@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}},
}

@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{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{19128,
  author       = {{Caylak, Ismail and Nörenberg, Nicole and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{191--192}},
  title        = {{{PC expansion for material parameters using artificial data and statistical methods}}},
  doi          = {{10.1002/pamm.201610084}},
  year         = {{2016}},
}

@article{19117,
  author       = {{Dridger, Alex and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{667--668}},
  title        = {{{A linear elastic Fuzzy Finite Element Method with two fuzzy input parameters}}},
  doi          = {{10.1002/pamm.201610322}},
  year         = {{2016}},
}

@article{19127,
  author       = {{Penner, Eduard and Caylak, Ismail and Nörenberg, Nicole and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{675--676}},
  title        = {{{SFEM for rubber-like materials at large deformations}}},
  doi          = {{10.1002/pamm.201610326}},
  year         = {{2016}},
}

@article{19134,
  author       = {{Dridger, Alex and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{551--552}},
  title        = {{{Uncertainty quantification for linear elastic bodies with two fluctuating input parameters}}},
  doi          = {{10.1002/pamm.201510266}},
  year         = {{2015}},
}

@article{19131,
  author       = {{Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{179--180}},
  title        = {{{Non-linear Stochastic Finite Element}}},
  doi          = {{10.1002/pamm.201510080}},
  year         = {{2015}},
}

@article{24707,
  abstract     = {{<jats:title>Abstract</jats:title>
               <jats:p>The alignment of polymer chains is a well known microstructural evolution effect due to straining of polymers. This has a drastic influence on the macroscopic properties of the initially isotropic material. In this work, cold forming is performed at room temperature on a tensile testing machine. Polycarbonate films are examined in two loading phases. In the first phase, the specimen is loaded to induce anisotropy, and in the second, it is re-loaded, while the material direction is varied. The investigations are supported by an optical measurement system to gain knowledge about the inhomogeneous material behavior in the initial loading phase and about the anisotropic homogeneous behavior during the re-loading phase. Two dimensional strain contours are obtained from the test data. Additionally, we propose a method for approximation of the macroscopic true stress and compare the results with a common approach based on volume consistency. In the future, the test data will set a basis for parameter identification of constitutive equations taking into account a combination of inhomogenous and homogenous material behavior, exhibiting strain induced anisotropy.</jats:p>}},
  author       = {{Dammann, C. and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{2195-8602}},
  journal      = {{International Polymer Processing}},
  pages        = {{260--271}},
  title        = {{{Experimental Investigation of PC-Films Using Optical Measurements}}},
  doi          = {{10.3139/217.2848}},
  year         = {{2014}},
}

@article{19116,
  author       = {{Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{0045-7949}},
  journal      = {{Computers & Structures}},
  pages        = {{172--182}},
  title        = {{{Stabilized mixed triangular elements with area bubble functions at small and large deformations}}},
  doi          = {{10.1016/j.compstruc.2014.01.006}},
  year         = {{2014}},
}

@article{19132,
  author       = {{Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{319--320}},
  title        = {{{Modeling of induced anisotropy at large deformations for polymers}}},
  doi          = {{10.1002/pamm.201210149}},
  year         = {{2012}},
}

@phdthesis{19187,
  author       = {{Caylak, Ismail}},
  isbn         = {{978-3-8440-0084-9}},
  pages        = {{158 Seiten}},
  publisher    = {{Shaker}},
  title        = {{{Stabilized Mixed Triangular and Tetrahedral Finite Elements with Volume and Area Bubble Functions}}},
  volume       = {{Band 4}},
  year         = {{2011}},
}

@article{25088,
  author       = {{Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{0045-7949}},
  journal      = {{Computers & Structures}},
  pages        = {{1844--1851}},
  title        = {{{Mixed finite element formulations with volume bubble functions for triangular elements}}},
  doi          = {{10.1016/j.compstruc.2011.07.004}},
  year         = {{2011}},
}

@article{19129,
  author       = {{Caylak, Ismail and Mahnken, Rolf and Widany, Kai-Uwe}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{201--202}},
  title        = {{{Stabilized mixed triangular finite elements at large deformations using area bubble functions}}},
  doi          = {{10.1002/pamm.201110092}},
  year         = {{2011}},
}

@inbook{19133,
  author       = {{Mahnken, Rolf and Caylak, Ismail}},
  booktitle    = {{Advances in Extended and Multifield Theories for Continua}},
  isbn         = {{9783642227370}},
  issn         = {{1613-7736}},
  title        = {{{Optical Measurements for a Cold-Box Sand and Aspects of Direct and Inverse Problems for Micropolar Elasto-Plasticity}}},
  doi          = {{10.1007/978-3-642-22738-7_9}},
  year         = {{2011}},
}

@article{19113,
  author       = {{Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  pages        = {{218--242}},
  title        = {{{Stabilization of mixed tetrahedral elements at large deformations}}},
  doi          = {{10.1002/nme.3320}},
  year         = {{2011}},
}

@article{19138,
  author       = {{Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1364-0461}},
  journal      = {{International Journal of Cast Metals Research}},
  pages        = {{176--184}},
  title        = {{{Thermomechanical characterisation of cold box sand including optical measurements}}},
  doi          = {{10.1179/174313309x451261}},
  year         = {{2010}},
}

@article{19118,
  author       = {{Widany, Kai-Uwe and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{227--228}},
  title        = {{{Stabilized Mixed Tetrahedrals with Volume and Area Bubble Functions at Large Deformations}}},
  doi          = {{10.1002/pamm.201010106}},
  year         = {{2010}},
}

@article{19130,
  author       = {{Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  pages        = {{4040013--4040014}},
  title        = {{{On the stabilization of tetrahedral finite elements using volume and area bubble functions}}},
  doi          = {{10.1002/pamm.200700224}},
  year         = {{2008}},
}

@article{19114,
  author       = {{Mahnken, Rolf and Caylak, Ismail}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  pages        = {{377--413}},
  title        = {{{Stabilization of bi‐linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions}}},
  doi          = {{10.1002/nme.2264}},
  year         = {{2007}},
}