@article{63676,
abstract = {{
Purpose
The purpose of this paper is to develop new methods of error representation to improve the accuracy and numerical efficiency of a posteriori and goal-oriented adaptive framework of elastoplasticity with Prandtl–Reuss type material laws.
Design/methodology/approach
To obtain new methods of error representation for a posteriori and goal-oriented error estimators, weak forms of primal and dual problems are investigated starting with the initial boundary value problem (IBVP). Then, we approximate both problems using temporal discretization. Additionally, we introduce a secant form considering the nonlinearity of elasto-plastic constitutive equations, which is approximated by a tangent form. Finally, we obtain numerical primal and dual solutions and their corresponding error approximations of discretized primal and dual problems, allowing to build several goal-oriented a posteriori error estimators on temporal and spatial adaptive refinement by inserting primal solutions, dual solutions and their error approximations as arguments in residuals of both weak forms as well as in the secant form of the bilinear residual.
Findings
An elasto-plastic material is investigated in a framework of goal-oriented error estimator by using separately several methods of error representation to deal with either temporal or spatial adaptive refinement, as well as with both refinements leading to an effective reduction of computational effort. Specifically, new error representations based on goal-oriented error estimators are presented and obtained from primal and dual residuals, which use only primal solutions or only dual solutions or a combination of primal and dual solutions as arguments. Error representations obtained from primal residuals and evaluated using only primal arguments do not require the formulation of a dual problem.
Research limitations/implications
The effectiveness of the different proposed methods is illustrated by an example of a perforated sheet for adaptive spatial refinement where new mesh adaptation methods of error representation are compared against existing mesh adaptation methods such as uniform mesh refinement, mesh refinement based on gradient indicators and adjoint-based methods in literature. The framework generates a balanced mesh consisting of fine, medium and coarse elements for accurate results, avoiding a numerically costly simulation with only fine elements.
Originality/value
All new proposed methods of error representation successfully estimate actual errors during mesh adaptivity. Furthermore, the proposed methods of error representation allow us to obtain significant reduction and equidistribution of spatial error at the end of the mesh adaptivity process. Their application to a framework of goal-oriented error estimation due to time and mesh adaptivity remains an open issue.
}},
author = {{Tchomgue Simeu, Arnold and Caylak, Ismail and Ostwald, Richard}},
issn = {{0264-4401}},
journal = {{Engineering Computations}},
pages = {{1--40}},
publisher = {{Emerald}},
title = {{{Error representations for goal-oriented a posteriori error estimation in elasto-plasticity with applications to mesh adaptivity}}},
doi = {{10.1108/ec-12-2023-0975}},
year = {{2026}},
}
@article{65037,
abstract = {{ABSTRACT
Homogenization methods simulate heterogeneous materials like composites effectively, but high computational demands can offset their benefits. This work balances accuracy and efficiency by assessing model and discretization errors of the finite element method (FEM) through an adaptive numerical scheme. Two model hierarchies are introduced, combining mean‐field and full‐field methods, and nonuniform transformation field analysis (NTFA) with full‐field methods. Both hierarchies use a full‐field FEM solution of the representative volume element (RVE) as reference. The study highlights the benefits of using effective constitutive equations from mean‐field and full‐field methods as well as NTFA methods, with a goal‐oriented a posteriori error estimator based on duality techniques controlling mesh and model errors in a forwards‐in‐time manner.}},
author = {{Simeu, Arnold Tchomgue and Caylak, Ismail and Ostwald, Richard}},
issn = {{0029-5981}},
journal = {{International Journal for Numerical Methods in Engineering}},
number = {{6}},
publisher = {{Wiley}},
title = {{{Mesh and Model Adaptivity for Multiscale Elastoplastic Models With Prandtl‐Reuss Type Material Laws}}},
doi = {{10.1002/nme.70294}},
volume = {{127}},
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{61138,
author = {{Zhan, Yingjie and Caylak, Ismail and Ostwald, Richard and Barth, Enrico and Uhlmann, Eckart}},
issn = {{2520-8160}},
journal = {{Multiscale and Multidisciplinary Modeling, Experiments and Design}},
number = {{10}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Damage-incorporated four-step mean-field method for simulating CFRP machining: a novel algorithmic approach}}},
doi = {{10.1007/s41939-025-01026-4}},
volume = {{8}},
year = {{2025}},
}
@article{42165,
abstract = {{AbstractComposite 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.}},
author = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
issn = {{1229-9197}},
journal = {{Fibers and Polymers}},
keywords = {{Polymers and Plastics, General Chemical Engineering, General Chemistry}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{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}}},
doi = {{10.1007/s12221-023-00122-x}},
year = {{2023}},
}
@article{41485,
author = {{Clemens, Robin and Barth, Enrico and Uhlmann, Eckart and Zhan, Yingjie and Caylak, Ismail and Mahnken, Rolf}},
issn = {{1556-5068}},
journal = {{SSRN Electronic Journal}},
keywords = {{General Earth and Planetary Sciences, General Environmental Science}},
publisher = {{Elsevier BV}},
title = {{{Effects on Process Forces of Individual Milling Tool Edges Depending on the Cutting Angle and Cutting Speed When Milling Cfrp}}},
doi = {{10.2139/ssrn.4259246}},
year = {{2022}},
}
@article{34075,
author = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf}},
issn = {{2325-3444}},
journal = {{Mathematics and Mechanics of Complex Systems}},
keywords = {{Computational Mathematics, Numerical Analysis, Civil and Structural Engineering}},
number = {{1}},
pages = {{21--50}},
publisher = {{Mathematical Sciences Publishers}},
title = {{{A polymorphic uncertainty model for the curing process of transversely fiber-reinforced plastics}}},
doi = {{10.2140/memocs.2022.10.21}},
volume = {{10}},
year = {{2022}},
}
@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{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{21681,
author = {{Penner, Eduard and Caylak, Ismail and Mahnken, Rolf and Dridger, Alex}},
issn = {{0961-7353}},
journal = {{Safety and Reliability}},
pages = {{1--19}},
title = {{{Fuzzy and stochastic approach applied to rubber like materials}}},
doi = {{10.1080/09617353.2020.1858678}},
year = {{2021}},
}
@article{24376,
author = {{Henkes, Alexander and Caylak, Ismail and Mahnken, Rolf}},
issn = {{0045-7825}},
journal = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{{A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures}}},
doi = {{10.1016/j.cma.2021.114070}},
year = {{2021}},
}
@article{24374,
author = {{Caylak, Ismail and Penner, Eduard and Mahnken, Rolf}},
issn = {{0045-7825}},
journal = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{{Mean-field and full-field homogenization with polymorphic uncertain geometry and material parameters}}},
doi = {{10.1016/j.cma.2020.113439}},
year = {{2020}},
}
@article{19297,
author = {{Dridger, A. and Caylak, Ismail and Mahnken, R. and Penner, Eduard}},
issn = {{0961-7353}},
journal = {{Safety and Reliability}},
pages = {{58--82}},
title = {{{A possibilistic finite element method for sparse data}}},
doi = {{10.1080/09617353.2018.1552477}},
year = {{2019}},
}
@article{19300,
author = {{Mäck, Markus and Caylak, Ismail and Edler, Philipp and Freitag, Steffen and Hanss, Michael and Mahnken, Rolf and Meschke, Günther and Penner, Eduard}},
issn = {{0936-7195}},
journal = {{GAMM-Mitteilungen}},
title = {{{Optimization with constraints considering polymorphic uncertainties}}},
doi = {{10.1002/gamm.201900005}},
year = {{2019}},
}
@article{19122,
author = {{Penner, Eduard and Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}},
issn = {{2325-3444}},
journal = {{Mathematics and Mechanics of Complex Systems}},
pages = {{99--129}},
title = {{{A polynomial chaos expanded hybrid fuzzy-stochastic model for transversely fiber reinforced plastics}}},
doi = {{10.2140/memocs.2019.7.99}},
year = {{2019}},
}
@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}},
}
@inproceedings{19306,
author = {{Dridger, Alex and Caylak, Ismail and Mahnken, Rolf and Penner, Eduard}},
booktitle = {{13th World Congress in Computational Mechanics }},
location = {{New York}},
title = {{{On the connection between possibility theory and probability box theory in structural mechanics}}},
year = {{2018}},
}
@article{19308,
author = {{Caylak, Ismail and Penner, Eduard and Dridger, Alex and Mahnken, Rolf}},
issn = {{0178-7675}},
journal = {{Computational Mechanics}},
pages = {{1273--1285}},
title = {{{Stochastic hyperelastic modeling considering dependency of material parameters}}},
doi = {{10.1007/s00466-018-1563-z}},
year = {{2018}},
}
@article{19303,
author = {{Caylak, Ismail and Penner, Eduard and Dridger, Alex and Mahnken, Rolf}},
issn = {{1617-7061}},
journal = {{PAMM}},
title = {{{A fuzzy‐stochastic model for transversely fiber reinforced plastics}}},
doi = {{10.1002/pamm.201800121}},
year = {{2018}},
}
@article{19124,
author = {{Penner, Eduard and Caylak, Ismail and Dridger, Alex and Mahnken, Rolf}},
issn = {{1617-7061}},
journal = {{PAMM}},
title = {{{Possibilistic and stochastic analysis using for rubber‐like materials}}},
doi = {{10.1002/pamm.201800153}},
year = {{2018}},
}