@article{64187, abstract = {{Carbon fiber-reinforced plastics (CFRPs) have become increasingly significant in recent decades due to their remarkable mechanical properties and lightweight nature. This study aims to advance the understanding and simulation of CFRP behavior through the development of a hyperelastic-plastic-damage homogenization method combined with mean-field theory. The material responses of both the fiber and matrix are modeled using strain energy functions that account for damage evolution, while a complete linearization of the homogenization process is derived to ensure the consistent implementation of the Newton–Raphson iteration scheme in large deformation simulations. The innovative aspect of this work lies in the constitutive linearization for the hyperelastic-plastic-damage formulation within a mean-field homogenization framework, providing an efficient Newton algorithm for modeling the nonlinear behavior of CFRP. A failure criterion for the hyperelastic model of fibers is introduced, along with a damage saturation variable in rate form for the matrix, effectively capturing damage evolution. Through discrete formulations for the homogenization, the proposed model’s capability is demonstrated via three numerical examples and validated against experimental investigations, proving its effectiveness and reliability in simulating CFRP damage.}}, author = {{Zhan, Yingjie and Caylak, Ismail and Ostwald, Richard and Mahnken, Rolf and Barth, Enrico and Uhlmann, Eckart}}, issn = {{1081-2865}}, journal = {{Mathematics and Mechanics of Solids}}, publisher = {{SAGE Publications}}, title = {{{A fully implicit mean-field damage formulation with consistent linearization at large deformations}}}, doi = {{10.1177/10812865261420809}}, year = {{2026}}, } @article{65266, abstract = {{ABSTRACT This work is concerned with the modeling of a cold‐box sand, a composition of sand grains and a resin binder. To this end, experiments are performed, which show the following characteristics: localization phenomena in the form of a shear band, softening behavior in the force‐displacement curve, and asymmetric behavior for compression and tension. To model this complex material behavior, a micromorphic continuum is used. In the present contribution, we focus on the linear‐elastic regime and demonstrate the identifiability of micromorphic material parameters under deliberately induced inhomogeneous deformation states. In addition to the degrees of freedom of a classical continuum, the micromorphic model has additional degrees of freedom, introduced here in a phenomenological sense to represent kinematically enriched deformation modes associated with the granular microstructure. Accordingly, the micromorphic fields are not interpreted as a separate physical scale (e.g., “binder” vs. “grains”), but as an effective continuum description at the specimen scale. This contribution addresses parameter identification for a micromorphic model of cold‐box sand, with a clear separation between homogeneous deformation states governing classical elastic parameters and inhomogeneous states required to activate and identify micromorphic length‐scale parameters. The main challenge lies in identifying the micro material parameters. To determine these, the corresponding gradient terms in the constitutive formulation must be triggered via properly tuned experiments. Micro‐parameter identification is demonstrated using synthetic data generated from a boundary‐value problem with inhomogeneous displacement fields. The chosen benchmark enables controlled activation of gradient terms and thereby renders optimization‐based identification of micromorphic parameters feasible. The synthetic example is deliberately chosen to assess feasibility and identifiability under controlled conditions, thereby isolating micromorphic identifiability aspects from experimental uncertainties. The novelty of the contribution lies in explicitly linking micromorphic parameter identifiability to kinematic inhomogeneity, and in demonstrating this link within a tractable forward– inverse setting for a linear‐elastic micromorphic continuum.}}, author = {{Börger, Alexander and Mahnken, Rolf and Caylak, Ismail and Ostwald, Richard}}, issn = {{1617-7061}}, journal = {{Proceedings in Applied Mathematics and Mechanics}}, number = {{2}}, publisher = {{Wiley}}, title = {{{Aspects of Parameter Identification for a Micromorphic Continuum applied to a Cold‐Box Sand}}}, doi = {{10.1002/pamm.70093}}, volume = {{26}}, year = {{2026}}, } @article{65458, author = {{Hamdoun, Ayoub and Mahnken, Rolf and Ostwald, Richard}}, journal = {{European Journal of Mechanics / A Solids}}, title = {{{A gradient-damage model for amorphous glassy polymers: Consistent formulation of viscoplasticity and damage evolution in a micromorphic framework}}}, doi = {{https://doi.org/10.1016/j.euromechsol.2026.106137}}, year = {{2026}}, } @article{65491, abstract = {{Abstract The micropolar continuum is a special case of a micromorphic material model and has additional degrees of freedom in the form of microrotations compared to the classical continuum. With the micropolar model, size effects can be considered and the boundary value problem can be regularized when localization effects occur. In order to map the microrotations, an additional strain measure and an additional stress are introduced. For simulation of plasticity, it is possible to define one yield function, and thus one plastic multiplier as well as one equivalent plastic strain occur. This approach is known as the single-surface plasticity approach. The macro- and micro-stresses are coupled in a common flow function. On the other hand, there is the so-called double-surface plasticity when one yield function, one plastic multiplier, and one equivalent plastic strain, respectively, are introduced for each of the macro- and micro-variables. The coupling of the macro- and micro-variables is established by a possible coupling of both yield functions. The purpose of this paper is to compare both approaches and to identify similarities and differences.}}, author = {{Börger, Alexander and Mahnken, Rolf}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, number = {{5}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Single-surface and double-surface plasticity for micropolar continuum}}}, doi = {{10.1007/s00419-026-03049-w}}, volume = {{96}}, year = {{2026}}, } @article{60124, author = {{Westermann, Hendrik and Mahnken, Rolf}}, issn = {{0020-7683}}, journal = {{International Journal of Solids and Structures}}, publisher = {{Elsevier BV}}, title = {{{Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua}}}, doi = {{10.1016/j.ijsolstr.2025.113465}}, year = {{2025}}, } @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{52218, author = {{Lenz, Peter and Mahnken, Rolf}}, issn = {{0020-7683}}, journal = {{International Journal of Solids and Structures}}, keywords = {{Applied Mathematics, Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, General Materials Science, Modeling and Simulation}}, publisher = {{Elsevier BV}}, title = {{{Multiscale simulation of polymer curing of composites combined mean-field homogenisation methods at large strains}}}, doi = {{10.1016/j.ijsolstr.2023.112642}}, volume = {{290}}, year = {{2024}}, } @article{52233, abstract = {{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.}}, author = {{Mahnken, Rolf and Westermann, Hendrik}}, issn = {{0178-7675}}, journal = {{Computational Mechanics}}, keywords = {{Applied Mathematics, Computational Mathematics, Computational Theory and Mathematics, Mechanical Engineering, Ocean Engineering, Computational Mechanics}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Construction of A-stable explicit last-stage diagonal implicit Runge–Kutta (ELDIRK) methods}}}, doi = {{10.1007/s00466-024-02442-y}}, year = {{2024}}, } @article{56212, abstract = {{AbstractTo increase the quality of computational results for heterogeneous materials like fiber‐reinforced composites with Prandtl–Reuss‐type material laws, goal‐oriented measures of the adaptive finite element method coupled to model adaptivity is established. The former is an adaptive mesh refinement on the macroscale, which allows to control the spatial discretization errors. The latter is an efficient combination of a numerically low cost nonuniform transformation field analysis (NTFA) and numerically high cost full‐field elasto‐plastic homogenization methods on the microscale. The present contribution deals with the application of the concept of downwind and upwind approximations to a goal‐oriented a posteriori error estimator based on duality techniques by means of reduced order homogenization schemes like NTFA, and with accuracy and numerical efficiency of the proposed goal‐oriented adaptive framework. NTFA consists of an offline phase and an online phase. During the offline phase, some relevant information of the micro system under consideration is precomputed allowing a reduced set of equations to be solved in the online phase. Thus, NTFA leads to a quite efficient homogenization method but less accurate compared to the full‐field homogenization method which is characterized with a high computational demand for accounting nonlinear microstructural mechanisms. Due to nonlinearities and time‐dependency of plasticity, the estimation of error transport and error generation are 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. Several numerical examples illustrate the effectiveness of the proposed adaptive approach based on downwind and upwind approximations.}}, author = {{Tchomgue Simeu, Arnold and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, publisher = {{Wiley}}, title = {{{Mesh‐ and model adaptivity for NTFA and full‐field elasto‐plastic homogenization based on downwind and upwind approximations}}}, doi = {{10.1002/pamm.202400074}}, year = {{2024}}, } @article{54281, 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}}, 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{54279, author = {{Hamdoun, Ayoub and Mahnken, Rolf}}, issn = {{0032-3861}}, journal = {{Polymer}}, publisher = {{Elsevier BV}}, title = {{{Uniaxial and biaxial experimental investigation of glassy polymers}}}, doi = {{10.1016/j.polymer.2024.126981}}, volume = {{299}}, year = {{2024}}, } @article{54280, abstract = {{AbstractCold 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.}}, author = {{Hamdoun, Ayoub and Mahnken, Rolf}}, issn = {{0939-1533}}, journal = {{Archive of Applied Mechanics}}, number = {{5}}, pages = {{1221--1242}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{A large deformation gradient theory for glassy polymers by means of micromorphic regularization}}}, doi = {{10.1007/s00419-024-02570-0}}, volume = {{94}}, year = {{2024}}, } @article{56721, author = {{Mahnken, Rolf and Tchomgue Simeu, Arnold}}, issn = {{0045-7825}}, journal = {{Computer Methods in Applied Mechanics and Engineering}}, publisher = {{Elsevier BV}}, title = {{{Downwind and upwind approximations for primal and dual problems of elasto-plasticity with Prandtl–Reuss type material laws}}}, doi = {{10.1016/j.cma.2024.117277}}, volume = {{432}}, year = {{2024}}, } @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{48465, author = {{Westermann, Hendrik and Mahnken, Rolf}}, issn = {{0045-7825}}, journal = {{Computer Methods in Applied Mechanics and Engineering}}, keywords = {{Computer Science Applications, General Physics and Astronomy, Mechanical Engineering, Mechanics of Materials, Computational Mechanics}}, publisher = {{Elsevier BV}}, title = {{{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}}}, doi = {{10.1016/j.cma.2023.116545}}, volume = {{418}}, year = {{2023}}, } @article{48673, author = {{Lenz, Peter and Kreutzheide, Phil and Mahnken, Rolf}}, issn = {{0045-7949}}, journal = {{Computers & Structures}}, keywords = {{Computer Science Applications, Mechanical Engineering, General Materials Science, Modeling and Simulation, Civil and Structural Engineering}}, publisher = {{Elsevier BV}}, title = {{{Multiphase elasto-plastic mean-field homogenisation and its consistent linearisation}}}, doi = {{10.1016/j.compstruc.2023.107160}}, volume = {{290}}, 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}}, } @phdthesis{52649, author = {{Penner, Eduard}}, publisher = {{Shaker Verlag}}, title = {{{Polymorphic uncertainty in constitutive modeling of polymer composites at different scales}}}, doi = {{10.2370/9783844093322}}, year = {{2023}}, } @article{54282, abstract = {{AbstractStretching 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.}}, author = {{Hamdoun, Ayoub and Mahnken, Rolf}}, issn = {{1617-7061}}, journal = {{PAMM}}, 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}}, }