Experimental investigations of uniaxial and biaxial cold stretching within PC‐films and bars using optical measurements - Hamdoun, Ayoub; Mahnken, Rolf (PAMM)
Abstract Polycarbonate (PC) is an amorphous polymer that is an extremely robust material with a high tenacity, and thus suitable for a lightweight construction with glass‐like transparency. Due to these advantageous properties, PC is often used in industry for example in medical devices, automotive headlamps, sporting equipment, electronics, and a variety of other products. PC is often subjected to uniaxial and biaxial loading conditions. Therefore, reliable material models have to take into account the various resulting experimental effects. For those reasons, we investigate PC specimens under uniaxial and biaxial loading by using different stretch rates and loading scenarios. In addition to that, we propose methods for optical measurement of local stretches to obtain the approximated local true stress. In future work, the displacement fields and the resulting reaction forces will be used for parameter identification of constitutive equations.
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains - Lenz, Peter; Mahnken, Rolf (International Journal of Solids and Structures)
Keywords: Applied Mathematics; Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics; General Materials Science; Modeling and Simulation

Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods - Mahnken, Rolf; Westermann, Hendrik (Computational Mechanics)
ELDIRK methods are defined to have an Explicit Last stage in the general Butcher array of Diagonal Implicit Runge-Kutta methods, with the consequence, that no additional system of equations must be solved, compared to the embedded RK method. Two general formulations for second- and third-order ELDIRK methods have been obtained recently in Mahnken [21] with specific schemes, e.g. for the embedded implicit Euler method, the embedded trapezoidal-rule and the embedded Ellsiepen method. In the first part of this paper, we investigate some general stability characteristics of ELDIRK methods, and it will be shown that the above specific RK schemes are not A-stable. Therefore, in the second part, the above-mentioned general formulations are used for further stability investigations, with the aim to construct new second- and third-order ELDIRK methods which simultaneously are A-stable. Two numerical examples are concerned with the curing for a thermosetting material and phase-field RVE modeling for crystallinity and orientation. The numerical results confirm the theoretical results on convergence order and stability.
Keywords: Applied Mathematics; Computational Mathematics; Computational Theory and Mathematics; Mechanical Engineering; Ocean Engineering; Computational Mechanics

A large deformation gradient theory for glassy polymers by means of micromorphic regularization - Hamdoun, Ayoub; Mahnken, Rolf (Archive of Applied Mechanics)
Abstract Cold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization.

Uniaxial and biaxial experimental investigation of glassy polymers - Hamdoun, Ayoub; Mahnken, Rolf (Polymer)

Experimental investigations of uniaxial and biaxial cold stretching within PC‐films and bars using optical measurements - Hamdoun, Ayoub; Mahnken, Rolf (PAMM)
Abstract Polycarbonate (PC) is an amorphous polymer that is an extremely robust material with a high tenacity, and thus suitable for a lightweight construction with glass‐like transparency. Due to these advantageous properties, PC is often used in industry for example in medical devices, automotive headlamps, sporting equipment, electronics, and a variety of other products. PC is often subjected to uniaxial and biaxial loading conditions. Therefore, reliable material models have to take into account the various resulting experimental effects. For those reasons, we investigate PC specimens under uniaxial and biaxial loading by using different stretch rates and loading scenarios. In addition to that, we propose methods for optical measurement of local stretches to obtain the approximated local true stress. In future work, the displacement fields and the resulting reaction forces will be used for parameter identification of constitutive equations.

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 - Penner, Eduard; Caylak, Ismail; Mahnken, Rolf (Fibers and Polymers)
Abstract Composite materials, such as fiber reinforced polymers, become increasingly important due to their excellent mechanical and lightweight properties. In this respect, this paper reports the characterization of a unidirectional carbon fiber reinforced polymer composite material. Particularly, the mechanical behavior of the overall composite and of the individual constituents of the composite is investigated. To this end, tensile and shear tests are performed for the composite. As a result, statistics for five transversely isotropic material parameters can be established for the composite. For the description of the mechanical properties of the constituents, tensile tests for the carbon fiber as well as for the polymer matrix are carried out. In addition, the volume fraction of fibers in the matrix is determined experimentally using an ashing technique and Archimedes’ principle. For the Young’s modulus of the fiber, the Young’s modulus and transverse contraction of the matrix, as well as the volume fraction of the constituents, statistics can be concluded. The resulting mechanical properties on both scales are useful for the application and validation of different material models and homogenization methods. Finally, in order to validate the obtained properties in the future, inhomogeneous tests were performed, once a flat plate with a hole and a flat plate with semicircular notches.
Keywords: Polymers and Plastics; General Chemical Engineering; General Chemistry

Non-local integral-type damage combined to mean-field homogenization methods for composites and its parallel implementation - Lenz, Peter; Mahnken, Rolf (Composite Structures)
Keywords: Civil and Structural Engineering; Ceramics and Composites

Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains - Lenz, Peter; Mahnken, Rolf (PAMM)
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

A Non-Linear Mean-Field Debonding Model at Large Strains for the Analysis of Fibre Kinking in Ud Composites - Cheng, Chun; Song, Chunlei; Mahnken, Rolf; Yuan, Zhipeng; Yu, Liang; Ju, Xiaozhe

A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations - Westermann, Hendrik; Mahnken, Rolf (PAMM)
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

A finite strain gradient theory for viscoplasticity by means of micromorphic regularization - Hamdoun, Ayoub; Mahnken, Rolf (PAMM)
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in elasto‐plasticity - Tchomgue Simeu, Arnold; Mahnken, Rolf (PAMM)
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

Derivation of third order Runge–Kutta methods (ELDIRK) by embedding of lower order implicit time integration schemes for local and global error estimation - Mahnken, Rolf (Computational Mechanics)
Abstract 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 Explicit Last stage in the general Butcher array of Diagonal Implicit Runge–Kutta (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.
Keywords: Applied Mathematics; Computational Mathematics; Computational Theory and Mathematics; Mechanical Engineering; Ocean Engineering; Computational Mechanics

Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind and upwind approximations - Tchomgue Simeu, Arnold; Mahnken, Rolf (XI International Conference on Adaptive Modeling and Simulation)

Numerical investigations of new low‐order explicit last stage diagonal implicit Runge–Kutta schemes with the finite‐element method - Westermann, Hendrik; Mahnken, Rolf (PAMM)
Abstract Initial value problems can be solved efficiently by means of Runge–Kutta algorithms with adaptive step size control. Diagonally implicit Runge–Kutta (DIRK) methods are the most popular class among the diverse family of Runge–Kutta algorithms. In this paper, the novel class of low‐order explicit last‐stage diagonally implicit Runge–Kutta (ELDIRK) methods are explored, which combine implicit schemes with an additional explicit evaluation as an explicit last stage. ELDIRK Butcher tableaus are used to control embedded RK methods to obtain solutions of different orders. The lower‐order solution is obtained by classical implicit RK stages and the higher‐order solution is obtained by additional explicit evaluation. As a result, a significant reduction in computational cost is achieved by skipping the iterative solution of nonlinear systems for the additional step. The examination of the heat problem and the use of the innovative Butcher tableau in the finite‐element method are the main contributions of this work. Thus, it is possible to establish adaptive step size control for the new low‐order embedded methods based on an empirical method for error estimation. Two‐dimensional simulations are used to show an appropriate algorithm for the ELDIRK schemes. The new Runge–Kutta schemes' predictions of higher‐order convergence are confirmed, and their successful outcomes are illustrated.
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

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 - Westermann, Hendrik; Mahnken, Rolf (Computer Methods in Applied Mechanics and Engineering)
Keywords: Computer Science Applications; General Physics and Astronomy; Mechanical Engineering; Mechanics of Materials; Computational Mechanics

Multiphase elasto-plastic mean-field homogenisation and its consistent linearisation - Lenz, Peter; Kreutzheide, Phil; Mahnken, Rolf (Computers & Structures)
Keywords: Computer Science Applications; Mechanical Engineering; General Materials Science; Modeling and Simulation; Civil and Structural Engineering

Downwind and upwind approximations for mesh and model adaptivity of elasto‐plastic composites - Tchomgue Simeu, Arnold; Mahnken, Rolf (PAMM)
Abstract The use of heterogeneous materials, such as composites with Prandtl‐Reuss‐type material laws, has increased in industrial praxis, making finite element modeling with homogenization techniques a well‐accepted tool. These methods are particularly advantageous to account for microstructural mechanisms which can be related to nonlinearities and time‐dependency due to elasto‐plasticity behavior. However, their advantages are diminished by increasing computational demand. The present contribution deals with the balance of accuracy and numerical efficiency of nonlinear homogenization associated with a framework of goal‐oriented adaptivity, which takes into account error accumulation over time. To this end, model adaptivity of homogenization methods is coupled to mesh adaptivity on the macro scale. Our new proposed adaptive procedure is driven by a goal‐oriented a posteriori error estimator based on duality techniques using downwind and upwind approximations. Due to nonlinearities and time‐dependency of the plasticity, the estimation of error transport and error generation is obtained with a backward‐in‐time dual method despite a high demand on memory capacity. In this contribution, the dual problem is solved with a forward‐in‐time dual method that allows estimating the full error during the resolution of the primal problem without the need for extra memory capacity. Finally, a numerical example illustrates the effectiveness of the proposed adaptive approach.
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

A micropolar model accounting for asymmetric behavior of cold‐box sand in relation to tensile and compression tests - Börger, Alexander; Mahnken, Rolf (PAMM)
Abstract Cold‐box sand (CBS) belongs to the granular materials and consists of sand and a binder. The behavior of CBS is simulated with a micropolar model, whereby the additional degree of freedom of the model describes the rotation of the sand grains. The model is used to generate a shear band under pressure for three different meshes, where the force‐displacement curves of the three meshes converge so that no mesh dependence occurs. Another requirement of the model is the consideration of asymmetric behavior for compression and tension. Due to the additional degree of freedom the implicit implementation of the micropolar continuum is very time‐consuming. Therefore, an explicit implementation is considered as an alternative possibility. This paper compares the advantages and disadvantages of both methods and the results for both calculations.
Keywords: Electrical and Electronic Engineering; Atomic and Molecular Physics; and Optics

Polymorphic uncertainty in constitutive modeling of polymer composites at different scales - Penner, Eduard

A finite strain gradient theory for viscoplasticity by means of micromorphic regularization - Hamdoun, Ayoub; Mahnken, Rolf (PAMM)
Abstract Stretching of polycarbonate films leads to the formation of shear bands in the necking zone [1]. Standard viscoplastic material models render mesh size dependent results, which requires a mathematical regularization. To this end, we present a finite strain gradient theory for a viscoplastic, isotropic material model where we extend the model presented in [2] to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom with its first gradient [3, 4]. The variable here has the meaning of a micro plastic strain, and is coupled with the macro plastic by a micro penalty term, forcing the macro‐plastic strain to be close to the micro‐plastic strain for the targeted shear band regularization effect. We have implemented the model equations as a three dimensional initial boundary value problem in an in house FE‐tool, to simulate different geometries with different thickness and to compare it the experimental tests. The analysis is performed for a uniaxial tensile geometry as well as for a biaxial tensile geometry. The numerical examples show the ability of the model to regularize the shear bands and solve the problem of localization.

Multiscale analysis of composite structures with goal-oriented mesh adaptivity and reduced order homogenization - Ju, Xiaozhe; Mahnken, Rolf; Xu, Yangjian; Liang, Lihua; Cheng, Chun; Zhou, Wangmin (Composite Structures)
Keywords: Civil and Structural Engineering; Ceramics and Composites

Strain mode-dependent weighting functions in hyperelasticity accounting for verification, validation, and stability of material parameters - Mahnken, Rolf (Archive of Applied Mechanics)
Abstract 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.
Keywords: Mechanical Engineering

Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua - Ju, Xiaozhe; Mahnken, Rolf; Xu, Yangjian; Liang, Lihua (Computational Mechanics)
Keywords: Applied Mathematics; Computational Mathematics; Computational Theory and Mathematics; Mechanical Engineering; Ocean Engineering; Computational Mechanics

Physics informed neural networks for continuum micromechanics - Henkes, Alexander; Wessels, Henning; Mahnken, Rolf (Computer Methods in Applied Mechanics and Engineering)
Keywords: Computer Science Applications; General Physics and Astronomy; Mechanical Engineering; Mechanics of Materials; Computational Mechanics

A statistically based strain energy function for polymer chains in rubber elasticity - Mahnken, Rolf; Mirzapour, Jamil (Archive of Applied Mechanics)
Keywords: Mechanical Engineering

Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp - Clemens, Robin; Barth, Enrico; Uhlmann, Eckart; Zhan, Yingjie; Caylak, Ismail; Mahnken, Rolf (SSRN Electronic Journal)
Keywords: General Earth and Planetary Sciences; General Environmental Science

NTFA-enabled goal-oriented adaptive space–time finite elements for micro-heterogeneous elastoplasticity problems - Ju, X.; Mahnken, Rolf; Xu, Y.; Liang, L. (Computer Methods in Applied Mechanics and Engineering)
Keywords: Computer Science Applications; General Physics and Astronomy; Mechanical Engineering; Mechanics of Materials; Computational Mechanics

A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics - Penner, Eduard; Caylak, Ismail; Mahnken, Rolf (Mathematics and Mechanics of Complex Systems)
Keywords: Computational Mathematics; Numerical Analysis; Civil and Structural Engineering

New low order Runge–Kutta schemes for asymptotically exact global error estimation of embedded methods without order reduction - Mahnken, Rolf (Computer Methods in Applied Mechanics and Engineering)
Keywords: Computer Science Applications; General Physics and Astronomy; Mechanical Engineering; Mechanics of Materials; Computational Mechanics

Microstructure transformations in a press hardening steel during tailored thermo‐mechanical processing - Westermann, Hendrik; Reitz, Alexander; Mahnken, Rolf; Schaper, Mirko; Grydin, Olexandr (steel research international)

Hybridprofile für Trag- und Crashstrukturen - Drossel, Welf-G; Bobbert, Mathias; Böhme, Marcus; Dammann, Christian; Dittes, Axel; Gießmann, Mina; Hühne, Christian; Ihlemann, Jörn; Kießling, Robert; Lampke, Thomas; Lenz, Peter; Mahnken, Rolf; et al. (Intrinsische Hybridverbunde für Leichtbautragstrukturen)

Constitutive modeling of viscoplasticity including phase transformations for graded thermo‐mechanical processing - Westermann, Hendrik; Reitz, Alexander; Mahnken, Rolf; Grydin, Olexandr; Schaper, Mirko (PAMM)

Damage simulation of thermo‐chemo‐elasto‐plastic fibre reinforced composites using mean‐field homogenization methods - Lenz, Peter; Mahnken, Rolf (PAMM)

An uncertainty model for the curing process of transversely fiber reinforced plastics - Penner, Eduard; Caylak, Ismail; Mahnken, Rolf (PAMM)

Constitutive modeling of dynamic recrystallization coupled to viscoplasticity - Westermann, Hendrik; Mahnken, Rolf (PAMM)

A deep learning driven uncertain full‐field homogenization method - Henkes, Alexander; Caylak, Ismail; Mahnken, Rolf (PAMM)

A non-equilibrium thermodynamic framework for viscoplasticity incorporating dynamic recrystallization at large strains - Mahnken, Rolf; Westermann, Hendrik (International Journal of Plasticity)

Fuzzy and stochastic approach applied to rubber like materials - Penner, Eduard; Caylak, Ismail; Mahnken, Rolf; Dridger, Alex (Safety and Reliability)

On the Thermodynamics of Dynamic Recrystallization for Viscoplasticity at Large Strains - Westermann, Hendrik; Mahnken, Rolf (14th WCCM-ECCOMAS Congress)

Non-linear mean-field modelling of UD composite laminates accounting for average asymmetric plasticity of the matrix, debonding and progressive failure - Cheng, C.; Wang, Z.; Jin, Z.; Ju, X.; Schweizer, Swetlana; Tröster, Thomas; Mahnken, Rolf (Composites Part B: Engineering)
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.
Keywords: Non-linear mean-field homogenization Average asymmetric plasticity of matrix Fibre–matrix interface debonding Micro-mechanical FE-simulation Progressive failure

A general framework for mean-field homogenization of multi-layered linear elastic composites subjected to thermal and curing induced strains - Lenz, Peter; Mahnken, Rolf (International Journal of Solids and Structures)

A nonuniform transformation field analysis for composites with strength difference effects in elastoplasticity - Ju, X.; Mahnken, Rolf; Xu, Y.; Liang, L.; Zhou, W. (International Journal of Solids and Structures)

A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures - Henkes, Alexander; Caylak, Ismail; Mahnken, Rolf (Computer Methods in Applied Mechanics and Engineering)

A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations - Cheng, C.; Mahnken, Rolf (Archive of Applied Mechanics)

Goal-oriented mesh adaptivity for inverse problems in linear micromorphic elasticity - Ju, X.; Mahnken, Rolf; Liang, L.; Xu, Y. (Computers & Structures)

Integral‐type non‐local damage simulation of composites using mean‐field homogenization methods - Lenz, Peter; Mahnken, Rolf (PAMM)

Physics informed neural networks for continuum micromechanics - Henkes, Alexander; Wessels, Henning; Mahnken, Rolf (PAMM)

Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters - Caylak, Ismail; Penner, Eduard; Mahnken, Rolf (Computer Methods in Applied Mechanics and Engineering)

A possibilistic finite element method for sparse data - Dridger, A.; Caylak, Ismail; Mahnken, R.; Penner, Eduard (Safety and Reliability)

"A possibilistic finite element method for sparse data" - Dridger, A.; Caylak, I.; Mahnken, R.; Penner, E. (Safety and Reliability)

"Goal-oriented h-type adaptive finite elements for micromorphic elastoplasticity" - Ju, Xiaozhe; Mahnken, Rolf (Computer Methods in Applied Mechanics and Engineering)

"Optimization with constraints considering polymorphic uncertainties" - Mäck, Markus; Caylak, Ismail; Edler, Philipp; Freitag, Steffen; Hanss, Michael; Mahnken, Rolf; Meschke, Günther; Penner, Eduard (GAMM-Mitteilungen)

Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity - Mahnken, Rolf; Ju, Xiaozhe (International Journal for Numerical Methods in Engineering)

Simulation of a resin transfer molding process using a phase field approach within the theory of porous media - Dammann, Christian; Mahnken, Rolf (Composites Part A: Applied Science and Manufacturing)

"Goal-oriented adaptivity on mean-field and full-field homogenization methods considering hierarchical unit cells" - Ju, X.; Mahnken, R. (PAMM)

"Damage simulation of fiber reinforced composites using mean-field homogenization methods" - Lenz, P.; Mahnken, R. (PAMM)

Optimization with constraints considering polymorphic uncertainties - Mäck, Markus; Caylak, Ismail; Edler, Philipp; Freitag, Steffen; Hanss, Michael; Mahnken, Rolf; Meschke, Günther; Penner, Eduard (GAMM-Mitteilungen)

A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics - Penner, Eduard; Caylak, Ismail; Dridger, Alex; Mahnken, Rolf (Mathematics and Mechanics of Complex Systems)

A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics - Caylak, Ismail; Penner, Eduard; Mahnken, Rolf (PAMM)

Model adaptivity on mean‐field and full‐field homogenization methods considering hierarchical unit cells - Ju, Xiaozhe; Mahnken, Rolf (PAMM)

Damage simulation of fiber reinforced composites using mean‐field homogenization methods - Lenz, Peter; Mahnken, Rolf (PAMM)

Lehrbuch der Technischen Mechanik - Band 2: Elastostatik - Mahnken, Rolf

Adaptive Finite Element Methods for Direct and Inverse Problems in Nonlinear Solid Mechanics - Widany, Kai-Uwe

Experimental Characterization and Constitutive Modeling of Reinforced Thermoplastic and Thermosetting Polymers - Damman, Christian

Adaptive Methods in the Mechanics of Heterogeneous Materials - Ju, Xiaozhe

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

„A coupled phase field/diffusion model for upper and lower bainitic transformation” - Düsing, M.; Mahnken, R. (International Journal of Solids and Structures)
Bainite is a steel microstructure consisting of three phases, bainitic ferrite, austenite and carbides. It forms in two different morphologies, upper and lower bainite, where different diffusion mechanisms are dominant. The aim of this work is to simulate both transformations within a unified model. To this end, we extend an own previously published model for lower bainite with diffusion across the phase interface. As a central idea we introduce weighted Helmholtz energy functions and a weighted mobility tensor, respectively. The individual Helmholtz energy functions and mobility terms are related to the different diffusion mechanisms which are responsible for the formation of both morphologies. Two representative examples illustrate the capability of the coupled phase field/diffusion model and show the expected behaviour.
Keywords: Coupled phase field/diffusion model; Bainite; Multiphase field method; Cahn–Hilliard diffusion; Diffusion across the interface; Lower bainitic transformation; Upper bainitic transformation; Thermodynamic framework; Microforce balance

"A least squares approach for effective shear properties in an n-layered sphere model" - Mahnken, Rolf; Lenz, Peter; Dammann, Christian (Archive of Applied Mechanics)

"Sequential biaxial stretching of polycarbonate-films for characterization of strain-induced anisotropy" - Dammann, Christian; Caylak, Ismail; Mahnken, Rolf (GAMM-Mitteilungen)

A multivariate stochastic material model with correlated material parameters - Penner, Eduard; Caylak, Ismail; Mahnken, Rolf (PAMM)

"Error-controlled homogenization for a class of linear elastic composite problems" - Ju, Xiaozhe; Mahnken, Rolf (PAMM)

"A coupled phase transformation and solute diffusion model for bainitic transformation" - Düsing, Martin; Mahnken, Rolf (PAMM)

"A fuzzy finite element method for sparse experimental data based on a possibilistic approach" - Dridger, Alex; Caylak, Ismail; Mahnken, Rolf (PAMM)

"Goal-oriented adaptivity for parameter identification in linear micromorphic elasticity" - Ju, Xiaozhe; Mahnken, Rolf (PAMM)

Goal-oriented adaptivity for linear elastic micromorphic continua based on primal and adjoint consistency analysis - Ju, X.; Mahnken, R. (International Journal for Numerical Methods in Engineering)

"Stochastic hyperelastic modeling considering dependency of material parameters" - Caylak, I.; Dridger, A.; Mahnken, R. (Computational Mechanics)

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

„On the connection between possibility theory and probability box theory in structural mechanics“ - Dridger, A.; Caylak, I.; Mahnken, R.; Penner, E. (13th World Congress in Computational Mechanics)

"Possibilistic and stochastic analysis using for rubber-like materials" - Penner, Eduard; Caylak, Ismail; Dridger, Alex; Mahnken, Rolf (PAMM)

"A fuzzy-stochastic model for transversely fiber reinforced plastics" - Caylak, Ismail; Penner, Eduard; Dridger, Alex; Mahnken, Rolf (PAMM)

"Simulation of upper and lower bainitic transformation with a coupled phase field/diffusion/deformation framework" - Düsing, Martin; Mahnken, Rolf (PAMM)

A coupled phase field/diffusional/mechanical framework for simulation of upper and lower bainitic transformation - Düsing, Martin; Mahnken, Rolf (International Journal of Solids and Structures)

On the connection between possibility theory and probability box theory in structural mechanics - Dridger, Alex; Caylak, Ismail; Mahnken, Rolf; Penner, Eduard (13th World Congress in Computational Mechanics)

Stochastic hyperelastic modeling considering dependency of material parameters - Caylak, Ismail; Penner, Eduard; Dridger, Alex; Mahnken, Rolf (Computational Mechanics)

A fuzzy‐stochastic model for transversely fiber reinforced plastics - Caylak, Ismail; Penner, Eduard; Dridger, Alex; Mahnken, Rolf (PAMM)

A least squares approach for effective shear properties in an $${{\varvec{n}}}$$ n -layered sphere model - Mahnken, Rolf; Lenz, Peter; Dammann, Christian (Archive of Applied Mechanics)

Derivation of an n-layered composite sphere model for thermo-chemo-mechanical effective properties - Dammann, Christian; Mahnken, Rolf; Lenz, Peter (PAMM)

Unschärfe in der Simulation im Kontext von Sicherheitsdiskursen - Dridger, Alex; Mahnken, Rolf (Wissenschaft im Angesicht »großer gesellschaftlicher Herausforderungen«)

Transformation strains for bainitic variant evolution in steel - Ehlenbröker, Ulrich; Petersmann, Manuel; Antretter, Thomas; Mahnken, Rolf (PAMM)

The effective shear modulus for ann-layered composite sphere - Lenz, Peter; Dammann, Christian; Mahnken, Rolf (PAMM)

A multi-mechanism model for cutting simulation: A Ginzburg-Landau type phase gradient and numerical implementations - Cheng, C.; Mahnken, Rolf (International Journal of Solids and Structures)

Possibilistic and stochastic analysis using for rubber‐like materials - Penner, Eduard; Caylak, Ismail; Dridger, Alex; Mahnken, Rolf (PAMM)

A multivariate stochastic material model with correlated material parameters - Penner, Eduard; Caylak, Ismail; Mahnken, Rolf (PAMM)

Shear strength and failure behaviour of laser nano-structured and conventionally pre-treated interfaces in intrinsically manufactured CFRP-steel hybrids - Zinn, Carolin; Bobbert, Mathias; Dammann, Christian; Wang, Zheng; Tröster, Thomas; Mahnken, Rolf; Meschut, Gerson; Schaper, Mirko (Composites Part B: Engineering)

"A variational formulation for fuzzy analysis in continuum mechanics" - Mahnken, Rolf (Mathematics and Mechanics of complex systems)
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.
Keywords: fuzzy analysis; α-level optimization; quantities of interest; optimization with simple constraints; large strain elasticity; large strain elastoplasticity

,,Identification of Material Parameters for Constitutive Equations “ - Mahnken, Rolf (Encyclopedia of Computational Mechanics)

"A POSSIBILISTIC APPROACH FOR LINEAR ISOTROPIC ELASTICITY USING THE FUZZY FINITE ELEMENT METHOD" - Dridger, Alex; Caylak, Ismail; Mahnken, Rolf (Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2017))

"A coupled phase field/diffusion model for upper and lower bainitic transformation" - Düsing, Martin; Mahnken, Rolf (International Journal of Solids and Structures)