@article{19124,
  author       = {{Penner, Eduard and Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  title        = {{{Possibilistic and stochastic analysis using for rubber‐like materials}}},
  doi          = {{10.1002/pamm.201800153}},
  year         = {{2018}},
}

@article{19307,
  author       = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{67--68}},
  title        = {{{A multivariate stochastic material model with correlated material parameters}}},
  doi          = {{10.1002/pamm.201710020}},
  year         = {{2018}},
}

@article{15958,
  author       = {{Zinn, Carolin and Bobbert, Mathias and Dammann, Christian and Wang, Zheng and Tröster, Thomas and Mahnken, Rolf and Meschut, Gerson and Schaper, Mirko}},
  issn         = {{1359-8368}},
  journal      = {{Composites Part B: Engineering}},
  pages        = {{173--185}},
  title        = {{{Shear strength and failure behaviour of laser nano-structured and conventionally pre-treated interfaces in intrinsically manufactured CFRP-steel hybrids}}},
  doi          = {{10.1016/j.compositesb.2018.05.030}},
  year         = {{2018}},
}

@article{9862,
  abstract     = {{In order to improve the credibility of modern simulation tools, uncertainties of different kinds have to be considered. 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. }},
  author       = {{Mahnken, Rolf}},
  issn         = {{ 2325-3444}},
  journal      = {{Mathematics and Mechanics of complex systems}},
  keywords     = {{fuzzy analysis, α-level optimization, quantities of interest, optimization with simple constraints, large strain elasticity, large strain elastoplasticity}},
  number       = {{3-4}},
  title        = {{{"A variational formulation for fuzzy analysis in continuum mechanics"}}},
  volume       = {{5}},
  year         = {{2017}},
}

@inbook{9872,
  author       = {{Mahnken, Rolf}},
  booktitle    = {{Encyclopedia of Computational Mechanics}},
  editor       = {{Stein, Erwin and de Borst, Rene and Hughes, Thomas J.R.}},
  isbn         = {{978-1-119-00379-3}},
  pages        = {{1165}},
  publisher    = {{John Wiley & Sons}},
  title        = {{{,,Identification of Material Parameters for Constitutive Equations “}}},
  volume       = {{4}},
  year         = {{2017}},
}

@inproceedings{9941,
  author       = {{Dridger, Alex and Caylak, Ismail and Mahnken, Rolf}},
  booktitle    = {{Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017)}},
  isbn         = {{9786188284449}},
  title        = {{{"A POSSIBILISTIC APPROACH FOR LINEAR ISOTROPIC ELASTICITY USING THE FUZZY FINITE ELEMENT METHOD"}}},
  doi          = {{10.7712/120217.5392.16813}},
  year         = {{2017}},
}

@article{9988,
  author       = {{Düsing, Martin and Mahnken, Rolf}},
  issn         = {{0020-7683}},
  journal      = {{International Journal of Solids and Structures}},
  pages        = {{172--183}},
  title        = {{{"A coupled phase field/diffusion model for upper and lower bainitic transformation"}}},
  doi          = {{10.1016/j.ijsolstr.2017.11.018}},
  year         = {{2017}},
}

@article{9989,
  author       = {{Ju, X. and Mahnken, R.}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  pages        = {{1017--1039}},
  title        = {{{"Goal-oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis"}}},
  doi          = {{10.1002/nme.5541}},
  year         = {{2017}},
}

@article{10004,
  author       = {{Ju, X. and Mahnken, R.}},
  issn         = {{0045-7825}},
  journal      = {{Computer Methods in Applied Mechanics and Engineering}},
  pages        = {{208--237}},
  publisher    = {{Elsevier}},
  title        = {{{"Model adaptivity on effective elastic properties coupled with adaptive FEM"}}},
  doi          = {{10.1016/j.cma.2017.04.013}},
  volume       = {{322}},
  year         = {{2017}},
}

@article{10006,
  author       = {{Dammann, Christian and Lenz, Peter and Mahnken, Rolf}},
  issn         = {{2212-8271}},
  journal      = {{Procedia CIRP}},
  pages        = {{51--56}},
  publisher    = {{Elsevier}},
  title        = {{{"Thermo-chemo-mechanical Effective Properties for Homogeneous and Heterogeneous n -Phase Mixtures with Application to Curing"}}},
  doi          = {{10.1016/j.procir.2017.03.360}},
  volume       = {{66}},
  year         = {{2017}},
}

@article{10007,
  author       = {{Mahnken, Rolf and Dammann, Christian and Lenz, Peter}},
  issn         = {{1543-1649}},
  journal      = {{International Journal for Multiscale Computational Engineering}},
  number       = {{4}},
  pages        = {{295--322}},
  title        = {{{(n)- AND (n + 1)-LAYERED COMPOSITE SPHERE MODELS FOR THERMO-CHEMO-MECHANICAL EFFECTIVE PROPERTIES}}},
  doi          = {{10.1615/intjmultcompeng.2017020304}},
  volume       = {{15}},
  year         = {{2017}},
}

@inproceedings{10008,
  author       = {{Penner, E. and Caylak, I. and Mahnken, R.}},
  booktitle    = {{Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, Rhode Island, 15.-17.06.2017}},
  location     = {{Rhode Island}},
  pages        = {{554--564}},
  title        = {{{"Fuzzy and stochastic analysis of rubber like materials"}}},
  year         = {{2017}},
}

@inproceedings{19309,
  author       = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
  booktitle    = {{Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017)}},
  isbn         = {{9786188284449}},
  title        = {{{MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS}}},
  doi          = {{10.7712/120217.5391.16785}},
  year         = {{2017}},
}

@article{19423,
  author       = {{Mahnken, Rolf and Dammann, Christian and Lenz, Peter}},
  issn         = {{1543-1649}},
  journal      = {{International Journal for Multiscale Computational Engineering}},
  pages        = {{295--322}},
  title        = {{{(n)- AND (n + 1)-LAYERED COMPOSITE SPHERE MODELS FOR THERMO-CHEMO-MECHANICAL EFFECTIVE PROPERTIES}}},
  doi          = {{10.1615/intjmultcompeng.2017020304}},
  year         = {{2017}},
}

@article{21710,
  author       = {{Dammann, Christian and Lenz, Peter and Mahnken, Rolf}},
  issn         = {{2212-8271}},
  journal      = {{Procedia CIRP}},
  pages        = {{51--56}},
  title        = {{{Thermo-chemo-mechanical Effective Properties for Homogeneous and Heterogeneous n -Phase Mixtures with Application to Curing}}},
  doi          = {{10.1016/j.procir.2017.03.360}},
  year         = {{2017}},
}

@inbook{24521,
  author       = {{Uhlmann, E. and Mahnken, Rolf and Ivanov, I. M. and Cheng, C.}},
  booktitle    = {{Lecture Notes in Production Engineering}},
  issn         = {{2194-0525}},
  title        = {{{Thermo-Mechanical Simulation of Hard Turning with Macroscopic Models}}},
  doi          = {{10.1007/978-3-319-57120-1_7}},
  year         = {{2017}},
}

@book{45108,
  author       = {{Mahnken, Rolf}},
  title        = {{{Effective meso properties for fibre reinforced polymer curing}}},
  year         = {{2017}},
}

@article{24644,
  abstract     = {{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       = {{Mahnken, Rolf and Caylak, Ismail and Dridger, Alex}},
  journal      = {{A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor}},
  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}},
  year         = {{2016}},
}

@article{24647,
  author       = {{Ehlenbröker, Ulrich and Mahnken, Rolf and Petersmann, M and Antretter, T}},
  issn         = {{1757-8981}},
  journal      = {{IOP Conference Series: Materials Science and Engineering}},
  title        = {{{Modeling of variant-interaction during bainitic phase transformation}}},
  doi          = {{10.1088/1757-899x/119/1/012016}},
  year         = {{2016}},
}

@article{24642,
  author       = {{Cheng, C. and Mahnken, Rolf}},
  issn         = {{0020-7683}},
  journal      = {{International Journal of Solids and Structures}},
  pages        = {{127--141}},
  title        = {{{Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization}}},
  doi          = {{10.1016/j.ijsolstr.2016.10.010}},
  year         = {{2016}},
}