@article{52217, abstract = {{AbstractPolycarbonate (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.}}, author = {{Hamdoun, Ayoub and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, publisher = {{Wiley}}, title = {{{Experimental investigations of uniaxial and biaxial cold stretching within PC‐films and bars using optical measurements}}}, doi = {{10.1002/pamm.202300114}}, year = {{2024}}, } @article{44888, author = {{Lenz, Peter and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, number = {{1}}, publisher = {{Wiley}}, title = {{{Thermo‐chemo‐mechanical modelling of a curing process combined with mean‐field homogenization methods at large strains}}}, doi = {{10.1002/pamm.202200214}}, volume = {{22}}, year = {{2023}}, } @article{44891, author = {{Westermann, Hendrik and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, number = {{1}}, publisher = {{Wiley}}, title = {{{A thermodynamic framework for the phase‐field approach considering carbide precipitation during phase transformations}}}, doi = {{10.1002/pamm.202200080}}, volume = {{22}}, year = {{2023}}, } @article{44892, author = {{Hamdoun, Ayoub and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, number = {{1}}, publisher = {{Wiley}}, title = {{{A finite strain gradient theory for viscoplasticity by means of micromorphic regularization}}}, doi = {{10.1002/pamm.202200074}}, volume = {{22}}, year = {{2023}}, } @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}}, } @inproceedings{46813, abstract = {{Modelling of dynamic systems plays an important role in many engineering disciplines. Two different approaches are physical modelling and data‐driven modelling, both of which have their respective advantages and disadvantages. By combining these two approaches, hybrid models can be created in which the respective disadvantages are mitigated, with discrepancy models being a particular subclass. Here, the basic system behaviour is described physically, that is, in the form of differential equations. Inaccuracies resulting from insufficient modelling or numerics lead to a discrepancy between the measurements and the model, which can be compensated by a data‐driven error correction term. Since discrepancy methods still require a large amount of measurement data, this paper investigates the extent to which a single discrepancy model can be trained for a physical model with additional parameter dependencies without the need for retraining. As an example, a damped electromagnetic oscillating circuit is used. The physical model is realised by a differential equation describing the electric current, considering only inductance and capacitance; dissipation due to resistance is neglected. This creates a discrepancy between measurement and model, which is corrected by a data‐driven model. In the experiments, the inductance and the capacity are varied. It is found that the same data‐driven model can only be used if additional parametric dependencies in the data‐driven term are considered as well.}}, author = {{Wohlleben, Meike Claudia and Muth, Lars and Peitz, Sebastian and Sextro, Walter}}, booktitle = {{Proceedings in Applied Mathematics and Mechanics}}, issn = {{1617-7061}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, publisher = {{Wiley}}, title = {{{Transferability of a discrepancy model for the dynamics of electromagnetic oscillating circuits}}}, doi = {{10.1002/pamm.202300039}}, year = {{2023}}, } @article{48464, abstract = {{AbstractInitial 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.}}, author = {{Westermann, Hendrik and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, number = {{2}}, publisher = {{Wiley}}, title = {{{Numerical investigations of new low‐order explicit last stage diagonal implicit Runge–Kutta schemes with the finite‐element method}}}, doi = {{10.1002/pamm.202300071}}, volume = {{23}}, year = {{2023}}, } @article{49866, abstract = {{AbstractThe 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.}}, author = {{Tchomgue Simeu, Arnold and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, publisher = {{Wiley}}, title = {{{Downwind and upwind approximations for mesh and model adaptivity of elasto‐plastic composites}}}, doi = {{10.1002/pamm.202300136}}, year = {{2023}}, } @article{52219, abstract = {{AbstractCold‐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.}}, author = {{Börger, Alexander and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, keywords = {{Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics}}, publisher = {{Wiley}}, title = {{{A micropolar model accounting for asymmetric behavior of cold‐box sand in relation to tensile and compression tests}}}, doi = {{10.1002/pamm.202300126}}, year = {{2023}}, } @article{21082, author = {{Itner, Dominik and Gravenkamp, Hauke and Dreiling, Dmitrij and Feldmann, Nadine and Henning, Bernd}}, issn = {{1617-7061}}, journal = {{PAMM}}, title = {{{Simulation of guided waves in cylinders subject to arbitrary boundary conditions for applications in material characterization}}}, doi = {{10.1002/pamm.202000232}}, year = {{2021}}, } @article{21583, author = {{Lanza, Lukas Johannes}}, issn = {{1617-7061}}, journal = {{PAMM}}, title = {{{Representation and stability of internal dynamics}}}, doi = {{10.1002/pamm.202000256}}, year = {{2021}}, } @inproceedings{34208, abstract = {{Computational homogenization is a powerful tool which allows to obtain homogenized properties of materials on the macroscale from the simulation of the underlying microstructure. The response of the microstructure is, however, strongly affected by variations in the microstructure geometry. The effect of geometry variations is even stronger in cases when the material exhibits plastic deformations. In this work we study a model of a steel alloy with arbitrary distributed elliptic voids. We model one single unit cell of the material containing one single void. The geometry of the void is not precisely known and is modeled as a variable orientation of an ellipse. Large deformations applied to the unit cell necessitate a finite elasto-plastic material model. Since the geometry variation is parameterized, we can utilize the method recently developed for stochastic problems but also applicable to all types of parametric problems — the isoparametric stochastic local FEM (SL-FEM). It is an ideal tool for problems with only a few parameters but strongly nonlinear dependency of the displacement fields on parameters. Simulations demonstrate a strong effect of parameter variation on the plastic strains and, thus, substantiate the use of the parametric computational homogenization approach.}}, author = {{Pivovarov, Dmytro and Mergheim, Julia and Willner, Kai and Steinmann, Paul}}, booktitle = {{PAMM}}, issn = {{1617-7061}}, number = {{1}}, publisher = {{Wiley}}, title = {{{Parametric FEM for computational homogenization of heterogeneous materials with random voids}}}, doi = {{10.1002/pamm.202000071}}, volume = {{20}}, year = {{2021}}, } @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{29090, author = {{Lenz, Peter and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, title = {{{Integral‐type non‐local damage simulation of composites using mean‐field homogenization methods}}}, doi = {{10.1002/pamm.202100081}}, year = {{2021}}, } @article{29091, author = {{Henkes, Alexander and Wessels, Henning and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, title = {{{Physics informed neural networks for continuum micromechanics}}}, doi = {{10.1002/pamm.202100040}}, year = {{2021}}, } @article{19120, author = {{Caylak, Ismail and Penner, Eduard and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, title = {{{A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics}}}, doi = {{10.1002/pamm.201900356}}, year = {{2019}}, }