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Integration efficiency for model reduction in micro-mechanical analyses.

Rody A van Tuijl1, Joris J C Remmers1, Marc G D Geers1

  • 1Eindhoven University of Technology, P.O. Box 513, Eindhoven, The Netherlands.

Computational Mechanics
|April 12, 2019
PubMed
Summary

Reduced order modeling techniques, including empirical interpolation and cubature methods, significantly reduce computational costs for micro-structural analysis. Both methods offer distinct advantages and disadvantages for approximating material behavior under various loading conditions.

Keywords:
Empirical cubature methodEmpirical interpolation methodHomogenizationMicro-mechanicsModel reduction

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Area of Science:

  • Materials Science
  • Computational Mechanics
  • Solid Mechanics

Background:

  • Micro-structural analyses are crucial for understanding macroscopic material behavior.
  • Computational demands of micro-structural analysis limit repetitive simulations.
  • Reduced order modeling (ROM) techniques offer solutions to computational challenges.

Purpose of the Study:

  • To assess the accuracy of two ROM techniques: empirical interpolation method (EIM) and empirical cubature method (ECM).
  • To compare EIM and ECM in approximating full-order micro-structural analysis results.
  • To quantify algorithmic speed-ups and identify pros/cons of each method.

Main Methods:

  • Consideration of a representative micro-structural volume element.
  • Application of four distinct load cases, including cyclic and path-dependent loading.
  • Evaluation of accuracy in approximating micro- and macroscopic quantities (e.g., micro-fluctuations, stresses).

Main Results:

  • Both EIM and ECM provide approximations of full-order results with varying accuracy.
  • Differences in approximating micro- and macroscopic quantities were highlighted.
  • Algorithmic speed-ups for both ROM methods compared to the full-order model were quantified.

Conclusions:

  • EIM and ECM represent two distinct classes of ROM techniques for micro-structural analysis.
  • The study clearly identifies the advantages and disadvantages of integrand interpolation versus cubature methods.
  • Both methods offer significant computational benefits for repetitive micro-structural simulations.