@Article{duepublico_mods_00083137,
  author = 	{Donval, Elodie
		and Schneider, Matti},
  title = 	{Convergence of Damped Polarization Schemes for the FFT-Based Computational Homogenization of Inelastic Media With Pores},
  journal = 	{BeyondRVE: Beyond Representative Volume Elements for Random Heterogeneous Materials},
  year = 	{2025},
  month = 	{Feb},
  day = 	{07},
  keywords = 	{damped fixed point method; Eyre--Milton scheme; FFT-based computational micromechanics; infinite material contrast; polarization method; porous material},
  abstract = 	{Porous microstructures represent a challenge for the convergence of FFT-based computational homogenization methods. In this contribution, we show that the damped Eyre--Milton iteration is linearly convergent for a class of nonlinear composites with a regular set of pores, provided the damping factor is chosen between zero and unity. First, we show that an abstract fixed-point method with non-expansive fixed-point operator and non-trivial damping converges linearly, provided the associated residual mapping satisfies a monotonicity condition on a closed subspace. Then, we transfer this result to the framework of polarization schemes and conclude the linear convergence of the damped Eyre--Milton scheme for porous materials. We present general arguments which apply to a class of nonlinear composites and mixed stress-strain loadings, as well. We show that the best contraction estimate is reached for a damping factor of 1 / 2 , that is, for the polarization scheme of Michel--Moulinec--Suquet, and derive the corresponding optimal reference material. Our results generalize the recent work of Sab and co-workers who showed that an adaptively damped Eyre--Milton scheme leads to linear convergence for a class of linear composites with pores. Finally, we report on computational experiments which support our findings.},
  note = 	{Funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) 507778349 is gratefully acknowledged by E.D. M.S. acknowledges support from the European Research Council within the Horizon Europe program - project 101040238.},
  note = 	{<p>Donval, E. and Schneider, M. (2025), Convergence of Damped Polarization Schemes for the FFT-Based Computational Homogenization of Inelastic Media With Pores.<em> Int J Numer Methods Eng</em>, 126: e7632. <a href="https://doi.org/10.1002/nme.7632">https://doi.org/10.1002/nme.7632</a></p>

<p>Issue Online: 07 February 2025</p>},
  note = 	{<p>Version of Record / Verlagsversion</p>

<p>Online: 07 February 2025</p>},
  note = 	{<p>BeyondRVE. Grant agreement ID: 101040238</p>

<p>Funded under European Research Council (ERC).</p>

<p>Start date 1 July 2022. End date 30 June 2027.</p>},
  doi = 	{10.1002/nme.7632},
  url = 	{https://duepublico2.uni-due.de/receive/duepublico_mods_00083137},
  url = 	{https://doi.org/10.1002/nme.7632},
  file = 	{:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00082651/Int_J_Numer_Methods_Eng_2025_126_e7632.pdf:PDF},
  language = 	{en}
}