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Zinn <i>et al.</i>, “Shear strength and failure behaviour of laser nano-structured and conventionally pre-treated interfaces in intrinsically manufactured CFRP-steel hybrids,” <i>Composites Part B: Engineering</i>, pp. 173–185, 2018, doi: <a href=\"https://doi.org/10.1016/j.compositesb.2018.05.030\">10.1016/j.compositesb.2018.05.030</a>."},"year":"2018","publication_identifier":{"issn":["1359-8368"]},"quality_controlled":"1","publication_status":"published"},{"year":"2017","citation":{"short":"R. Mahnken, Mathematics and Mechanics of Complex Systems 5 (2017).","bibtex":"@article{Mahnken_2017, title={“A variational formulation for fuzzy analysis in continuum mechanics”}, volume={5}, number={3–4}, journal={Mathematics and Mechanics of complex systems}, author={Mahnken, Rolf}, year={2017} }","mla":"Mahnken, Rolf. “‘A Variational Formulation for Fuzzy Analysis in Continuum Mechanics.’” <i>Mathematics and Mechanics of Complex Systems</i>, vol. 5, no. 3–4, 2017.","apa":"Mahnken, R. (2017). “A variational formulation for fuzzy analysis in continuum mechanics.” <i>Mathematics and Mechanics of Complex Systems</i>, <i>5</i>(3–4).","ieee":"R. 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This work is focused on epistemic uncertainties in the framework of continuum mechanics, which are taken into account by fuzzy analysis. The underlying min-max optimization problem of the extension principle is approximated by α-discretization, resulting in a separation of minimum and maximum problems. To become more universal, so-called quantities of interest are employed, which allow a general formulation for the target problem of interest. In this way, the relation to parameter identification problems based on least-squares functions is highlighted. The solutions of the related optimization problems with simple constraints are obtained with a gradient-based scheme, which is derived from a sensitvity analysis for the target problem by means of a variational formulation. Two numerical examples for the fuzzy analysis of material parameters are concerned with a necking problem at large strain elastoplasticity and a perforated strip at large strain hyperelasticity to demonstrate the versatility of the proposed variational formulation. 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Mahnken, “,,Identification of Material Parameters for Constitutive Equations “,” in <i>Encyclopedia of Computational Mechanics</i>, 2nd ed., vol. 4, E. Stein, R. de Borst, and T. J. R. Hughes, Eds. John Wiley &#38; Sons, 2017, p. 1165.","chicago":"Mahnken, Rolf. “,,Identification of Material Parameters for Constitutive Equations “.” In <i>Encyclopedia of Computational Mechanics</i>, edited by Erwin Stein, Rene de Borst, and Thomas J.R. Hughes, 2nd ed., 4:1165. John Wiley &#38; Sons, 2017.","short":"R. Mahnken, in: E. Stein, R. de Borst, T.J.R. 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John Wiley &#38; Sons."},"publication_identifier":{"isbn":["978-1-119-00379-3"]},"publication_status":"published","edition":"2","language":[{"iso":"eng"}],"_id":"9872","department":[{"_id":"154"}],"user_id":"78813","editor":[{"full_name":"Stein, Erwin","last_name":"Stein","first_name":"Erwin"},{"first_name":"Rene","last_name":"de Borst","full_name":"de Borst, Rene"},{"full_name":"Hughes, Thomas J.R.","last_name":"Hughes","first_name":"Thomas J.R."}],"status":"public","publication":"Encyclopedia of Computational Mechanics","type":"book_chapter"},{"status":"public","type":"conference","publication":"Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017)","language":[{"iso":"eng"}],"_id":"9941","user_id":"78813","department":[{"_id":"154"}],"year":"2017","citation":{"ama":"Dridger A, Caylak I, Mahnken R. “A POSSIBILISTIC APPROACH FOR LINEAR ISOTROPIC ELASTICITY USING THE FUZZY FINITE ELEMENT METHOD.” In: <i>Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017)</i>. ; 2017. doi:<a href=\"https://doi.org/10.7712/120217.5392.16813\">10.7712/120217.5392.16813</a>","ieee":"A. 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Cheng, “Thermo-Mechanical Simulation of Hard Turning with Macroscopic Models,” in <i>Lecture Notes in Production Engineering</i>, Cham, 2017."},"place":"Cham","year":"2017","publication_status":"published","publication_identifier":{"issn":["2194-0525","2194-0533"]},"quality_controlled":"1","language":[{"iso":"eng"}],"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"24521","status":"public","type":"book_chapter","publication":"Lecture Notes in Production Engineering"},{"type":"book","quality_controlled":"1","citation":{"chicago":"Mahnken, Rolf. <i>Effective Meso Properties for Fibre Reinforced Polymer Curing</i>, 2017.","ieee":"R. Mahnken, <i>Effective meso properties for fibre reinforced polymer curing</i>. 2017.","ama":"Mahnken R. <i>Effective Meso Properties for Fibre Reinforced Polymer Curing</i>.; 2017.","apa":"Mahnken, R. (2017). <i>Effective meso properties for fibre reinforced polymer curing</i>.","bibtex":"@book{Mahnken_2017, title={Effective meso properties for fibre reinforced polymer curing}, author={Mahnken, Rolf}, year={2017} }","mla":"Mahnken, Rolf. <i>Effective Meso Properties for Fibre Reinforced Polymer Curing</i>. 2017.","short":"R. Mahnken, Effective Meso Properties for Fibre Reinforced Polymer Curing, 2017."},"status":"public","year":"2017","author":[{"first_name":"Rolf","last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf"}],"date_created":"2023-05-17T13:23:35Z","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"date_updated":"2023-05-17T13:25:31Z","_id":"45108","main_file_link":[{"url":"https://scholar.google.com/scholar?hl=de&as_sdt=0%2C5&q=Effective+meso+properties+for+fibre+reinforced+polymer+curing&btnG="}],"language":[{"iso":"eng"}],"title":"Effective meso properties for fibre reinforced polymer curing"},{"user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"24644","language":[{"iso":"eng"}],"type":"journal_article","publication":"A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor","status":"public","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","last_name":"Mahnken","id":"335","full_name":"Mahnken, Rolf"},{"first_name":"Ismail","id":"75","full_name":"Caylak, Ismail","last_name":"Caylak"},{"last_name":"Dridger","full_name":"Dridger, Alex","first_name":"Alex"}],"date_created":"2021-09-17T10:09:52Z","date_updated":"2023-01-24T14:22:25Z","doi":"10.24352/UB.OVGU-2017-003","title":"A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor","quality_controlled":"1","citation":{"mla":"Mahnken, Rolf, et al. “A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor.” <i>A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor</i>, 2016, doi:<a href=\"https://doi.org/10.24352/UB.OVGU-2017-003\">10.24352/UB.OVGU-2017-003</a>.","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).","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={<a href=\"https://doi.org/10.24352/UB.OVGU-2017-003\">10.24352/UB.OVGU-2017-003</a>}, 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} }","apa":"Mahnken, R., Caylak, I., &#38; Dridger, A. (2016). A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor. <i>A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor</i>. <a href=\"https://doi.org/10.24352/UB.OVGU-2017-003\">https://doi.org/10.24352/UB.OVGU-2017-003</a>","ama":"Mahnken R, Caylak I, Dridger A. A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor. <i>A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor</i>. Published online 2016. doi:<a href=\"https://doi.org/10.24352/UB.OVGU-2017-003\">10.24352/UB.OVGU-2017-003</a>","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.” <i>A Stochastic Finite Element Method with a Deviatoric-Volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor</i>, 2016. <a href=\"https://doi.org/10.24352/UB.OVGU-2017-003\">https://doi.org/10.24352/UB.OVGU-2017-003</a>.","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,” <i>A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor</i>, 2016, doi: <a href=\"https://doi.org/10.24352/UB.OVGU-2017-003\">10.24352/UB.OVGU-2017-003</a>."},"year":"2016"},{"type":"journal_article","publication":"IOP Conference Series: Materials Science and Engineering","status":"public","user_id":"335","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"_id":"24647","language":[{"iso":"eng"}],"article_number":"012016","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["1757-8981","1757-899X"]},"citation":{"mla":"Ehlenbröker, Ulrich, et al. “Modeling of Variant-Interaction during Bainitic Phase Transformation.” <i>IOP Conference Series: Materials Science and Engineering</i>, 012016, 2016, doi:<a href=\"https://doi.org/10.1088/1757-899x/119/1/012016\">10.1088/1757-899x/119/1/012016</a>.","bibtex":"@article{Ehlenbröker_Mahnken_Petersmann_Antretter_2016, title={Modeling of variant-interaction during bainitic phase transformation}, DOI={<a href=\"https://doi.org/10.1088/1757-899x/119/1/012016\">10.1088/1757-899x/119/1/012016</a>}, number={012016}, journal={IOP Conference Series: Materials Science and Engineering}, author={Ehlenbröker, Ulrich and Mahnken, Rolf and Petersmann, M and Antretter, T}, year={2016} }","short":"U. Ehlenbröker, R. Mahnken, M. Petersmann, T. Antretter, IOP Conference Series: Materials Science and Engineering (2016).","apa":"Ehlenbröker, U., Mahnken, R., Petersmann, M., &#38; Antretter, T. (2016). Modeling of variant-interaction during bainitic phase transformation. <i>IOP Conference Series: Materials Science and Engineering</i>, Article 012016. <a href=\"https://doi.org/10.1088/1757-899x/119/1/012016\">https://doi.org/10.1088/1757-899x/119/1/012016</a>","ama":"Ehlenbröker U, Mahnken R, Petersmann M, Antretter T. Modeling of variant-interaction during bainitic phase transformation. <i>IOP Conference Series: Materials Science and Engineering</i>. Published online 2016. doi:<a href=\"https://doi.org/10.1088/1757-899x/119/1/012016\">10.1088/1757-899x/119/1/012016</a>","chicago":"Ehlenbröker, Ulrich, Rolf Mahnken, M Petersmann, and T Antretter. “Modeling of Variant-Interaction during Bainitic Phase Transformation.” <i>IOP Conference Series: Materials Science and Engineering</i>, 2016. <a href=\"https://doi.org/10.1088/1757-899x/119/1/012016\">https://doi.org/10.1088/1757-899x/119/1/012016</a>.","ieee":"U. Ehlenbröker, R. Mahnken, M. Petersmann, and T. Antretter, “Modeling of variant-interaction during bainitic phase transformation,” <i>IOP Conference Series: Materials Science and Engineering</i>, Art. no. 012016, 2016, doi: <a href=\"https://doi.org/10.1088/1757-899x/119/1/012016\">10.1088/1757-899x/119/1/012016</a>."},"year":"2016","date_created":"2021-09-17T10:13:34Z","author":[{"full_name":"Ehlenbröker, Ulrich","last_name":"Ehlenbröker","first_name":"Ulrich"},{"full_name":"Mahnken, Rolf","id":"335","last_name":"Mahnken","first_name":"Rolf"},{"last_name":"Petersmann","full_name":"Petersmann, M","first_name":"M"},{"first_name":"T","last_name":"Antretter","full_name":"Antretter, T"}],"date_updated":"2023-01-24T14:23:11Z","doi":"10.1088/1757-899x/119/1/012016","title":"Modeling of variant-interaction during bainitic phase transformation"},{"_id":"24642","department":[{"_id":"9"},{"_id":"154"},{"_id":"321"}],"user_id":"335","language":[{"iso":"eng"}],"publication":"International Journal of Solids and Structures","type":"journal_article","status":"public","date_updated":"2023-01-24T14:21:51Z","author":[{"first_name":"C.","full_name":"Cheng, C.","last_name":"Cheng"},{"first_name":"Rolf","last_name":"Mahnken","full_name":"Mahnken, Rolf","id":"335"}],"date_created":"2021-09-17T10:08:53Z","title":"Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization","doi":"10.1016/j.ijsolstr.2016.10.010","publication_identifier":{"issn":["0020-7683"]},"quality_controlled":"1","publication_status":"published","year":"2016","page":"127-141","citation":{"ama":"Cheng C, Mahnken R. Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization. <i>International Journal of Solids and Structures</i>. Published online 2016:127-141. doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">10.1016/j.ijsolstr.2016.10.010</a>","chicago":"Cheng, C., and Rolf Mahnken. “Extension of a Multi-Mechanism Model: Hardness-Based Flow and Transformation Induced Plasticity for Austenitization.” <i>International Journal of Solids and Structures</i>, 2016, 127–41. <a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">https://doi.org/10.1016/j.ijsolstr.2016.10.010</a>.","ieee":"C. Cheng and R. Mahnken, “Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization,” <i>International Journal of Solids and Structures</i>, pp. 127–141, 2016, doi: <a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">10.1016/j.ijsolstr.2016.10.010</a>.","apa":"Cheng, C., &#38; Mahnken, R. (2016). Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization. <i>International Journal of Solids and Structures</i>, 127–141. <a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">https://doi.org/10.1016/j.ijsolstr.2016.10.010</a>","short":"C. Cheng, R. Mahnken, International Journal of Solids and Structures (2016) 127–141.","mla":"Cheng, C., and Rolf Mahnken. “Extension of a Multi-Mechanism Model: Hardness-Based Flow and Transformation Induced Plasticity for Austenitization.” <i>International Journal of Solids and Structures</i>, 2016, pp. 127–41, doi:<a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">10.1016/j.ijsolstr.2016.10.010</a>.","bibtex":"@article{Cheng_Mahnken_2016, title={Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization}, DOI={<a href=\"https://doi.org/10.1016/j.ijsolstr.2016.10.010\">10.1016/j.ijsolstr.2016.10.010</a>}, journal={International Journal of Solids and Structures}, author={Cheng, C. and Mahnken, Rolf}, year={2016}, pages={127–141} }"}}]