Concurrent multiresolution finite element: Formulation and algorithmic aspects

Shan Tang, Adrian M. Kopacz, Stephanie Chan O'Keeffe, Gregory B. Olson, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


A multiresolution concurrent theory for heterogenous materials is proposed with novel macro scale and micro scale constitutive laws that include the plastic yield function at different length scales. In contrast to the conventional plasticity, the plastic flow at the micro zone depends on the plastic strain gradient. The consistency condition at the macro and micro zones can result in a set of algebraic equations. Using appropriate boundary conditions, the finite element discretization was derived from a variational principle with the extra degrees of freedom for the micro zones. In collaboration with LSTC Inc, the degrees of freedom at the micro zone and their related history variables have been augmented in LS-DYNA. The 3D multiresolution theory has been implemented. Shear band propagation and the large scale simulation of a shear driven ductile fracture process were carried out. Our results show that the proposed multiresolution theory in combination with the parallel implementation into LS-DYNA can capture the effects of the microstructure on shear band propagation and allows for realistic modeling of ductile fracture process.

Original languageEnglish (US)
Pages (from-to)1265-1279
Number of pages15
JournalComputational Mechanics
Issue number6
StatePublished - Dec 2013


  • Concurrent multiresolution
  • Finite element method
  • Heterogenous microstructure
  • Multiscale

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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