SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE

Authors

  • Martin Doškář Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7/2077, 166 29 Prague 6, Czech Republic
  • Jan Novák Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7/2077, 166 29 Prague 6, Czech Republic
  • Jan Zeman Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7/2077, 166 29 Prague 6, Czech Republic The Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodárenskou veží 4, 182 08 Prague 8, Czech Republic

DOI:

https://doi.org/10.14311/APP.2017.13.0029

Keywords:

Wang tiling, microstructure synthesis, microstructure-informed enrichment functions,

Abstract

Inspired by the first order numerical homogenization, we present a method for extracting continuous fluctuation fields from the Wang tile based compression of a material microstructure. The fluctuation fields are then used as enrichment basis in Extended Finite Element Method (XFEM) to reduce number of unknowns in problems with fully resolved microstructural geometry synthesized by means of the tiling concept. In addition, the XFEM basis functions are taken as reduced modes of a detailed discretization in order to circumvent the need for non-standard numerical quadratures. The methodology is illustrated with a scalar steady-state problem.

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Published

2017-11-13

Issue

Vol. 13 (2017): NMM 2017 - Nano & Macro Mechanics 2017

Section

Articles

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