@article{65037,
  abstract     = {{<jats:title>ABSTRACT</jats:title>
                  <jats:p>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.</jats:p>}},
  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{13805,
  author       = {{Mahnken, Rolf and Ju, Xiaozhe}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  title        = {{{Goal‐oriented adaptivity based on a model hierarchy of mean‐field and full‐field homogenization methods in linear elasticity}}},
  doi          = {{10.1002/nme.6209}},
  year         = {{2019}},
}

@article{62785,
  abstract     = {{<jats:title>SUMMARY</jats:title><jats:p>We introduce a material model for the simulation of polycrystalline materials undergoing solid‐to‐solid phase‐transformations. As a basis, we present a scalar‐valued phase‐transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The analysis of the related overall Gibbs energy density allows for the calculation of energy barriers. With these quantities at hand, we use a statistical‐physics‐based approach to determine the resulting evolution of volume fractions. Though the model facilitates to take into account an arbitrary number of solid phases of the underlying material, we restrict this work to the simulation of phase‐transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar model is embedded into a computational micro‐sphere formulation in view of the simulation of three‐dimensional boundary value problems. The final modelling approach necessary for macroscopic simulations is accomplished by a finite element formulation, where the local material behaviour at each integration point is governed by the response of the micro‐sphere model.Copyright © 2014 John Wiley &amp; Sons, Ltd.</jats:p>}},
  author       = {{Ostwald, Richard and Bartel, Thorsten and Menzel, Andreas}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  number       = {{12}},
  pages        = {{851--877}},
  publisher    = {{Wiley}},
  title        = {{{A Gibbs‐energy‐barrier‐based computational micro‐sphere model for the simulation of martensitic phase‐transformations}}},
  doi          = {{10.1002/nme.4601}},
  volume       = {{97}},
  year         = {{2014}},
}

@article{26256,
  author       = {{Mahnken, Rolf}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  pages        = {{1753--1788}},
  title        = {{{Geometry update driven by material forces for simulation of brittle crack growth in functionally graded materials}}},
  doi          = {{10.1002/nme.2468}},
  year         = {{2008}},
}

@article{19114,
  author       = {{Mahnken, Rolf and Caylak, Ismail}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  pages        = {{377--413}},
  title        = {{{Stabilization of bi‐linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions}}},
  doi          = {{10.1002/nme.2264}},
  year         = {{2007}},
}

@article{28779,
  author       = {{Mahnken, Rolf and Schlimmer, Michael}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  pages        = {{1461--1477}},
  title        = {{{Simulation of strength difference in elasto-plasticity for adhesive materials}}},
  doi          = {{10.1002/nme.1315}},
  year         = {{2005}},
}

@article{45416,
  author       = {{Mahnken, Rolf}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{7}},
  pages        = {{1015--1036}},
  publisher    = {{Wiley}},
  title        = {{{An inverse finite-element algorithm for parameter identification of thermoelastic damage models}}},
  doi          = {{10.1002/(sici)1097-0207(20000710)48:7<1015::aid-nme912>3.0.co;2-4}},
  volume       = {{48}},
  year         = {{2005}},
}

@article{45433,
  author       = {{Mahnken, Rolf and Stein, E. and Bischoff, D.}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{5}},
  pages        = {{1015--1029}},
  publisher    = {{Wiley}},
  title        = {{{A stabilization procedure by line-search computation for first order approximation strategies in structural optimization}}},
  doi          = {{10.1002/nme.1620350505}},
  volume       = {{35}},
  year         = {{2005}},
}

@article{45435,
  author       = {{Mahnken, Rolf and Stein, Erwin}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{7}},
  pages        = {{1619--1633}},
  publisher    = {{Wiley}},
  title        = {{{Adaptive time-step control in creep analysis}}},
  doi          = {{10.1002/nme.1620280711}},
  volume       = {{28}},
  year         = {{2005}},
}

@article{45425,
  author       = {{Johansson, Magnus and Mahnken, Rolf and Runesson, Kenneth}},
  issn         = {{0029-5981}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  keywords     = {{Applied Mathematics, General Engineering, Numerical Analysis}},
  number       = {{11}},
  pages        = {{1727--1747}},
  publisher    = {{Wiley}},
  title        = {{{Efficient integration technique for generalized viscoplasticity coupled to damage}}},
  doi          = {{10.1002/(sici)1097-0207(19990420)44:11<1727::aid-nme568>3.0.co;2-p}},
  volume       = {{44}},
  year         = {{2002}},
}