@article{44890,
  author       = {{Tchomgue Simeu, Arnold and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  keywords     = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}},
  number       = {{1}},
  publisher    = {{Wiley}},
  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}},
  volume       = {{22}},
  year         = {{2023}},
}

@article{45757,
  abstract     = {{<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.
</jats:p>}},
  author       = {{Mahnken, Rolf}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  publisher    = {{Springer Science and Business Media LLC}},
  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          = {{10.1007/s00466-023-02347-2}},
  year         = {{2023}},
}

@inproceedings{46762,
  author       = {{Tchomgue Simeu, Arnold and Mahnken, Rolf}},
  booktitle    = {{XI International Conference on Adaptive Modeling and Simulation}},
  publisher    = {{CIMNE}},
  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}},
  year         = {{2023}},
}

@article{31185,
  author       = {{Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua and Cheng, Chun and Zhou, Wangmin}},
  issn         = {{0263-8223}},
  journal      = {{Composite Structures}},
  keywords     = {{Civil and Structural Engineering, Ceramics and Composites}},
  publisher    = {{Elsevier BV}},
  title        = {{{Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization}}},
  doi          = {{10.1016/j.compstruct.2022.115699}},
  year         = {{2022}},
}

@article{30656,
  abstract     = {{<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>}},
  author       = {{Mahnken, Rolf}},
  issn         = {{0939-1533}},
  journal      = {{Archive of Applied Mechanics}},
  keywords     = {{Mechanical Engineering}},
  number       = {{3}},
  pages        = {{713--754}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters}}},
  doi          = {{10.1007/s00419-021-02069-y}},
  volume       = {{92}},
  year         = {{2022}},
}

@article{30655,
  author       = {{Ju, Xiaozhe and Mahnken, Rolf and Xu, Yangjian and Liang, Lihua}},
  issn         = {{0178-7675}},
  journal      = {{Computational Mechanics}},
  keywords     = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}},
  number       = {{3}},
  pages        = {{847--863}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua}}},
  doi          = {{10.1007/s00466-021-02117-y}},
  volume       = {{69}},
  year         = {{2022}},
}

@article{30657,
  author       = {{Henkes, Alexander and Wessels, Henning and Mahnken, Rolf}},
  issn         = {{0045-7825}},
  journal      = {{Computer Methods in Applied Mechanics and Engineering}},
  keywords     = {{Computer Science Applications, General Physics and Astronomy, Mechanical Engineering, Mechanics of Materials, Computational Mechanics}},
  publisher    = {{Elsevier BV}},
  title        = {{{Physics informed neural networks for continuum micromechanics}}},
  doi          = {{10.1016/j.cma.2022.114790}},
  volume       = {{393}},
  year         = {{2022}},
}

@article{34074,
  author       = {{Mahnken, Rolf and Mirzapour, Jamil}},
  issn         = {{0939-1533}},
  journal      = {{Archive of Applied Mechanics}},
  keywords     = {{Mechanical Engineering}},
  number       = {{11}},
  pages        = {{3295--3323}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{A statistically based strain energy function for polymer chains in rubber elasticity}}},
  doi          = {{10.1007/s00419-022-02237-8}},
  volume       = {{92}},
  year         = {{2022}},
}

@article{41485,
  author       = {{Clemens, Robin and Barth, Enrico and Uhlmann, Eckart and Zhan, Yingjie and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1556-5068}},
  journal      = {{SSRN Electronic Journal}},
  keywords     = {{General Earth and Planetary Sciences, General Environmental Science}},
  publisher    = {{Elsevier BV}},
  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}},
  year         = {{2022}},
}

@article{32592,
  author       = {{Ju, X. and Mahnken, Rolf and Xu, Y. and Liang, L.}},
  issn         = {{0045-7825}},
  journal      = {{Computer Methods in Applied Mechanics and Engineering}},
  keywords     = {{Computer Science Applications, General Physics and Astronomy, Mechanical Engineering, Mechanics of Materials, Computational Mechanics}},
  publisher    = {{Elsevier BV}},
  title        = {{{NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems}}},
  doi          = {{10.1016/j.cma.2022.115199}},
  volume       = {{398}},
  year         = {{2022}},
}

@article{34075,
  author       = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{2325-3444}},
  journal      = {{Mathematics and Mechanics of Complex Systems}},
  keywords     = {{Computational Mathematics, Numerical Analysis, Civil and Structural Engineering}},
  number       = {{1}},
  pages        = {{21--50}},
  publisher    = {{Mathematical Sciences Publishers}},
  title        = {{{A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics}}},
  doi          = {{10.2140/memocs.2022.10.21}},
  volume       = {{10}},
  year         = {{2022}},
}

@article{33801,
  author       = {{Mahnken, Rolf}},
  issn         = {{0045-7825}},
  journal      = {{Computer Methods in Applied Mechanics and Engineering}},
  keywords     = {{Computer Science Applications, General Physics and Astronomy, Mechanical Engineering, Mechanics of Materials, Computational Mechanics}},
  publisher    = {{Elsevier BV}},
  title        = {{{New low order Runge–Kutta schemes for asymptotically exact global error estimation of embedded methods without order reduction}}},
  doi          = {{10.1016/j.cma.2022.115553}},
  volume       = {{401}},
  year         = {{2022}},
}

@article{23794,
  author       = {{Westermann, Hendrik and Reitz, Alexander and Mahnken, Rolf and Schaper, Mirko and Grydin, Olexandr}},
  issn         = {{1611-3683}},
  journal      = {{steel research international}},
  title        = {{{Microstructure transformations in a press hardening steel during tailored thermo‐mechanical processing}}},
  doi          = {{10.1002/srin.202100346}},
  year         = {{2022}},
}

@article{29089,
  author       = {{Westermann, Hendrik and Reitz, Alexander and Mahnken, Rolf and Grydin, Olexandr and Schaper, Mirko}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  title        = {{{Constitutive modeling of viscoplasticity including phase transformations for graded thermo‐mechanical processing}}},
  doi          = {{10.1002/pamm.202100041}},
  year         = {{2021}},
}

@article{21708,
  author       = {{Lenz, Peter and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  title        = {{{Damage simulation of thermo‐chemo‐elasto‐plastic fibre reinforced composites using mean‐field homogenization methods}}},
  doi          = {{10.1002/pamm.202000265}},
  year         = {{2021}},
}

@article{24392,
  author       = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  title        = {{{An uncertainty model for the curing process of transversely fiber reinforced plastics}}},
  doi          = {{10.1002/pamm.202000178}},
  year         = {{2021}},
}

@article{24384,
  author       = {{Westermann, Hendrik and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  title        = {{{Constitutive modeling of dynamic recrystallization coupled to viscoplasticity}}},
  doi          = {{10.1002/pamm.202000186}},
  year         = {{2021}},
}

@article{24397,
  author       = {{Henkes, Alexander and Caylak, Ismail and Mahnken, Rolf}},
  issn         = {{1617-7061}},
  journal      = {{PAMM}},
  title        = {{{A deep learning driven uncertain full‐field homogenization method}}},
  doi          = {{10.1002/pamm.202000180}},
  year         = {{2021}},
}

@article{24390,
  author       = {{Mahnken, Rolf and Westermann, Hendrik}},
  issn         = {{0749-6419}},
  journal      = {{International Journal of Plasticity}},
  title        = {{{A non-equilibrium thermodynamic framework for viscoplasticity incorporating dynamic recrystallization at large strains}}},
  doi          = {{10.1016/j.ijplas.2021.102988}},
  year         = {{2021}},
}

@article{21681,
  author       = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf and Dridger, Alex}},
  issn         = {{0961-7353}},
  journal      = {{Safety and Reliability}},
  pages        = {{1--19}},
  title        = {{{Fuzzy and stochastic approach applied to rubber like materials}}},
  doi          = {{10.1080/09617353.2020.1858678}},
  year         = {{2021}},
}