I, Dridger A. A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor. A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor. Published online 2016. doi:10.24352/UB.OVGU-2017-003 apa: Mahnken, R., Caylak, I., & Dridger, A. (2016). A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor. A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor. https://doi.org/10.24352/UB.OVGU-2017-003 bibtex: '@article{Mahnken_Caylak_Dridger_2016, title={A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor}, DOI={10.24352/UB.OVGU-2017-003}, journal={A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor}, author={Mahnken, Rolf and Caylak, Ismail and Dridger, Alex}, year={2016} }' chicago: Mahnken, Rolf, Ismail Caylak, and Alex Dridger. “A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor.” A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor, 2016. https://doi.org/10.24352/UB.OVGU-2017-003. ieee: 'R. Mahnken, I. Caylak, and A. Dridger, “A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor,” A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor, 2016, doi: 10.24352/UB.OVGU-2017-003.' mla: Mahnken, Rolf, et al. “A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor.” A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor, 2016, doi:10.24352/UB.OVGU-2017-003. short: R. Mahnken, I. Caylak, A. Dridger, A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor (2016). date_created: 2021-09-17T10:09:52Z date_updated: 2023-01-24T14:22:25Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.24352/UB.OVGU-2017-003 language: - iso: eng publication: A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor quality_controlled: '1' status: public title: A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor type: journal_article user_id: '335' year: '2016' ... --- _id: '19128' author: - first_name: Ismail full_name: Caylak, Ismail id: '75' last_name: Caylak - first_name: Nicole full_name: Nörenberg, Nicole last_name: Nörenberg - first_name: Rolf full_name: Mahnken, Rolf id: '335' last_name: Mahnken citation: ama: Caylak I, Nörenberg N, Mahnken R. PC expansion for material parameters using artificial data and statistical methods. PAMM. Published online 2016:191-192. doi:10.1002/pamm.201610084 apa: Caylak, I., Nörenberg, N., & Mahnken, R. (2016). PC expansion for material parameters using artificial data and statistical methods. PAMM, 191–192. https://doi.org/10.1002/pamm.201610084 bibtex: '@article{Caylak_Nörenberg_Mahnken_2016, title={PC expansion for material parameters using artificial data and statistical methods}, DOI={10.1002/pamm.201610084}, journal={PAMM}, author={Caylak, Ismail and Nörenberg, Nicole and Mahnken, Rolf}, year={2016}, pages={191–192} }' chicago: Caylak, Ismail, Nicole Nörenberg, and Rolf Mahnken. “PC Expansion for Material Parameters Using Artificial Data and Statistical Methods.” PAMM, 2016, 191–92. https://doi.org/10.1002/pamm.201610084. ieee: 'I. Caylak, N. Nörenberg, and R. Mahnken, “PC expansion for material parameters using artificial data and statistical methods,” PAMM, pp. 191–192, 2016, doi: 10.1002/pamm.201610084.' mla: Caylak, Ismail, et al. “PC Expansion for Material Parameters Using Artificial Data and Statistical Methods.” PAMM, 2016, pp. 191–92, doi:10.1002/pamm.201610084. short: I. Caylak, N. Nörenberg, R. Mahnken, PAMM (2016) 191–192. date_created: 2020-09-08T10:27:20Z date_updated: 2023-01-24T14:16:32Z department: - _id: '9' - _id: '154' - _id: '321' doi: 10.1002/pamm.201610084 language: - iso: eng page: 191-192 publication: PAMM publication_identifier: issn: - 1617-7061 publication_status: published status: public title: PC expansion for material parameters using artificial data and statistical methods type: journal_article user_id: '335' year: '2016' ...