A. Hamdoun and R. Mahnken, “Experimental investigations of uniaxial and biaxial cold stretching within PCfilms and bars using optical measurements,”10.1002/pamm.202300114__PAMM, 2024, doi:10.1002/pamm.202300114 .

P. Lenz and R. Mahnken, “Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains,”10.1016/j.ijsolstr.2023.112642__International Journal of Solids and Structures, vol. 290, Art. no. 112642, 2024, doi:10.1016/j.ijsolstr.2023.112642 .

R. Mahnken and H. Westermann, “Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods,”10.1007/s00466-024-02442-y__Computational Mechanics, 2024, doi:10.1007/s00466-024-02442-y .

A. Hamdoun and R. Mahnken, “A large deformation gradient theory for glassy polymers by means of micromorphic regularization,”10.1007/s00419-024-02570-0__Archive of Applied Mechanics, vol. 94, no. 5, pp. 1221–1242, 2024, doi:10.1007/s00419-024-02570-0 .

A. Hamdoun and R. Mahnken, “Uniaxial and biaxial experimental investigation of glassy polymers,”10.1016/j.polymer.2024.126981__Polymer, vol. 299, Art. no. 126981, 2024, doi:10.1016/j.polymer.2024.126981 .

A. Hamdoun and R. Mahnken, “Experimental investigations of uniaxial and biaxial cold stretching within PCfilms and bars using optical measurements,”10.1002/pamm.202300114__PAMM, 2024, doi:10.1002/pamm.202300114 .

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,”10.1007/s12221-023-00122-x__Fibers and Polymers, 2023, doi:10.1007/s12221-023-00122-x .

P. Lenz and R. Mahnken, “Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation,”10.1016/j.compstruct.2023.116911__Composite Structures, Art. no. 116911, 2023, doi:10.1016/j.compstruct.2023.116911 .

P. Lenz and R. Mahnken, “Thermochemomechanical modelling of a curing process combined with meanfield homogenization methods at large strains,”10.1002/pamm.202200214__PAMM, vol. 22, no. 1, 2023, doi:10.1002/pamm.202200214 .

C. Cheng, C. Song, R. Mahnken, Z. Yuan, L. Yu, and X. Ju, “A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites.” Elsevier BV, 2023.

H. Westermann and R. Mahnken, “A thermodynamic framework for the phasefield approach considering carbide precipitation during phase transformations,”10.1002/pamm.202200080__PAMM, vol. 22, no. 1, 2023, doi:10.1002/pamm.202200080 .

A. Hamdoun and R. Mahnken, “A finite strain gradient theory for viscoplasticity by means of micromorphic regularization,”10.1002/pamm.202200074__PAMM, vol. 22, no. 1, 2023, doi:10.1002/pamm.202200074 .

A. Tchomgue Simeu and R. Mahnken, “Goaloriented adaptivity based on a model hierarchy of meanfield and fullfield homogenization methods in elastoplasticity,”10.1002/pamm.202200053__PAMM, vol. 22, no. 1, 2023, doi:10.1002/pamm.202200053 .

R. Mahnken, “Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation,”10.1007/s00466-023-02347-2__Computational Mechanics, 2023, doi:10.1007/s00466-023-02347-2 .

A. Tchomgue Simeu and R. Mahnken, “Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind  and upwind approximations,”10.23967/admos.2023.054__2023, doi:10.23967/admos.2023.054 .

H. Westermann and R. Mahnken, “Numerical investigations of new loworder explicit last stage diagonal implicit Runge–Kutta schemes with the finiteelement method,”10.1002/pamm.202300071__PAMM, vol. 23, no. 2, 2023, doi:10.1002/pamm.202300071 .

H. Westermann and R. Mahnken, “On the accuracy, stability and computational efficiency of explicit last-stage diagonally implicit Runge–Kutta methods (ELDIRK) for the adaptive solution of phase-field problems,”10.1016/j.cma.2023.116545__Computer Methods in Applied Mechanics and Engineering, vol. 418, Art. no. 116545, 2023, doi:10.1016/j.cma.2023.116545 .

P. Lenz, P. Kreutzheide, and R. Mahnken, “Multiphase elasto-plastic mean-field homogenisation and its consistent linearisation,”10.1016/j.compstruc.2023.107160__Computers &;amp; Structures, vol. 290, Art. no. 107160, 2023, doi:10.1016/j.compstruc.2023.107160 .

A. Tchomgue Simeu and R. Mahnken, “Downwind and upwind approximations for mesh and model adaptivity of elastoplastic composites,”10.1002/pamm.202300136__PAMM, 2023, doi:10.1002/pamm.202300136 .

A. Börger and R. Mahnken, “A micropolar model accounting for asymmetric behavior of coldbox sand in relation to tensile and compression tests,”10.1002/pamm.202300126__PAMM, 2023, doi:10.1002/pamm.202300126 .

E. Penner, Polymorphic uncertainty in constitutive modeling of polymer composites at different scales. Shaker Verlag, 2023.

A. Hamdoun and R. Mahnken, “A finite strain gradient theory for viscoplasticity by means of micromorphic regularization,”10.1002/pamm.202200074__PAMM, vol. 22, no. 1, 2023, doi:10.1002/pamm.202200074 .

X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, and W. Zhou, “Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization,”10.1016/j.compstruct.2022.115699__Composite Structures, Art. no. 115699, 2022, doi:10.1016/j.compstruct.2022.115699 .

R. Mahnken, “Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters,”10.1007/s00419-021-02069-y__Archive of Applied Mechanics, vol. 92, no. 3, pp. 713–754, 2022, doi:10.1007/s00419-021-02069-y .

X. Ju, R. Mahnken, Y. Xu, and L. Liang, “Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua,”10.1007/s00466-021-02117-y__Computational Mechanics, vol. 69, no. 3, pp. 847–863, 2022, doi:10.1007/s00466-021-02117-y .

A. Henkes, H. Wessels, and R. Mahnken, “Physics informed neural networks for continuum micromechanics,”10.1016/j.cma.2022.114790__Computer Methods in Applied Mechanics and Engineering, vol. 393, Art. no. 114790, 2022, doi:10.1016/j.cma.2022.114790 .

R. Mahnken and J. Mirzapour, “A statistically based strain energy function for polymer chains in rubber elasticity,”10.1007/s00419-022-02237-8__Archive of Applied Mechanics, vol. 92, no. 11, pp. 3295–3323, 2022, doi:10.1007/s00419-022-02237-8 .

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,”10.2139/ssrn.4259246__SSRN Electronic Journal, 2022, doi:10.2139/ssrn.4259246 .

X. Ju, R. Mahnken, Y. Xu, and L. Liang, “NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems,”10.1016/j.cma.2022.115199__Computer Methods in Applied Mechanics and Engineering, vol. 398, Art. no. 115199, 2022, doi:10.1016/j.cma.2022.115199 .

E. Penner, I. Caylak, and R. Mahnken, “A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics,”10.2140/memocs.2022.10.21__Mathematics and Mechanics of Complex Systems, vol. 10, no. 1, pp. 21–50, 2022, doi:10.2140/memocs.2022.10.21 .

R. Mahnken, “New low order Runge–Kutta schemes for asymptotically exact global error estimation of embedded methods without order reduction,”10.1016/j.cma.2022.115553__Computer Methods in Applied Mechanics and Engineering, vol. 401, Art. no. 115553, 2022, doi:10.1016/j.cma.2022.115553 .

H. Westermann, A. Reitz, R. Mahnken, M. Schaper, and O. Grydin, “Microstructure transformations in a press hardening steel during tailored thermomechanical processing,”10.1002/srin.202100346__steel research international, 2022, doi:10.1002/srin.202100346 .

W.-G. Drossel et al., “Hybridprofile für Trag- und Crashstrukturen,” in Intrinsische Hybridverbunde für Leichtbautragstrukturen, Berlin, Heidelberg, 2021.

H. Westermann, A. Reitz, R. Mahnken, O. Grydin, and M. Schaper, “Constitutive modeling of viscoplasticity including phase transformations for graded thermomechanical processing,”10.1002/pamm.202100041__PAMM, 2021, doi:10.1002/pamm.202100041 .

P. Lenz and R. Mahnken, “Damage simulation of thermochemoelastoplastic fibre reinforced composites using meanfield homogenization methods,”10.1002/pamm.202000265__PAMM, 2021, doi:10.1002/pamm.202000265 .

E. Penner, I. Caylak, and R. Mahnken, “An uncertainty model for the curing process of transversely fiber reinforced plastics,”10.1002/pamm.202000178__PAMM, 2021, doi:10.1002/pamm.202000178 .

H. Westermann and R. Mahnken, “Constitutive modeling of dynamic recrystallization coupled to viscoplasticity,”10.1002/pamm.202000186__PAMM, 2021, doi:10.1002/pamm.202000186 .

A. Henkes, I. Caylak, and R. Mahnken, “A deep learning driven uncertain fullfield homogenization method,”10.1002/pamm.202000180__PAMM, 2021, doi:10.1002/pamm.202000180 .

R. Mahnken and H. Westermann, “A non-equilibrium thermodynamic framework for viscoplasticity incorporating dynamic recrystallization at large strains,”10.1016/j.ijplas.2021.102988__International Journal of Plasticity, Art. no. 102988, 2021, doi:10.1016/j.ijplas.2021.102988 .

E. Penner, I. Caylak, R. Mahnken, and A. Dridger, “Fuzzy and stochastic approach applied to rubber like materials,”10.1080/09617353.2020.1858678__Safety and Reliability, pp. 1–19, 2021, doi:10.1080/09617353.2020.1858678 .

H. Westermann and R. Mahnken, “On the Thermodynamics of Dynamic Recrystallization for Viscoplasticity at Large Strains,”10.23967/wccm-eccomas.2020.261__2021, doi:10.23967/wccm-eccomas.2020.261 .

C. Cheng et al., “Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure,”10.1016/j.compositesb.2021.109209__Composites Part B: Engineering, vol. 224, Art. no. 109209, 2021, doi:10.1016/j.compositesb.2021.109209 .

P. Lenz and R. Mahnken, “A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains,”10.1016/j.ijsolstr.2021.111266__International Journal of Solids and Structures, Art. no. 111266, 2021, doi:10.1016/j.ijsolstr.2021.111266 .

X. Ju, R. Mahnken, Y. Xu, L. Liang, and W. Zhou, “A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity,”10.1016/j.ijsolstr.2021.111103__International Journal of Solids and Structures, Art. no. 111103, 2021, doi:10.1016/j.ijsolstr.2021.111103 .

A. Henkes, I. Caylak, and R. Mahnken, “A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures,”10.1016/j.cma.2021.114070__Computer Methods in Applied Mechanics and Engineering, Art. no. 114070, 2021, doi:10.1016/j.cma.2021.114070 .

C. Cheng and R. Mahnken, “A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations,”10.1007/s00419-021-01982-6__Archive of Applied Mechanics, pp. 3869–3888, 2021, doi:10.1007/s00419-021-01982-6 .

X. Ju, R. Mahnken, L. Liang, and Y. Xu, “Goal-oriented mesh adaptivity for inverse problems in linear micromorphic elasticity,”10.1016/j.compstruc.2021.106671__Computers &; Structures, Art. no. 106671, 2021, doi:10.1016/j.compstruc.2021.106671 .

P. Lenz and R. Mahnken, “Integraltype nonlocal damage simulation of composites using meanfield homogenization methods,”10.1002/pamm.202100081__PAMM, 2021, doi:10.1002/pamm.202100081 .

A. Henkes, H. Wessels, and R. Mahnken, “Physics informed neural networks for continuum micromechanics,”10.1002/pamm.202100040__PAMM, 2021, doi:10.1002/pamm.202100040 .

I. Caylak, E. Penner, and R. Mahnken, “Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters,”10.1016/j.cma.2020.113439__Computer Methods in Applied Mechanics and Engineering, Art. no. 113439, 2020, doi:10.1016/j.cma.2020.113439 .

A. Dridger, I. Caylak, R. Mahnken, and E. Penner, “A possibilistic finite element method for sparse data,” Safety and Reliability, pp. 58–82, 2019.

A. Dridger, I. Caylak, R. Mahnken, and E. Penner, “‘A possibilistic finite element method for sparse data,’” Safety and Reliability, pp. 58–82, 2019.

X. Ju and R. Mahnken, “‘Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity,’” Computer Methods in Applied Mechanics and Engineering, pp. 297–329, 2019.

M. Mäck et al., “‘Optimization with constraints considering polymorphic uncertainties,’” GAMM-Mitteilungen, 2019.

R. Mahnken and X. Ju, “Goaloriented adaptivity based on a model hierarchy of meanfield and fullfield homogenization methods in linear elasticity,” International Journal for Numerical Methods in Engineering, 2019.

C. Dammann and R. Mahnken, “Simulation of a resin transfer molding process using a phase field approach within the theory of porous media,” Composites Part A: Applied Science and Manufacturing, vol. 120, pp. 147–160, 2019.

X. Ju and R. Mahnken, “‘Goal-oriented adaptivity on mean-field and full-field homogenization methods considering hierarchical unit cells,’” PAMM, vol. 19.

P. Lenz and R. Mahnken, “‘Damage simulation of fiber reinforced composites using mean-field homogenization methods’ ,” PAMM, vol. 19, 2019.

M. Mäck et al., “Optimization with constraints considering polymorphic uncertainties,”10.1002/gamm.201900005__GAMM-Mitteilungen, Art. no. e201900005, 2019, doi:10.1002/gamm.201900005 .

E. Penner, I. Caylak, A. Dridger, and R. Mahnken, “A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics,”10.2140/memocs.2019.7.99__Mathematics and Mechanics of Complex Systems, pp. 99–129, 2019, doi:10.2140/memocs.2019.7.99 .

I. Caylak, E. Penner, and R. Mahnken, “A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics,”10.1002/pamm.201900356__PAMM, 2019, doi:10.1002/pamm.201900356 .

X. Ju and R. Mahnken, “Model adaptivity on meanfield and fullfield homogenization methods considering hierarchical unit cells,”10.1002/pamm.201900177__PAMM, 2019, doi:10.1002/pamm.201900177 .

P. Lenz and R. Mahnken, “Damage simulation of fiber reinforced composites using meanfield homogenization methods,”10.1002/pamm.201900370__PAMM, 2019, doi:10.1002/pamm.201900370 .

R. Mahnken, Lehrbuch der Technischen Mechanik - Band 2: Elastostatik. Berlin, Heidelberg, 2019.

K.-U. Widany, Adaptive Finite Element Methods for Direct and Inverse Problems in Nonlinear Solid Mechanics. Shaker, 2019.

C. Damman, Experimental Characterization and Constitutive Modeling of Reinforced Thermoplastic and Thermosetting Polymers. Shaker, 2019.

X. Ju, Adaptive Methods in the Mechanics of Heterogeneous Materials. 2019.

C. Cheng, A multi-mechanism model for cutting simulations combining asymmetric effects and gradient phase transformations. 2019.

M. Düsing and R. Mahnken, A coupled phase field/diffusion model for upper and lower bainitic transformation”,” International Journal of Solids and Structures, vol. 135, pp. 1723183, 2018.

R. Mahnken, P. Lenz, and C. Dammann, “‘A least squares approach for effective shear properties in an n-layered sphere model,’” Archive of Applied Mechanics, pp. 2081–2099, 2018.

C. Dammann, I. Caylak, and R. Mahnken, “‘Sequential biaxial stretching of polycarbonate-films for characterization of strain-induced anisotropy,’” GAMM-Mitteilungen, 2018.

E. Penner, I. Caylak, and R. Mahnken, “A multivariate stochastic material model with correlated material parameters,” PAMM, pp. 67–68, 2018.

X. Ju and R. Mahnken, “‘Error-controlled homogenization for a class of linear elastic composite problems,’” PAMM, pp. 601–602, 2018.

M. Düsing and R. Mahnken, “‘A coupled phase transformation and solute diffusion model for bainitic transformation,’” PAMM, pp. 505–506, 2018.

A. Dridger, I. Caylak, and R. Mahnken, “‘A fuzzy finite element method for sparse experimental data based on a possibilistic approach,’” PAMM, pp. 55–56, 2018.

X. Ju and R. Mahnken, “‘Goal-oriented adaptivity for parameter identification in linear micromorphic elasticity,’” PAMM, 2018.

X. Ju and R. Mahnken, “Goal-oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis,” International Journal for Numerical Methods in Engineering, pp. 472–473, 2018.

I. Caylak, A. Dridger, and R. Mahnken, “‘Stochastic hyperelastic modeling considering dependency of material parameters,’” Computational Mechanics, vol. 62, no. 6, pp. 1273–1285, 2018.

X. Ju and R. Mahnken, Goal-oriented adaptivity on mean-field and full-field homogenization methods with a view to hierarchical unit cells“,” in 31st International Workshop on Research in Mechnanics of Composite, Bad Herrenalb, 2018.

A. Dridger, I. Caylak, R. Mahnken, and E. Penner, On the connection between possibility theory and probability box theory in structural mechanics“,” in 13th World Congress in Computational Mechanics , New York, 2018.

E. Penner, I. Caylak, A. Dridger, and R. Mahnken, “‘Possibilistic and stochastic analysis using for rubber-like materials,’” PAMM, 2018.

I. Caylak, E. Penner, A. Dridger, and R. Mahnken, “‘A fuzzy-stochastic model for transversely fiber reinforced plastics,’” PAMM, 2018.

M. Düsing and R. Mahnken, “‘Simulation of upper and lower bainitic transformation with a coupled phase field/diffusion/deformation framework,’” PAMM, vol. 18, 2018.

M. Düsing and R. Mahnken, “A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation,” International Journal of Solids and Structures, vol. 162, pp. 45–59, 2018.

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.

I. Caylak, E. Penner, A. Dridger, and R. Mahnken, “Stochastic hyperelastic modeling considering dependency of material parameters,”10.1007/s00466-018-1563-z__Computational Mechanics, pp. 1273–1285, 2018, doi:10.1007/s00466-018-1563-z .

I. Caylak, E. Penner, A. Dridger, and R. Mahnken, “A fuzzystochastic model for transversely fiber reinforced plastics,”10.1002/pamm.201800121__PAMM, 2018, doi:10.1002/pamm.201800121 .

R. Mahnken, P. Lenz, and C. Dammann, “A least squares approach for effective shear properties in an                                                                 10.1007/s00419-018-1431-5__$$\'76arvecn$$                                                                            n                                                                    -layered sphere model,”10.1007/s00419-018-1431-5__Archive of Applied Mechanics, pp. 2081–2099, 2018, doi:10.1007/s00419-018-1431-5 .

C. Dammann, R. Mahnken, and P. Lenz, “Derivation of an n-layered composite sphere model for thermo-chemo-mechanical effective properties,”10.1002/pamm.201710260__PAMM, pp. 581–582, 2018, doi:10.1002/pamm.201710260 .

A. Dridger and R. Mahnken, “Unschärfe in der Simulation im Kontext von Sicherheitsdiskursen,” in Wissenschaft im Angesichtf»großer gesellschaftlicher Herausforderungen«, 2018.

U. Ehlenbröker, M. Petersmann, T. Antretter, and R. Mahnken, “Transformation strains for bainitic variant evolution in steel,”10.1002/pamm.201710263__PAMM, pp. 587–588, 2018, doi:10.1002/pamm.201710263 .

P. Lenz, C. Dammann, and R. Mahnken, “The effective shear modulus for ann-layered composite sphere,”10.1002/pamm.201710274__PAMM, pp. 609–610, 2018, doi:10.1002/pamm.201710274 .

C. Cheng and R. Mahnken, “A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations,”10.1016/j.ijsolstr.2018.10.007__International Journal of Solids and Structures, pp. 1–17, 2018, doi:10.1016/j.ijsolstr.2018.10.007 .

E. Penner, I. Caylak, A. Dridger, and R. Mahnken, “Possibilistic and stochastic analysis using for rubberlike materials,”10.1002/pamm.201800153__PAMM, 2018, doi:10.1002/pamm.201800153 .

E. Penner, I. Caylak, and R. Mahnken, “A multivariate stochastic material model with correlated material parameters,”10.1002/pamm.201710020__PAMM, pp. 67–68, 2018, doi:10.1002/pamm.201710020 .

C. Zinn et al., “Shear strength and failure behaviour of laser nano-structured and conventionally pre-treated interfaces in intrinsically manufactured CFRP-steel hybrids,”10.1016/j.compositesb.2018.05.030__Composites Part B: Engineering, pp. 173–185, 2018, doi:10.1016/j.compositesb.2018.05.030 .

R. Mahnken, “‘A variational formulation for fuzzy analysis in continuum mechanics,’” Mathematics and Mechanics of complex systems, vol. 5, no. 3–4, 2017.

R. Mahnken, “,,Identification of Material Parameters for Constitutive Equations “,” in Encyclopedia of Computational Mechanics, 2nd ed., vol. 4, E. Stein, R. de Borst, and T. J. R. Hughes, Eds. John Wiley &; Sons, 2017, p. 1165.

A. Dridger, I. Caylak, and R. Mahnken, “‘A POSSIBILISTIC APPROACH FOR LINEAR ISOTROPIC ELASTICITY USING THE FUZZY FINITE ELEMENT METHOD,’” in Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017), 2017.

M. Düsing and R. Mahnken, “‘A coupled phase field/diffusion model for upper and lower bainitic transformation,’” International Journal of Solids and Structures, pp. 172–183, 2017.