Prof. Dr. Rolf Mahnken - Kontakt (Universität Paderborn)

Microstructure transformations in a press hardening steel during tailored thermo‐mechanical processing

H. Westermann, A. Reitz, R. Mahnken, M. Schaper, O. Grydin, steel research international (2022)

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https://doi.org/10.1002/srin.202100346 [Titel anhand dieser DOI in Citavi-Projekt übernehmen]

Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters

R. Mahnken, Archive of Applied Mechanics (2022), 92(3), pp. 713-754

Abstract

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<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>

Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua

X. Ju, R. Mahnken, Y. Xu, L. Liang, Computational Mechanics (2022), 69(3), pp. 847-863

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Physics informed neural networks for continuum micromechanics

A. Henkes, H. Wessels, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2022), 393, 114790

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Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization

X. Ju, R. Mahnken, Y. Xu, L. Liang, C. Cheng, W. Zhou, Composite Structures (2022), 115699

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Constitutive modeling of dynamic recrystallization coupled to viscoplasticity

H. Westermann, R. Mahnken, PAMM (2021)

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An uncertainty model for the curing process of transversely fiber reinforced plastics

E. Penner, I. Caylak, R. Mahnken, PAMM (2021)

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A deep learning driven uncertain full‐field homogenization method

A. Henkes, I. Caylak, R. Mahnken, PAMM (2021)

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Damage simulation of thermo‐chemo‐elasto‐plastic fibre reinforced composites using mean‐field homogenization methods

P. Lenz, R. Mahnken, PAMM (2021)

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Constitutive modeling of viscoplasticity including phase transformations for graded thermo‐mechanical processing

H. Westermann, A. Reitz, R. Mahnken, O. Grydin, M. Schaper, PAMM (2021)

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Hybridprofile für Trag- und Crashstrukturen

W. Drossel, M. Bobbert, M. Böhme, C. Dammann, A. Dittes, M. Gießmann, C. Hühne, J. Ihlemann, R. Kießling, T. Lampke, P. Lenz, R. Mahnken, G. Meschut, R. Müller, M. Nier, R. Prussak, M. Riemer, S. Sander, M. Schaper, I. Scharf, M. Scholze, S. Schwöbel, S. Sharafiev, M. Sinapius, D. Stefaniak, T. Tröster, M.F.-. Wagner, Z. Wang, C. Zinn, in: Intrinsische Hybridverbunde für Leichtbautragstrukturen, 2021

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A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity

X. Ju, R. Mahnken, Y. Xu, L. Liang, W. Zhou, International Journal of Solids and Structures (2021), 111103

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A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations

C. Cheng, R. Mahnken, Archive of Applied Mechanics (2021), pp. 3869-3888

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Goal-oriented mesh adaptivity for inverse problems in linear micromorphic elasticity

X. Ju, R. Mahnken, L. Liang, Y. Xu, Computers & Structures (2021), 106671

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Integral‐type non‐local damage simulation of composites using mean‐field homogenization methods

P. Lenz, R. Mahnken, PAMM (2021)

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Physics informed neural networks for continuum micromechanics

A. Henkes, H. Wessels, R. Mahnken, PAMM (2021)

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A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains

P. Lenz, R. Mahnken, International Journal of Solids and Structures (2021), 111266

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Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure

C. Cheng, Z. Wang, Z. Jin, X. Ju, S. Schweizer, T. Tröster, R. Mahnken, Composites Part B: Engineering (2021), 224, 109209

Abstract

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As an effective and accurate method for modelling composite materials, mean-field homogenization is still not well studied in modelling non-linear and damage behaviours of UD composites. Investigated micro FE-simulations show that the matrix of UD composites exhibits different average plastic behaviour, named as average asymmetric matrix plasticity (AAMP), when the composite behaves different under shear, longitudinal and transverse loadings. In this study, a non-linear mean-field debonding model (NMFDM) combining a mean-field model and a fibre–matrix interface debonding model, is developed to simulate UD composites under consideration of AAMP, fibre–matrix interface damage and progressive failure. AAMP is considered by using so-called stress mode factor, which is expressed in terms of basic invariants of the matrix deviatoric stress tensor and is used as an indicator for detection of differences in the loading mode. The material behaviour of UD composites with imperfect interface is assumed identical as for perfect interface and stiffness reduced fibres. Progressive failure criteria are established with consideration of fibre breakage and matrix crack for different fibre orientations. As a representative example for the NMFDM, a C30/E201 UD composite is studied. To verify the model, experiments are conducted on polymers, carbon fibres and UD CFRPs. Finally, the model is applied to simulate a perforated CFRP laminate, which shows excellent prediction ability on deformation, debonding and progressive failure.

A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures

A. Henkes, I. Caylak, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2021), 114070

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A non-equilibrium thermodynamic framework for viscoplasticity incorporating dynamic recrystallization at large strains

R. Mahnken, H. Westermann, International Journal of Plasticity (2021), 102988

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On the Thermodynamics of Dynamic Recrystallization for Viscoplasticity at Large Strains

H. Westermann, R. Mahnken, in: 14th WCCM-ECCOMAS Congress, 2021

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Fuzzy and stochastic approach applied to rubber like materials

E. Penner, I. Caylak, R. Mahnken, A. Dridger, Safety and Reliability (2021), pp. 1-19

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Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters

I. Caylak, E. Penner, R. Mahnken, Computer Methods in Applied Mechanics and Engineering (2020), 113439

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A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics

I. Caylak, E. Penner, R. Mahnken, PAMM (2019)

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Damage simulation of fiber reinforced composites using mean‐field homogenization methods

P. Lenz, R. Mahnken, PAMM (2019)

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Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells

X. Ju, R. Mahnken, PAMM (2019)

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Lehrbuch der Technischen Mechanik - Band 2: Elastostatik

R. Mahnken, 2019

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A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics

E. Penner, I. Caylak, A. Dridger, R. Mahnken, Mathematics and Mechanics of Complex Systems (2019), pp. 99-129

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Transformation strains for bainitic variant evolution in steel

U. Ehlenbröker, M. Petersmann, T. Antretter, R. Mahnken, PAMM (2018), pp. 587-588

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The effective shear modulus for ann-layered composite sphere

P. Lenz, C. Dammann, R. Mahnken, PAMM (2018), pp. 609-610

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Derivation of an n-layered composite sphere model for thermo-chemo-mechanical effective properties

C. Dammann, R. Mahnken, P. Lenz, PAMM (2018), pp. 581-582

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A least squares approach for effective shear properties in an $${{\varvec{n}}}$$ n -layered sphere model

R. Mahnken, P. Lenz, C. Dammann, Archive of Applied Mechanics (2018), pp. 2081-2099

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Unschärfe in der Simulation im Kontext von Sicherheitsdiskursen

A. Dridger, R. Mahnken, in: Wissenschaft im Angesicht »großer gesellschaftlicher Herausforderungen«, 2018

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A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations

C. Cheng, R. Mahnken, International Journal of Solids and Structures (2018), pp. 1-17

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(n)- AND (n + 1)-LAYERED COMPOSITE SPHERE MODELS FOR THERMO-CHEMO-MECHANICAL EFFECTIVE PROPERTIES

R. Mahnken, C. Dammann, P. Lenz, International Journal for Multiscale Computational Engineering (2017), pp. 295-322

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Thermo-chemo-mechanical Effective Properties for Homogeneous and Heterogeneous n -Phase Mixtures with Application to Curing

C. Dammann, P. Lenz, R. Mahnken, Procedia CIRP (2017), pp. 51-56

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Thermo-Mechanical Simulation of Hard Turning with Macroscopic Models

E. Uhlmann, R. Mahnken, I.M. Ivanov, C. Cheng, in: Lecture Notes in Production Engineering, 2017

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MULTIDIMENSIONAL STOCHASTIC MATERIAL MODELING AT LARGE DEFORMATIONS CONSIDERING PARAMETER CORRELATIONS

E. Penner, I. Caylak, R. Mahnken, in: Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017), 2017

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Two accuracy improvements on nonuniform transformation field analysis for plasticity coupled to softening

X. Ju, R. Mahnken, PAMM (2016), pp. 527-528

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A thermodynamic framework for coupled multiphase field and diffusion models for lower bainite transformation

M. Düsing, R. Mahnken, PAMM (2016), pp. 321-322

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Determination of effective properties for CFRP curing coupled to viscoleasticity based on a three-scale framework

C. Dammann, R. Mahnken, PAMM (2016), pp. 517-518

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The concept of generalized stresses for computational manufacturing and beyond

R. Mahnken, C. Cheng, M. Düsing, U. Ehlenbröker, T. Leismann, GAMM-Mitteilungen (2016), pp. 229-265

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A linear elastic Fuzzy Finite Element Method with two fuzzy input parameters

A. Dridger, I. Caylak, R. Mahnken, PAMM (2016), pp. 667-668

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SFEM for rubber-like materials at large deformations

E. Penner, I. Caylak, N. Nörenberg, R. Mahnken, PAMM (2016), pp. 675-676

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PC expansion for material parameters using artificial data and statistical methods

I. Caylak, N. Nörenberg, R. Mahnken, PAMM (2016), pp. 191-192

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Macromodelling of Transformation Induced Plasticity combined with Viscoplasticity for Low-Alloy Steels

A. Schneidt, R. Mahnken, steel research international (2016), pp. 116-123

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A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor

R. Mahnken, I. Caylak, A. Dridger, A Stochastic Finite Element Method with a Deviatoric-volumetric Split for the Stochastic Linear Isotropic Elasticity Tensor (2016)

Abstract

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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.

A three-scale framework for fibre-reinforced-polymer curing part II: Mesoscopic modeling and macroscopic effective properties

R. Mahnken, C. Dammann, International Journal of Solids and Structures (2016), pp. 356-375

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Modeling of variant-interaction during bainitic phase transformation

U. Ehlenbröker, R. Mahnken, M. Petersmann, T. Antretter, IOP Conference Series: Materials Science and Engineering (2016), 012016

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A thermodynamic framework for coupled multiphase Ginzburg-Landau/Cahn-Hilliard systems for simulation of lower bainitic transformation

M. Düsing, R. Mahnken, Archive of Applied Mechanics (2016), pp. 1947-1964

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A three-scale framework for fibre-reinforced-polymer curing Part I: Microscopic modeling and mesoscopic effective properties

R. Mahnken, C. Dammann, International Journal of Solids and Structures (2016), pp. 341-355

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Extension of a multi-mechanism model: Hardness-based flow and transformation induced plasticity for austenitization

C. Cheng, R. Mahnken, International Journal of Solids and Structures (2016), pp. 127-141

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An NTFA-based homogenization framework considering softening effects

X. Ju, R. Mahnken, Mechanics of Materials (2016), pp. 106-125

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On the Design, Characterization and Simulation of Hybrid Metal-Composite Interfaces

R. Kießling, J. Ihlemann, M. Pohl, M. Stommel, C. Dammann, R. Mahnken, M. Bobbert, G. Meschut, F. Hirsch, M. Kästner, Applied Composite Materials (2016), pp. 251-269

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Lehrbuch der Technischen Mechanik - Band 1: Starrkörperstatik

R. Mahnken, 2016

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Adaptive FEM with goal-oriented error estimation and an approximation of the dual problem for inelastic problems

K. Widany, R. Mahnken, PAMM (2015), pp. 607-608

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A coupled phase-field - Cahn-Hilliard model for lower bainitic transformation

M. Düsing, R. Mahnken, PAMM (2015), pp. 285-286

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Transition from hyperelastic micromorphic to micropolar and microstrain continua

T. Leismann, R. Mahnken, PAMM (2015), pp. 329-330

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Non-linear Stochastic Finite Element

I. Caylak, A. Dridger, R. Mahnken, PAMM (2015), pp. 179-180

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Uncertainty quantification for linear elastic bodies with two fluctuating input parameters

A. Dridger, I. Caylak, R. Mahnken, PAMM (2015), pp. 551-552

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Simulation of lower bainitic transformation with the phase-field method considering carbide formation

M. Düsing, R. Mahnken, Computational Materials Science (2015), pp. 91-100

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Dual-based adaptive FEM for inelastic problems with standard FE implementations

K. Widany, R. Mahnken, International Journal for Numerical Methods in Engineering (2015), pp. 127-154

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Evaluation of different approaches for modeling phase transformations in machining simulation

V. Schulze, E. Uhlmann, R. Mahnken, A. Menzel, D. Biermann, A. Zabel, P. Bollig, I.M. Ivanov, C. Cheng, R. Holtermann, T. Bartel, Production Engineering (2015), pp. 437-449

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A Novel Finite Element Approach to Modeling Hard Turning in Due Consideration of the Viscoplastic Asymmetry Effect

E. Uhlmann, R. Mahnken, I.M. Ivanov, C. Cheng, Procedia CIRP (2015), pp. 471-476

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A multi-mechanism model for cutting simulations based on the concept of generalized stresses

C. Cheng, R. Mahnken, Computational Materials Science (2015), pp. 144-158

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Parameter identification for rubber materials with artificial spatially distributed data

N. Nörenberg, R. Mahnken, Computational Mechanics (2015), pp. 353-370

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Comparison of hyperelastic micromorphic, micropolar and microstrain continua

T. Leismann, R. Mahnken, International Journal of Non-Linear Mechanics (2015), pp. 115-127

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A macroscopic consitutive model on induced anisotropy for polymers with weighting functions

C. Dammann, R. Mahnken, PAMM (2014), pp. 387-388

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Macroscopic and mesoscopic modeling based on the concept of generalized stresses for cutting simulation

C. Cheng, R. Mahnken, E. Uhlmann, I.M. Ivanov, PAMM (2014), pp. 419-420

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Parameter identification for rubber materials with artificial higher dimensional data

R. Mahnken, N. Nörenberg, PAMM (2014), pp. 427-428

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Bainitic variant evolution in a low-alloyed steel including numerical aspects

U. Ehlenbröker, R. Mahnken, PAMM (2014), pp. 381-382

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Approximation of the dual problem for error estimation in inelastic problems

K. Widany, R. Mahnken, PAMM (2014), pp. 273-274

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Self-understanding {\" a} rte thermoplastic composites - composite materials (part 2)

H.. Heim, A.. Ries, V. Sch {\ "o} ppner, A.. Wibbeke, S. Turek, H. Damanik, R. Mahnken, C. Dammann, O. W {\ "u} nsch, .A.. Al-Baldawi, B.{.o.r.. Rohde, A. Br {\ "u} ckner-Foit, J.{.u.r. Gausemeier, I.. Gr { \ "a} {\ ss} ler, M. Petersen, Kunststoffe (2014), 104, pp. 72-78

Abstract

Based on research results from the Collaborative Research Center Transregio 30, it is shown how composites made of self-reinforced, partially crystalline or highly stretched amorphous foils and fabrics for lightweight construction applications can be produced and which properties can be achieved. A locally differential, thermo-mechanical process control can be varied very efficiently, and thus graded properties can be set in the sense of functionalization.

Self-Reinforced Thermoplastic Composites - Composite Materials (Part 1)

H.. Heim, A.. Ries, V. Sch {\ "o} ppner, A.. Wibbeke,, S.. Turek, .H. Damanik, R. Mahnken, C.. Dammann, .O. W {\ "u} nsch, A. Al-Baldawi, .B.{.o.r. Rohde, A. Br {\ "u} ckner-Foit, J.{.u.r. Gausemeier, .I. Gr { \ "a} {\ ss} ler, M. Petersen, Kunststoffe international} (2014), 104, pp. 31-35

Abstract

With self-reinforced thermoplastics, it is possible to produce composite systems that, unlike traditional fiber composite materials, do not contain any foreign fibers for reinforcement. Instead, thermoplastic fibers or tapes, for example made of PP or PE, are used in an identical matrix. This opens up a high potential for lightweight construction and, at the same time, very good recyclability.

Self-understanding {\" a} rte thermoplastic composites - composite materials (part 1)

.H. Heim, A. Ries, V. Sch {\ "o} ppner, A.. Wibbeke, S. Turek, H. Damanik, R. Mahnken, C.. Dammann, O. W {\ "u} nsch, A. Al-Baldawi, B.{. Rohde, A. Br {\ , J.{. Gausemeier, I. Gr { \ "a} {\ ss} ler, M. Petersen, Kunststoffe (2014), 104, pp. 35-39

Abstract

With self-reinforced thermoplastics, it is possible to produce composite systems that, unlike traditional fiber composite materials, do not contain any foreign fibers for reinforcement. Instead, thermoplastic fibers or tapes, for example made of PP or PE, are used in an identical matrix. This opens up a high potential for lightweight construction and, at the same time, very good recyclability.

Self-Reinforced Thermoplastic Composites - Composite Materials (Part 2)

H.. Heim, A.. Ries, V. Sch {\ "o} ppner, A.. Wibbeke, S.. Turek, H.. Damanik, R. Mahnken, .C.. Dammann, .O.. W {\ "u} nsch, A.. Al-Baldawi, B.{.o.r.. Rohde, A. Br {\ "u} ckner-Foit, J.{.u.r. Gausemeier, .I.. Gr { \ "a} {\ ss} ler, M. Petersen, Kunststoffe international (2014)

Abstract

Based on research results from the Collaborative Research Center Transregio 30, it is shown how composites made of self-reinforced, partially crystalline or highly stretched amorphous foils and fabrics for lightweight construction applications can be produced and which properties can be achieved. A locally differential, thermo-mechanical process control can be varied very efficiently, and thus graded properties can be set in the sense of functionalization.

Multi-scale modeling of bainitic phase transformation in multi-variant polycrystalline low alloy steels

R. Mahnken, A. Schneidt, T. Antretter, U. Ehlenbröker, M. Wolff, International Journal of Solids and Structures (2014), pp. 156-171

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On the simulation of strain induced anisotropy for polymers

C. Dammann, R. Mahnken, 2014

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Experimental Investigation of PC-Films Using Optical Measurements

C. Dammann, I. Caylak, R. Mahnken, International Polymer Processing (2014), pp. 260-271

Abstract

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<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>

Stabilized mixed triangular elements with area bubble functions at small and large deformations

I. Caylak, R. Mahnken, Computers & Structures (2014), pp. 172-182

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A Multi-Mechanism Model for Cutting Simulations Combining Visco-plastic Asymmetry and Phase Transformation

C. Cheng, R. Mahnken, E. Uhlmann, I.M. Ivanov, PAMM (2013), pp. 149-150

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Finite Deformation Plasticity with Void Growth and Asymmetric Compression-Tension Behavior

R. Mahnken, E. Stein, in: IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains, 2013

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Experimental Investigations on the Induced Anisotropy of Mechanical Properties in Polycarbonate Films

A. Wibbeke, V. Schöeppner, R. Mahnken, ISRN Materials Science (2013), pp. 1-8

Abstract

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<jats:p>The prime aim of this paper is to investigate, with the help of experiments, the induced anisotropy of mechanical properties in polycarbonate films. It is known that a molecular orientation in polymer materials occurs through cold-forming. In this study, cold forming is performed at room temperature on a tensile testing machine. The polycarbonate films are examined in two phases. In the first phase, the specimen is loaded, while the prestrain is varied, and in the second, it is loaded, while the material direction is varied. The main findings are that the prestrain has virtually no influence on the anisotropy and that the material direction does exert a major influence. Furthermore, this paper summarizes comparisons of anisotropic characteristic data, maximum stresses, elasticity moduli and failure strain.</jats:p>

Parameter Identification in Continuum Mechanics: From Hand-Fitting to Stochastic Modelling

R. Mahnken, in: The History of Theoretical, Material and Computational Mechanics - Mathematics Meets Mechanics and Engineering, 2013

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A multi-mechanism model for cutting simulations combining visco-plastic asymmetry and phase transformation

R. Mahnken, M. Wolff, C. Cheng, International Journal of Solids and Structures (2013), pp. 3045-3066

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Thermodynamic consistent modeling of polymer curing coupled to visco–elasticity at large strains

R. Mahnken, International Journal of Solids and Structures (2013), pp. 2003-2021

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Goal-oriented adaptive refinement for phase field modeling with finite elements

R. Mahnken, International Journal for Numerical Methods in Engineering (2013), pp. 418-440

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